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contents
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Welcome ........................................................... 1
LSAT Basics ................................................ 2
Game Time ...................................................... 10
The Big Two ................................................... 12
Game Plan ...................................................... 17
The Questions ................................................. 23
World of Ordering ........................................ 30
Basic Ordering .............................................. 32
Games Logic ................................................... 42
1:1 Ordering ..................................................... 70
Under/Overbooked Ordering ...................... 91
Tiered Ordering .............................................. 95
Hello, Grouping ................................................ 103
The Big Four .................................................. 113
In and Out .................................................... 121
Two Groups ..................................................... 136
Three or More Groups ................................. 142
Profiling ........................................................... 144
Combo ............................................................... 151
Neither ............................................................. 155
Play the Numbers ........................................ 159
Scenarios ......................................................... 174
Timing ............................................................... 197
What’s Next ...............................................................
203
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1/WELCOME
The Blueprint
Welcome to The Blueprint for LSAT Logic Games, the best guide to Logic Games ever
created. We are very pleased that you have selected Blueprint, and we are confident we
can help you substantially improve your performance on this challenging section.
Blueprint was founded in 2005 by a group of people who believe that it’s possible to
learn difficult concepts and have fun at the same time. In general, LSAT prep materials
are about as exciting as listening to hold music while waiting for tech support. At
Blueprint, we don’t think you have to be bored to achieve a high LSAT score. In fact, we
believe students learn better when they’re having fun. To that end, we’ve designed our
courses, lecture videos, and books to be entertaining as well as informative.
Now, don’t get us wrong. At Blueprint, our first priority is the LSAT. And we definitely
know the LSAT. We actually know far more than any group of people really should know
about the LSAT (at least if they’d like to maintain healthy personal relationships). But
this deep LSAT knowledge has enabled us to help tens of thousands of students improve
their scores significantly.
I’m Matt Riley, the author of the Blueprint Logic Games curriculum. I don’t like to talk
about myself, so this will be the only paragraph in which I do so. As my Mom would
agree, I only excel at three things in life: Connect Four, spinning a basketball on my
unnaturally flat index finger, and solving games. I scored a 179 on my own exam and I
have never missed a question on the games section of a real LSAT. But what I really enjoy
is articulting the Blueprint method and teaching it to others. I’ve taught thousands of
students personally and I know this stuff works. Hope you enjoy!
We’re happy that you’re here. Strap in, kick back, and grab a writing utensil.
It’s going to be a fun and educational ride.
blueprintprep.com/lsat
Welcome /
1
2/LSATbasics
LSAT Overview
The LSAT, for those of you
who accidentally opened this
book instead of US Weekly,
is a standardized test that
every student who wants to
attend an ABA-approved law
school1 must take. It consists
of four timed sections of 35
minutes each (older tests had
more sections so don’t let
that confuse you). The test
is scored on a scale of 120
(lowest - not great) to 180
(highest - wow).
Sections of the LSAT
The scored sections of the LSAT include one section of Logical Reasoning, one section of
Reading Comprehension, and one section of Logic Games, not necessarily in that order. In
addition to the three scored sections, there is an “experimental” section. If that sounds like it
involves a secret laboratory and possible radioactive spiders2, not to worry: The experimental
section is not scored. The section can vary between Logical Reasoning, Logic Games, and
Reading Comprehension. The Law School Admissions Council (LSAC), which administers the
LSAT, uses this section to test future LSAT questions. In addition, the experimental section is not
identified during the exam, so you will have the pleasure of expending energy on a portion of the
test that in no way affects your score.
There is also a writing exercise that must be completed through your online LSAC account. Like
the experimental section, the writing sample does not figure into your overall score. However,
it is sent to law schools along with your LSAT score. The writing sample challenges you to craft
an argument in favor of one plan of action over another under a completely fictional set of
2
1
What is an ABA-approved law school, you ask? ‘ABA’ stands for the American Bar Association, whose job it
is to make sure that law schools are reputable -- and to make your post-grad life relevant with a little thing
called the Bar Exam, but that’s a test for another book.. If your law school is not ABA accredited, it means you
may not be able to take the Bar Exam in any other state, thus potentially limiting your options for working as a
lawyer and purchasing very expensive automobiles.
2
We assume these conditions are scary for everyone not named Peter Parker.
/ Chapter 2
blueprintprep.com/lsat
circumstances. Generally law schools place little emphasis on the writing sample.
Here’s a table that illustrates the five different sections of the LSAT:
Section
Time
# of Questions
Logical Reasoning
35 Minutes
24 - 26
Logic Games
35 Minutes
22 - 24
Reading Comprehension
35 Minutes
26 - 28
Experimental (Not Scored)
35 Minutes
22 - 28
Writing Sample (Not Scored)
35 Minutes
N/A
Logical Reasoning
Everyone in Biba’s neighborhood is 1.
permitted to swim at Barton Pool at
some time during each day that it is
open. No children under the age of
6 are permitted to swim at Barton
Pool between noon and 5 P.M. From
5 P.M. until closing, Barton Pool is
reserved for adults only.
If all the sentences above are true, then which one of the following
must be true?
(A) Few children under the age of 6 live in Biba’s neighborhood.
(B) If Biba’s next-door neighbor has a child under the age of 6, then
Barton Pool is open before noon.
(C) If most children who swim in Barton Pool swim in the afternoon,
then the pool is generally less crowded after 5 P.M.
(D) On days when Barton Pool is open, at least some children swim
there in the afternoon.
(E) Any child swimming in Barton Pool before 5 P.M. must be
breaking Barton Pool rules.
There is one scored section of Logical Reasoning on the LSAT. It contains between 24 and 26
questions, so Logical Reasoning makes up approximately one third of the test.
In this section, you will read a short passage followed by a question. Above is a question about a
nice guy named Biba. You’ll have the joy of doing this 24 to 26 times in 35 minutes. Sometimes
the questions ask what must be true or false based on the information; sometimes you’ll be
asked to weaken or strengthen an argument. Still other times, you’ll be required to identify how
an argument is flawed.
What LSAC is testing with Logical Reasoning is your ability to break down and assess
information quickly. This section crucially depends on your ability to judge the validity of
arguments without focusing on whether the statements are true or false. In this way, Logical
Reasoning prepares you quite well for being a lawyer.
blueprintprep.com/lsat
LSAT Basics /
3
Reading Comprehension
Reading Comprehension consists of three long passages and a comparative reading
passage (itself made up of two, shorter passages). The subject matter is invariably riveting,
encompassing everything from the oral traditions of Native American communities to various
theories on the extinction of the dinosaurs.
Each passage is 50 to 65 lines long and is followed by five to eight questions. All told, Reading
Comprehension is typically the longest section on the LSAT and totals between 26 and 28
questions.
Logic Games
The third scored section on the LSAT is known in fuddy-duddy parlance as Analytical Reasoning,
but we, and most of the known world, affectionately refer to it as Logic Games. In this section,
you will be presented with an introductory paragraph laying out some variables and rules to
govern them, then asked questions about the way in which the variable sets can be organized.
Logic Games might involve clowns getting out of cars, cereals displayed at grocery stores, or
flowers being sorted into bouquets. Despite the wide-ranging and sometimes absurd nature of
games, it turns out that the number of game types is actually quite small.
the moment of truth: scoring
In order to understand scoring on the LSAT, we’ll need to discuss the difference between a raw
score and a scaled LSAT score.
Let’s use an example to show you how
this works. Meet Sue. Sue took the
May 2020 LSAT. Sue abandoned all
of her other worldly responsibilities to
study for the test and was rewarded by
answering 59 questions correctly out
of a possible 76. After LSAC ran all of
the tests through their fancy algorithms
they determined that Sue and her 59
correct answers placed her in the 90th
percentile. This means Sue beat out
90 percent of other test takers. LSAC
then referenced her score against a percentile table and emailed Sue her final score about three
weeks later—in this case, a 163.
4
/ Chapter 2
blueprintprep.com/lsat
Raw Score
Scaled Score
75
180
71 - 72
174 - 176
68
170
63
165
56
160
49
155
42
150
Here is a truncated version
of the score conversion chart
from the May 2020 LSAT.
The score conversion chart
changes slightly for different
LSATs depending on how the
test-taking population fares,
but it tends to stay relatively
consistent.
Remember, your score is
determined by how you fare
in comparison to thousands of
other test takers.
What does the LSAT test?
Now that you have an understanding of how scoring on the LSAT works, it’s quite natural to
wonder what it tests. In a nutshell, the LSAT tests the skills you’ll need as a law student and as a
lawyer. This includes constructing and analyzing arguments (Logical Reasoning), understanding
dense passages of material (Reading Comprehension), organizing information intelligibly (Logic
Games), and how to bend a spoon with your mind.3
What the LSAT does not test, however, is rote memorization. Rather than asking you for the
capital of North Dakota (Bismarck) or the German Chancellor during World War I (Bismarck),
the test challenges you to think in a certain way. This could involve weakening an argument,
identifying the main idea of a passage on Thurgood Marshall, or deciding whether or not the
third mannequin wears a blue hat.
The downside of this method of testing is that
you cannot “cram” for the LSAT; you must acquire
the skills for it through diligence and repetition.
While this is unfortunate news for those of you
who scraped by in college writing your papers
hours before they were due, it’s good news for
those of you who enjoy reading and thinking
critically. Like all skills in life, some good practice
can really enhance your abilities in these areas.
3
This is not actually tested on the LSAT. But if you can do it, you
should know that this is a highly marketable skill, and you may want to consider a side career in spoon-bendery.
blueprintprep.com/lsat
LSAT Basics /
5
lsat administrations
Historically, the LSAT was administered four times a year: February, June, September/October,
and December. But over the past few years, LSAC has added more test dates. The plan is to
stick to a schedule where the exam is offered 10 times per year, in every month except May and
December. Before you ask, we don’t know what they have against May and December. They
seem like perfectly reasonable months to us as well. Refer to the LSAC website for upcoming
test dates.
The LSAT historically was given early on a Saturday morning, due to LSAC’s insidious plot to ruin
your entire day. But, nowadays, there’s more flexibility and more frequent administrations on
other days if that is more your speed.4
Is there a “best” time to take the LSAT?
There is a “best” time to take the LSAT, but probably not in the way you’re thinking.
Unfortunately, it is not the case that one LSAT administration is easier than the others. If you
ponder this for a second, you’ll probably see why. If the February test, for example, were
always easier than the August test, this would be spectacularly unfair for the August test
takers. More to the point: No one would take the August test, and everyone would take the
February exam. To guard against this, LSAC institutes elaborate procedures to ensure that all
the exams are fairly equal.
However, the simple ease of the test isn’t the only reason to take a particular administration.
Most law schools work on a rolling admissions basis in which students are admitted as
applications come in. It’s generally better to apply earlier in the process because there are
tend to be more seats available.
Law schools typically begin accepting applications in early fall, so taking the test by early
fall will ensure your score arrives early in the process. All law schools accept later tests
(November and January are both popular), but you’ll want to be absolutely sure your
applications are ready to go by the time you get your LSAT score.
But whether you apply early or late, the biggest component of your application is the LSAT
score itself. It is such an important piece, in fact, that applying later with a better LSAT score
usually outweighs applying earlier with a lower score. To that end, the “best” time to take the
LSAT is when you have the most time to prepare for it. That is why so many people take the
August/September/October tests, when the principal part of their study time falls during the
summer months when school is out.
4
6
If you need six cups of coffee and a defibrillator to wake up before 8 AM, think about an afternoon test.
/ Chapter 2
blueprintprep.com/lsat
is it really worth the work?
The LSAT is the single most important piece of your law school application.5 Conventional
wisdom holds that the LSAT carries the weight of about 60% of your application. Because of
its importance in the application process, the better your LSAT score, the better the law school
you can typically attend. As law firms become increasingly selective in their hiring processes, a
better law school can mean a better job. A better job often equates to more opportunities to
hobnob with interesting and fancy people, which statistically means you’re more likely to get a
chance to meet Ryan Reynolds.6 In other words, a higher LSAT score has direct implications on
your future prospects of hanging out with Deadpool. That’s just math.
Not only can a higher LSAT score get you into a better law school, it can also result in
scholarship money once you’re there. Why not save on tuition so you can use your money
for better things, like purchasing a taco truck or an exotic pet farm? Or meeting the man who
brought Detective Pikachu to life?7
Finally, more so than any other standardized test, better performance on the LSAT correlates
to better performance in law school. So in studying for the LSAT, you have the satisfaction of
knowing it can pay dividends in law school.
Why devote a whole book to Logic Games?
Of the different sections on the LSAT, we find that our students are initially most frightened
of Logic Games. (Logical Reasoning generally causes amused resignation, and Reading
Comprehension mostly leads to anger.) This is probably because Logic Games look nothing
like anything you’ve seen before. Most people are familiar with long passages (Reading
Comprehension) or with paragraphs of information (Logical Reasoning). But trying to
decide whether the third dinosaur is green or mauve can be a foreign experience (unless
you’re a paleontologist throwing a Mardi Gras party).
There is good news, however! As odd as logic games initially appear, they are eminently
learnable because they don’t actually test that many different skills. In fact, we find that
most of our students see their biggest increases in Logic Games.
More to the point, learning to master Logic Games will reward you on other sections of the
LSAT. For example, the diagramming skills that enable you to see that the veal being served
on Wednesday forces the tilefish to be served on Friday will also have a big payoff in Logical
Reasoning.
5
Provided you’ve made your yearly sacrifice. Blood for the Blood God.
6
Ryan, if you’re reading this, feel free to stop by Blueprint HQ. We’ve got donuts!
7
Seriously Ryan. Any time.
blueprintprep.com/lsat
LSAT Basics /
7
The Blueprint Advantage
Now that you’re convinced you need to hone your games skills, you might question why our
Logic Games method is better than other companies’, or why you can’t just tackle logic games
with good old-fashioned know-how.
Blueprint has devised the most effective approach to Logic Games. We break down all
the games into just a few categories, then provide you with the tools to 1) recognize
which category the game falls into and 2) solve it.
As you will soon see, our approach is simple, yet powerful. Rather than throwing random games
at you, we have isolated the basic processes driving all games. By helping you identify these
salient features on your own, our methods will help you simplify any game that is thrown in your
direction.
After reading every single logic game available to man, woman, or armadillo (one of nature’s
more under-appreciated animals), we’ve also figured out that there’s a whole bunch of stuff
the test makers ask about repeatedly, so we can give you tips on how to look out for common
patterns as well. In the end, we collapsed all of that knowledge into this book so you’ll
absolutely kill the Logic Games section on your LSAT. And by “kill,” we mean achieve a score
that will get you a nice glass office and an array of expensive vacation homes.
Your Study Group
Now that we’ve covered the basics of the LSAT, it’s time to meet your study group. No one likes
to study alone. You’re probably reading this by yourself, possibly somewhere in the badlands of
South Dakota. We all need friends, particularly for something as traumatic as LSAT study. This
particular friend group is rather mythological in origin.8
Athena:
Athena is the goddess of wisdom. So she’s real smart, like, definitionally. Your
goal is to join Athena in Greek Goddess-tier mastery of the LSAT, for she
knows games like she was born by exploding out of their metaphorical skull.9
At various points, she will contribute Godly Guidance to which you should pay
close attention. These will be advanced comments about specific games or
techniques, so listen up!
Broseidon, Lord of the Brocean:
8
8
If anything, this should make them even more fun to hang out with. The ancient Grecian peoples knew their philosophy, but they also knew how to throw a wild shindig.
9
Mythology is weird.
/ Chapter 2
blueprintprep.com/lsat
Ah, Broseidon. The Lord of the Brocean thinks he’s the hottest thing to hit
Greece since Prometheus brought fire to mankind.11 Unfortunately, he’s not
always the best at thinking things through, not that that’s ever stopped him
from sharing his opinion. Because of that, Broseidon’s advice is iffy at best.
Luckily, his tendency to overshare serves another purpose. We’ve all rushed
headlong into things without taking a moment to consider what the best
course of action is. Reading Broseidon’s Bro Tips is a good way to introduce
yourself to some common missteps basically everyone takes on their LSAT
journey. Once you’ve watched this “cool” guy faceplant into a mistake, it’ll be
much easier to pull off the actually cool feat of slaying the LSAT.
BP Minotaur:
Finally, we come to the Minotaur. He’s a master of erudition, and his study
smells of rich mahogany. In case you were not aware, he dwelt in a maze and
ate Athenian youths sent to Crete as tribute.10 Now, he’s the perfect figure to
lead you through the labyrinth of Logic Games. The Minotaur will be the voice
of Blueprint and lend helpful tactical hints along the way. Plus, we like his
horns and his monocle.
So that’s it for the introduction, friends. As we stated earlier, the world of the LSAT and law
school admissions is a competitive one. There is a pot of gold at the end of the rainbow, but you
have to beat out all the other leprechauns. If other students are studying harder or better than
you, this will hurt your chances on test day. You can, however, rest easily knowing this book will
help you ensure that is not the case.
You’ve come to the right place to become
an expert in Logic Games, and this is
the right guide to take you through the
process. Someday, when you’re an elder
with a wee tyke on your knee for whom
you’ve set up a trust fund (provided he
or she doesn’t squander it on loot boxes),
you’ll look back on what you did here and
say: “Man, Blueprint *+%*ing rocked.”
9
10
Broseidon, Lord of the Brocean, is not cool. He likes to think he is, but, as astute logic masters in training, we
(and Athena) know better.
Probably don’t bring that part up in front of Athena, she’s still a little upset about it.
blueprintprep.com/lsat
LSAT Basics /
9
3/GAMEtime
Logic Games?
At some point, someone decided to call the Analytical Reasoning section of the LSAT “Logic
Games.” That person deserves to have a star on the Law School Walk of Fame.1
For most students, games will feel very foreign at first. Unlike other sections of the LSAT,
your education has provided very little training in how to arrange six different dresses on
consecutively-numbered hangers (something you get to attempt!). Though called “games,”
when you first encounter these little logic puzzles, they will have very little in common with
Scrabble or Taboo. They will feel more like an organic chemistry final. Or a root canal. Or a
holiday dinner with “that” family member. These so-called “games” will chew you up and spit you
out. But you will get your revenge. With rigorous tutelage and lots of practice, this book will
give you the tools to master Logic Games.
Logic Games is the most abstract section of the
LSAT. While you may have some experience reading academic
passages or analyzing arguments, you simply have not honed your
ability to assign jugglers to circus rings yet.
BP Minotaur:
Can I get better?
That’s a fair question. Logic games are a new skill you have to develop. Think about it this
way: Could you improve your skills on a pogo stick if you really wanted to? Of course. Many
students perform horrifically on the games section initially. But there is hope.
Thankfully, the people who write this wonderful exam appear to be stuck in a rut. We
can only assume they’re the kind of people who watch nothing but CSI reruns, eat toast
sandwiches2 for dinner every night, and paint every wall in their house beige. They also make
the same types of games over and over and over again. When one game challenges you to
schedule game show contestants and another game involves secret computer codes, it can
be difficult to recognize any similarities between the two. However, this book will give you
the tools to recognize the repetitive features in any game you encounter. Once you realize
you are doing the same types of games over and over again, your performance will improve
dramatically.
10
1
Sure, there isn’t one yet, but you have to admit it sounds pretty nifty!
2
Yes, these are a real thing. It’s toast between two slices of bread. Honestly? Not bad!
/ Chapter 3
blueprintprep.com/lsat
Games, Undressed...
We at Blueprint feel the best way to get to know something is to break it down into parts. In the
Logic Games section, there are always four distinct games, and each game has three basic parts:
the introduction, the rules, and the questions. Say hello to a game:
Introduction
This paragraph lays out the situation for the game. It will identify what the game is asking
you to do (put tigers into cages, dress up mannequins, etc.) and the players in the game (soft
drinks, cookies, dinosaurs, etc.).
Questions 7-12
A soft drink manufacturer surveyed consumer preferences
for exactly seven proposed names for its new soda:
Jazz, Kola, Luck, Mist, Nipi, Oboy, and Ping. The
manufacturer ranked the seven names according to the
number of votes they received. The name that received
the most votes was ranked first. Every name received a
different number of votes. Some of the survey results are
as follows:
Jazz received more votes than Oboy.
Oboy received more votes than Kola.
Kola received more votes than Mist.
Nipi did not receive the fewest votes.
Ping received fewer votes than Luck but more votes
than Nipi and more votes than Oboy.
7.
Which one of the following could be an accurate list
of the seven names in rank order from first through
seventh?
(A)
(B)
(C)
(D)
(E)
8.
Jazz, Luck, Ping, Nipi, Kola, Oboy, Mist
Jazz, Luck, Ping, Oboy, Kola, Mist, Nipi
Luck, Ping, Jazz, Nipi, Oboy, Kola, Mist
Luck, Ping, Nipi, Oboy, Jazz, Kola, Mist
Ping, Luck, Jazz, Oboy, Nipi, Kola, Mist
Which one of the following statements must be true?
(A)
(B)
(C)
(D)
(E)
Jazz received more votes than Nipi.
Kola received more votes than Nipi.
Luck received more votes than Jazz.
Nipi received more votes than Oboy.
Ping received more votes than Kola.
Rules
The rules establish the conditions that must be followed for the duration of the game. They are
often vague and ambiguous and must be interpreted to figure out what they actually mean. In
this regard, reading the rules may remind you of talking to your significant other.
Questions
Finally, the payoff. Maybe. Each game has between five and seven questions. They are
designed to test how well you understand the introduction to the game and the rules.
However, if you’ve done what you’re supposed to do with the introduction and the rules, most
of your work should be done by the time you get to the questions.
And when you are done... repeat three times. Oh, and remember, you have 35
minutes to complete all four games. Sound like fun?
blueprintprep.com/lsat
Game Time /
11
4/theBIGtwo
Can It Really Be That Simple?
It’s time to talk strategy. When you are first confronted with games, they might seem
overwhelming. This is largely because there appears to be hundreds of different types of games.
One minute, you’re helping friends move furniture. The next, you’re scheduling workers at a
convenience store. Then, you find yourself choosing cookies for a cookie jar.
Bro Tip:
There’s no chance I’m going to learn to do all that.
Broseidon, you might be right. However, here’s the great news: you don’t have to!1 It turns
out that, in Logic Games, you don’t have to learn to complete hundreds of different tasks. The
masterminds who make this test just want you to think you do. While the subject matter may
vary widely from game to game (from monkeys to swim teams to toothbrush colors), this is
completely irrelevant to the task at hand. The subject matter of a game may be interesting or
even entertaining, but the topic never determines how you approach a game. Rather, the basic
process you are being asked to perform is what really defines a game.
Great news - Blueprint has cracked the code and discovered
there are only a small number of game types that appear on the LSAT.
BP Minotaur:
You might find this hard to believe, but there aren’t hundreds of types of games. There aren’t
even twenty, or ten, or five. Hold on to your seat...
At Blueprint, our revolutionary approach classifies every single game in the history of
the LSAT according to which of two basic elements it contains: ordering or grouping.
Yep, just two. All of the hundreds of games in the history of the LSAT can be boiled down to
ordering or grouping. Put simply, you are either lining people up (ordering) or making teams
(grouping). Once you recognize this fact, Logic Games becomes much more manageable.
Perhaps (dare we say it?) even fun.
1
12
If we were talking to you in person, we would try to recreate the scene from The Matrix in which Neo asks
Morpheus if, one day, he will be able to dodge bullets. Morpheus famously responds, “Some day, you won’t have
to.” This is an equally dramatic moment in your LSAT metamorphosis. Also, yes, we do still love The Matrix.
/ Chapter 4
blueprintprep.com/lsat
Ordering
Let’s take a look at ordering, the first task that you must master. Ordering games are all about
spatial relationships and discerning the relative positions of the participants.
Which show is ranked first? How many people finish before Timmy? Who could have
an appointment on Thursday? Which turtle must place second?
You are guaranteed to see an ordering game
on your LSAT, and there’s normally more than one.
Godly Guidance:
Here are some examples of ordering games:
Seven third-graders must be ranked according to their speed on a
tricycle, from fastest (first) to slowest (seventh).
The doctor must schedule appointments with six different patients this
week, between Monday and Friday.
The animals are assigned to a row of consecutively numbered cages,
from 1 through 7.
At the talent show, each child must fill one time slot. The time slots
begin at 1 P.M. and end at 8 P.M.
At first glance, these games might seem to be quite distinct from each other. However, the basic
process in each game is the same: You are determining the order for a set of players. You should
always build a setup similar to the following to work through ordering games:
^
1
2
3
4
5
6
7
8
The rules for ordering games place spatial restrictions on the players. Some rules concern only
one player, and other rules will place two players in relation to each other. For example:
Azadeh is faster than Benjamin.
Christi cannot perform at 3 P.M.
Bartholomew cannot visit the doctor before Devi.
The ferret is in a lower-numbered cage than either the lion or the koala.
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13
Ordering games will
be the first challenge
we tackle in this
book. They come
in many different
shapes and sizes, but
the basic process is
always the same.
1
2
3
4
5
6
7
8
Grouping
The second task for you to conquer is grouping. You are very likely to see at least one grouping
game on the fateful day you take the LSAT. Grouping games are not concerned with spatial
relationships, but rather focus on assigning people to different groups.
Who is on the blue team? Which friends are coming to the party? Who cannot be
selected with Harry? How many students can be in classroom 4?
Here are some examples of grouping games:
Of the eight former child stars who auditioned, exactly five were
chosen for Celebrity Rehab.
Each of the seven parents must serve on either the recycling committee
or the academics committee.
The volunteers must be separated into three different work teams.
Each child receives at least one of three different types of gifts for
Christmas/Hanukkah/Kwanzaa.
These games are clearly different
from the previous ordering
games. However, there is a
common element to them: Each
of these situations requires you
to assign the players to different
groups. As with ordering games,
we will also use a consistent
setup for grouping games.
x:
y:
The rules in grouping games will focus on the relationship between the players, restricting the
players that must, can, or can’t be assigned to the same group. There are some examples on the
next page.
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If Azadeh is chosen, then Benjamin is also chosen.
Bartholomew and Devi cannot serve on the same committee.
Each work team must have at least two volunteers.
Ebenezer receives more gifts than Gertrude.
Some grouping games only select
one group, others assign players
to two groups, and really intense
games might have up to four or five
groups. But they all have groups,
and your job is to assign players to
them.
That covers the two basic processes that drive games. Once
in a while, the makers of the exam want to throw a new challenge at you
by asking you to take on ordering and grouping in the same game. But don’t
worry, the same principles still apply.
BP Minotaur:
Combo
You knew there had to be a twist coming. There are tons of ordering games, and you are going
to get sick of seeing grouping games. But what happens when the LSAT wants to add some
complexity? It makes a game that combines the two. We call these combo games (creative,
we know). While not as common as either ordering or grouping games, they do rear their ugly
heads on occasion.
Here are some examples of combo games:
At the family picnic, the eight family members are separated into two
four-person teams for the relay race. Each team will complete four
consecutive legs, numbered 1 through 4.
A teacher must select six of eight students to compete in the math
competition. The six competitors are ranked from first to sixth.
Note that there are both ordering and grouping elements to these games. Later in the book, we
will teach you the techniques to build effective setups for combo games. Since there is a lot of
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The Big Two /
15
information to juggle, it is crucial to keep everything organized. The good news is that the rules
and deductions you will find in combo games are the same as ordering and grouping games;
you just have to deal with both at the same time.
The dreaded combo games tend to appear
toward the end of the section, undoubtedly another
tactic by the LSAT to test your fortitude.
BP Minotaur:
Neither Games
The vast majority of our time will be spent on ordering and grouping games, with a few combo
games thrown in for fun. While it is overwhelmingly likely that these categories will cover all
four of the games you will see on your LSAT, there are a few outliers. Once in a while, the
LSAT throws a real curve ball. Instead of asking you to rank people or make teams, you will be
required to draw a map, discern or repeat a pattern, or put a lightbulb in your mouth and pull it
back out again.1 These games include neither ordering nor grouping. They are very rare, but
we will take a brief look at them later in the book.
This chapter provides an outline for the entire
Blueprint approach to Logic Games. Since
ordering and grouping are the basic tasks that
drive all games, most of the later chapters will
focus on ways to master these processes. This
elegantly simple structure provides you with a
huge advantage over other test takers.
Up next, we are going to discuss the general approach you should use to attack all games,
regardless of type.
1
16
Do not try this! It is a bad idea! Real LSAT questions never risk personal injury - the test is for future lawyers, for
goodness sake.
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5/gamePLAN
The Four Step Program
Games can be intimidating because it’s not always clear when to do what. The process does not
seem as linear in nature as other parts of the exam, and this can lead to frustrating indecision.
When should I build my setup? Should I spend more time on the rules? Did I
find all of the deductions? Should I move to the next question? Should I just
fold my scratch paper into a paper airplane and weep quietly?
These questions can haunt students and hurt their performance. Fortunately, we have the
best strategy in the known universe1 for solving games. We’ll show you how to tackle any
logic game with just four steps. By approaching games the same way every time, not only
will you be armed with an effective methodology, but you’ll also be able to solve the games
within the time allotted.
Every great strategist has a game plan. Up next is Blueprint’s four step approach for solving
any logic game.
Solving a game is dependent on successfully completing each
of these four steps. Neglecting any one of the steps will spell disaster.
BP Minotaur:
Step 1: Read the Introduction
The first step in each game is to read the introductory paragraph. This is when you must identify
the situation, the players, and your task. Understanding these aspects of a game will largely
determine the next eight to ten minutes of your life.21
1
2
Aliens, if you’re out there and are have mastered the intergalactic LSAT—give us a call, we just want to talk.
To help understand the four steps, we are going to make an extended analogy. Getting through a game is
analogous to a successful night at a gathering of friends In our analogy, this first step is assessing the room
- seeing who’s there and what they are doing. Or, let’s be honest, avidly searching for the cat or dog and
zooming right on over to talk to it and give it pets. Look, we know what we’re about.
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Game Plan /
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You will have a natural urge to get to the
rules and questions as quickly as possible, but read the intro
to each game very slowly and carefully.
Godly Guidance:
During the first stage of a game, there are two
main objectives. First, you need to classify the
type of game that you are facing (Ordering?
Grouping? Combo?) in order to build the
appropriate setup. The specifics of constructing
setups will be covered extensively later in this
book. For now, just know that you will need to
create an effective setup as part of the first step
in each game. It is vital to identify the type of
game you are tackling so you can construct the
appropriate setup. Otherwise, you might build a
beautiful ordering setup... for a grouping game.
Not a good scene.
October 1993: Questions 14-18
Three boys—Karl, Luis, and Miguel—and three girls—
Rita, Sarah, and Tura—are giving a dance recital. Three
dances—1, 2, and 3—are to be performed. Each dance
involves three pairs of children, a boy and a girl partnering
each other in each pair, according to the following
conditions:
Karl partners Sarah in either dance 1 or dance 2.
Whoever partners Rita in dance 2 must partner Sarah in
dance 3.
No two children can partner each other in more than
one dance.
1
The second objective is to identify the variable sets in the introductory paragraph. You need
to account for people, places, gerbils, airplanes, colors, jock straps, lipstick brands, turtles, or
anything else that might show up. Simplify all of these variables near your setup (normally, the
first letter of each will do).
Objective 1: Classify the type of game and build a setup.
Objective 2: Identify all of the variable sets that are present.
In very rare cases, you will not be able to identify the
type of game from the intro paragraph. Athena will teach you to tackle
such games later. Athena has been known to talk in the third person.
Godly Guidance:
Step 2: Symbolize the Rules
Following the introductory paragraph, there are always a number of indented rules. These rules
lay out the conditions that must be followed for the duration of the game.
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There are a number of objectives to keep in mind while you work through the rules.32
1.
Always represent rules uniformly. You
will be presented with the same types of
rules again and again, and consistently
representing them accurately will help you
recognize familiar patterns. Don’t worry,
we’ll show you how to do this soon.
2. Represent as many rules as possible
directly on your setup. Your focus will be
largely on your setup as you work through
the questions, so inserting rules directly
into your setup will be helpful.
3. Combine rules whenever possible. If Larry
arrives before Mo and Mo arrives before
Curly, these rules should be combined. It
is always favorable to deal with fewer rules
as you move forward in a game.
October 1993: Questions 14-18
Three boys—Karl, Luis, and Miguel—and three girls—
Rita, Sarah, and Tura—are giving a dance recital. Three
dances—1, 2, and 3—are to be performed. Each dance
involves three pairs of children, a boy and a girl partnering
each other in each pair, according to the following
conditions:
Karl partners Sarah in either dance 1 or dance 2.
Whoever partners Rita in dance 2 must partner Sarah in
dance 3.
No two children can partner each other in more than
one dance.
2
Always pay close attention when one player is mentioned
in more than one rule. If Javaris is mentioned in the second rule and
the fourth rule, a deduction is sure to follow.
BP Minotaur:
4. The fourth and final objective is simple: read each of the rules twice. Horror stories
abound of students who misread or misinterpreted a rule. If a rule states that Pedro is
taller than Oscar, and you symbolize that Oscar is taller than Pedro, you will be accepted
at the Fantasyland School of Legal Stuff quicker than you can say Fantasyland School of
Legal Stuff. After you symbolize a rule, you should go back and read the rule again to
ensure you understood and symbolized it correctly.
Here is a quick summary of the important points to remember about the rules:
1. Symbolize rules consistently.
2. Represent rules directly on your setup where you can.
3. Combine rules whenever possible.
4. Don’t f#$% it up (read each rule at least twice).
3
Back to our party analogy: The rules in a game are analogous to the information you get from the other partygoers. These are the social cues that will guide your evening. Tariq is “going through some stuff right now”.
Bryleigh has just joined an MLM and is ready to tell you all about essential oils. The cat is named Gary and he
loves tuna treats. Now you know the rules.
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Game Plan /
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Step 3: Make Deductions
Remember how Sherlock Holmes could solve a murder by discovering a piece of hair in the
carpet and combining that with the direction of the breeze to deduce that the butler used the
candlestick in the library?43 Now you can take a shot at being just like Sherlock. Step Three is
the all-important deduction phase. Despite the fact that this is the most crucial phase in Logic
Games, it is also the most commonly overlooked by students.54
If you make the proper deductions, the
game will feel like a vacation in Hawaii
with a fruity umbrella drink. If you don’t,
the questions will feel like a particularly
unpleasant root canal.
In later chapters, we will cover a variety
of common deductions and bug you
incessantly to spend an extended amount
of time searching for deductions. Students
always have the inherent urge to jump into
the questions because, after all, that’s where
you get the points. But that is a dangerous
mistake. In games, the true challenge is to
process the setup and rules, to get a good
grasp on a game before you ever look at the
questions. Here’s a motto to live by:
October 1993: Questions 14-18
Three boys—Karl, Luis, and Miguel—and three girls—
Rita, Sarah, and Tura—are giving a dance recital. Three
dances—1, 2, and 3—are to be performed. Each dance
involves three pairs of children, a boy and a girl partnering
each other in each pair, according to the following
conditions:
Karl partners Sarah in either dance 1 or dance 2.
Whoever partners Rita in dance 2 must partner Sarah in
dance 3.
No two children can partner each other in more than
one dance.
3
You win or lose every game before you look at a single question.
As you improve in games, you will spend more and more time making deductions. Additionally,
as games increase in complexity, they require more time up front. Here is how a poor student
(you, at the beginning of this book) approaches a game on the LSAT.
20
Setup, Rules, + Deductions
Questions
3 Minutes
10 Minutes
= 13 Min.
4
Sherlock would be infuriating to play Clue with.
5
Returning to our party, the deductions will determine the outcome of your night. Sure, you have all the
information at your fingertips, but how are you going to use it? Will you dodge Bryleigh, or wind up hosting a
“party” of your own? Will you talk Tariq through things and help him cry it out? Will Gary come and sit on your
lap if you give him enough treats?
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This 13-minute plan is exactly what you need to avoid. It will lead to frustration, random
guessing, wrong answers, and nightmares in the weeks following the test. Here is how an
advanced student (you, at the completion of this book) destroys a game.
Setup, Rules, + Deductions
Questions
6 Minutes
2 Minutes
= 8 Min.
As you work through games, do not judge your
success solely by right and wrong answers. Your ability to spot
key deductions is equally important.
Godly Guidance:
As you will see, spending more time in the deduction stage trims valuable minutes off the total
amount of time you spend on a game. Okay, enough nagging about deductions... for now.
Step 4: Move to the Questions
Now, and only now, are you ready to jump into the questions. Armed with a good setup, a
deep understanding of the rules, and some powerful deductions, it’s time to show this game
who’s boss. The questions will present you with a variety of challenges to test how well you
understand the game.65
In the next chapter, we will discuss
specifics regarding the questions you are
going to face. Questions require different
tactics, but we will teach you the best
strategies for approaching any question
you encounter. As long as you have
built the proper setup, symbolized the
rules correctly, and made the necessary
deductions, the questions should be
smooth sailing.
6
14. If Sarah partners Luis in dance 3, which one of the
following is a complete and accurate list of the girls any
one of whom could partner Miguel in dance 1?
(A)
(B)
(C)
(D)
(E)
Rita
Sarah
Tura
Rita, Sarah
Rita, Tura
4
Back to our party analogy: You’ve now met all the other guests. You picked up on the appropriate social cues,
and when the time was right, you made your move. Tariq’s feeling better, Bryleigh’s recruitment attempts were
thwarted, and you’re pretty sure you’re now Gary’s favorite human. Now it is time to reap the benefits. Just
don’t screw it up now by mentioning that you have a dog within Gary’s earshot.
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Game Plan /
21
As we work through games, we will use the same process every time. Repetition is key. Logic
games are a linear process, and you have to practice the correct steps every time.
Moving right along, we are going to zoom in and discuss the questions.
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6/theQUESTIONS
What Do They Want?
When you work through your first logic game, you will see that games will present you with a
variety of different questions. In order to answer the questions correctly, you must understand
the requirements for the correct answer choice and the criteria that allows you to eliminate the
incorrect answers. If you don’t understand the question, it can be rather complicated to find the
answer. Consider the following exchange:
Maria: Hey honey, how was your day?
Bob: Gorilla brains.
You don’t want to be Bob. If you try to answer the wrong question, then you will choose the
wrong answer. For example, if you are searching for an answer that must be true when the
question actually requires one that could be true, you’re going to have a tough time.
The LSAT intentionally includes answer choices designed to
catch people who misread the questions. As you practice, paraphrase the
criteria for the correct and incorrect answer choices.
BP Minotaur:
Correct answer choices will meet one of four different criteria:
(1) must be true; (2) could be true; (3) could be false; or (4) must be false.
The same game will often include many or all of the different types. You must be able to quickly
adjust your mindset. This table outlines the criteria for the correct and incorrect answer choices.
Correct Answer (Winner)
Incorrect Answers (Losers)
Must Be True
Could Be False
Could Be True
Must Be False
Could Be False
Must Be True
Must Be False
Could Be True
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The Questions /
23
For example, say you are presented with the following question:
If Tony is assigned to the technology committee, then which one of the following could be false?
Here, you should attempt to find an answer that could be false and eliminate the four answers
that must be true.
EXCEPT Questions
Some questions are complicated by the use of the word EXCEPT. Many students miss the
word altogether or get confused about the implications for the answer choices. These
questions just add one step to our approach. Consider the following example:
If Tony is assigned to the technology committee, then each of the following could be true EXCEPT:
This question flips things around a bit. Normally, a question will ask you for an answer choice
that could be true and you should dismiss answer choices that must be false. Here, four of
the answer choices could be true. You must now dismiss any answer that could be true and
pick the one that must be false.
Bro Tip:
It seems like they want something that could be false.
Actually, no, Broseidon. And that can be a dangerous mistake. Since the right answer
choice to this question cannot be true, you are looking for the one that must be false.
Luckily, we have another table to help you out.
Question
Incorrect Answers (Losers)
Correct Answer (Winner)
Must Be True EXCEPT
Must Be True
Could Be False
Could Be True EXCEPT
Could Be True
Must Be False
Could Be False EXCEPT
Could Be False
Must Be True
Must Be False EXCEPT
Must Be False
Could Be True
Now that you have an understanding of the criteria for correct and incorrect answers, it’s time to
take a look at the specific types of questions you’ll see while working through logic games.
There are only three basic types of questions in games: Elimination, Absolute, and
Conditional. Each type requires a slightly different approach, so let’s take a look.
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Elimination Questions
Like it or not, many decisions in life are made through the process of elimination. From selecting
schools to ordering dinner to choosing group project members, you’re often left picking the last
option available (don’t worry, we won’t tell them).
In general, we want to avoid using the process of elimination on Logic Games. It’s more timeconsuming than using your setup to anticipate and locate the correct answer. However, there
is one large exception to this general rule. On some questions, the process of elimination is not
only always possible, but it is always the best approach. Say hello to elimination questions.
An elimination question asks you to identify one possible outcome in a game.
On elimination questions, you do not have to worry about what must be the case. Rather, your
task is to identify one combination that could work based on the introduction and the rules.
Here are some examples of elimination questions:
Which one of the following could be a complete
and accurate list of the types of cookies sold by the
bakery?
Which one of the following could be a complete and
accurate list, from Monday through Friday, of the
contestants on the game show?
Which one of the following could be a complete
and accurate matching of the team captains with the
colors of their uniforms?
Nearly every game starts
with an elimination question,
and some games have more
than one. It’s a great
chance to visualize how the
rules function in a game, and
pick up an easy point.
Get ready for some good news. You’re going to fall in lust with elimination questions.1 Since
these questions are asking for one possible outcome, the correct answer choice simply must not
violate any of the rules in the game.
The best way to find the correct answer is to use the rules to eliminate wrong answer choices
(hence the name of the question type). As soon as an answer choice violates a rule, you can
eliminate it. Run through the rules, and you will quickly arrive at the correct answer.
The following is an example of the
Blueprint strategy for an elimination
question. Turn the page to see how to
quickly identify the correct answer.
1
Which one of the following could be a list of the
factories in the order of their scheduled inspections,
from day 1 through day 6?
You were probably expecting us to say love, but let’s be real. This is the LSAT. Fleeting attraction is the most
you can hope for.
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The Questions /
25
First, it’s important to recognize that you’re looking at an elimination question. This type of
question asks you to identify one possible outcome, given the original conditions of the game.
Almost every game, including this one, starts with an elimination question.
The next step is to work through the rules, one by one, and use each rule to eliminate any answer
choices that violate it until there is only one remaining.
F is inspected on either day 1 or day 6.
J is inspected on an earlier day than Q is inspected.
Q is inspected on the day immediately before R is
inspected.
If G is inspected on day 3, Q is inspected on day 5.
(A)
(B)
(C)
(D)
(E)
F, Q, R, H, J, G
G, H, J, Q, R, F
G, J, Q, H, R, F
G, J, Q, R, F, H
J, H, G, Q, R, F
The first rule states that F is inspected on either day 1 or day 6. In (D), F is inspected
on day 5. That is not day 1, nor is it day 6. Bye-bye to (D).
F is inspected on either day 1 or day 6.
J is inspected on an earlier day than Q is inspected.
Q is inspected on the day immediately before R is
inspected.
If G is inspected on day 3, Q is inspected on day 5.
(A)
(B)
(C)
(D)
(E)
F, Q, R, H, J, G
G, H, J, Q, R, F
G, J, Q, H, R, F
G, J, Q, R, F, H
J, H, G, Q, R, F
The second rule states that J is inspected on an earlier day than Q. In (A), J is
inspected on day 5 and Q is inspected on day 2. That’s not earlier, so there goes (A).
F is inspected on either day 1 or day 6.
J is inspected on an earlier day than Q is inspected.
Q is inspected on the day immediately before R is
inspected.
If G is inspected on day 3, Q is inspected on day 5.
(A)
(B)
(C)
(D)
(E)
F, Q, R, H, J, G
G, H, J, Q, R, F
G, J, Q, H, R, F
G, J, Q, R, F, H
J, H, G, Q, R, F
The third rule states that Q is inspected on the day immediately before R is inspected.
In (C), Q is on day 3 and R is on day 5. Close but no cigar, so (C) is outta here.
F is inspected on either day 1 or day 6.
J is inspected on an earlier day than Q is inspected.
Q is inspected on the day immediately before R is
inspected.
If G is inspected on day 3, Q is inspected on day 5.
(A)
(B)
(C)
(D)
(E)
F, Q, R, H, J, G
G, H, J, Q, R, F
G, J, Q, H, R, F
G, J, Q, R, F, H
J, H, G, Q, R, F
The last rule: If G is inspected on day 3, Q must be inspected on day 5. In (E), G is on
day 3 but Q is on day 4. Not so good. (E) goes away. (B) is our winner.
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As you can see, we just eliminated the four incorrect answer choices without referencing
anything but the rules. The final step is to happily choose the remaining answer.
In that example, each rule eliminated one answer choice.
That happens frequently, but sometimes one rule will knock out more than
one answer or no answers at all. Never fret; collectively, the rules will
always eliminate four and leave you with just one remaining answer.
Godly Guidance:
Not too bad, huh? This approach will work for all elimination questions on any type of game.
No one knows why the LSAT allows this strategy to work; it is one of life’s great mysteries.2 But
don’t question it - just sit back and enjoy.
Once you are comfortable with this strategy, you are never allowed to get an elimination
question wrong. Never.3
Absolute Questions
Absolute questions constitute the second category of questions in Logic Games. Although
the name may sound intimidating (or like vodka), these questions are fairly straightforward.
An absolute question asks you to find something that is true or false based on the original
introduction and rules. In a perfect world, you should be able to identify the answer to an
absolute question without doing any additional work. (Of course, in a perfect world, you would
have inherited billions of dollars from a long-lost relative and all of this would be unnecessary.)
An absolute question tests your understanding of the original conditions in a game.
Here are some examples of absolute questions:
Which one of the following CANNOT be true?
Which one of the following is the latest day on which
Chuck could appear on the game show?
Which one of the following must be true?
Which one of the following is a complete and
accurate list of teams, any of which CANNOT wear
the yellow uniform?
2
3
Want an easy way
to spot an absolute
question? As you can
see, they almost always
start with the word
“which.”
Other notable mysteries: How Donald Glover accomplishes so much stuff and the notion of nonfat ice cream.
Never.
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The Questions /
27
Absolute questions should be less time-consuming than other
questions. If you are running short on time, jump to the absolute questions.
BP Minotaur:
Absolute questions are a moment of reckoning for you. Since they are based on the original
conditions in the game, they are designed to test whether you spotted important deductions.
If the answers come easily, you are in good shape. If not, is it time to panic? Not necessarily, but
it might be time to go back to the rules and look for more deductions.
Since they regard basic facts about a game, answers to
absolute questions can be helpful for later questions. For example, if you
learn on an early absolute question that Theodore cannot be questioned later
than day 4, you can use this valuable morsel of information on later questions.
Godly Guidance:
Conditional Questions
Occasionally, the rules change. In life, you might have a different set of rules that you follow
on Halloween or a tropical vacation than you have at a formal family dinner (Grandma might
not appreciate the French maid outfit). In logic games, you also have to be able to adapt and
incorporate new rules.
Conditional questions are the third and final question type. They introduce new information
and require you to quickly determine how it interacts with the previous rules. Unlike absolute
questions, conditional questions normally do require additional work. You will frequently need to
construct a quick hypothetical to help you visualize the new situation.
A conditional question tests your ability to incorporate new information.
Here are some examples of conditional questions:
If peanut butter cookies are made on Tuesday, then
which one of the following could be true?
If Lisa appears before Kendall, then each one of the
following must be true EXCEPT:
If Tiffany’s team wears green, then which one of the
following CANNOT be true?
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Can you guess the word that
normally begins a conditional
question? Look for it... look
for it. That’s right - “if” is
a good indicator.
blueprintprep.com/lsat
Conditional questions introduce new information, but this doesn’t negate the importance of the
original setup and rules. Rather, the new conditions build off the foundation of the game.
On a conditional question, the new information is
only in play for that one question. If they tell you that Theodore is
questioned on day 3 for question #17, this does not need to be true for
question #18. When you move on, the new information stays behind.
Godly Guidance:
With that, we end our overview of the questions you are
going to face. It’s important to understand what you are
looking for in the correct answer and the most effective
approach for each one. There will be lots of variations
as we work through different types of games, but the
general characteristics will be the same.
In the next chapter, it’s time to start breaking down game
types!
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7/WORLDofORDERING
Line them Up
Welcome to the exciting world of ordering games. While perhaps not as exciting as watching
the newest viral baby/kitten video, ordering games are pretty thrilling in the LSAT world. We
will spend the next several chapters covering all the various types of ordering games. These
games are all about spatial relationships; they require you to determine the relative placement
of different players. You might have to assign tigers to consecutive cages, figure out a batting
order for a baseball team, rank performances on an exam, or determine Stella’s meeting
schedule.
The following are examples of ordering games:
Each of seven television programs—H, J, L, P, Q, S, V—is
assigned a different rank: from first through seventh (from
most popular to least popular). The ranking is consistent with the
following conditions:
The eight partners of a law firm are Gregg, Hodges, Ivan, James,
King, MacNeil, Nader, and Owens. In each of the years 1961
through 1968, exactly one of the partners joined the firm.
Exactly seven toy-truck models—F, G, H, J, K, M, and S—are
assembled on seven assembly lines, exactly one model to a
line. The seven lines are arranged side by side and numbered
consecutively 1 through 7. Assignment of models to lines must
meet the following conditions:
During a single week, from Monday through Friday, tours
will be conducted of a company’s three divisions—Operations,
Production, Sales. Exactly five tours will be conducted that week,
one each day. The schedule of tours for the week must conform to
the following restrictions:
Exactly five cars—Frank’s, Marquitta’s, Orlando’s, Taishah’s, and
Vinquetta’s—are washed, each exactly once. The cars are washed
one at a time, with each receiving exactly one kind of wash:
regular, super, or premium. The following conditions must apply:
Note the wording italicized in these examples. That is the
type of wording that will indicate you are doing an ordering game.
Godly Guidance:
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The Setup
An ordering game always contains at least two variable sets, such as students and grades, animals
and cages, or products and aisles. Your task is to figure out the arrangement of at least one of the
variable sets. For example, you may have to decipher whether CJ is in seat 4 or seat 6 or whether
the monkey is in cage 3 or cage 7. The easiest way to visualize this task is to identify the variable
set with an inherent order and use that variable set as the base of your setup.
In ordering games, the variable set with an inherent order
(rankings, days, lanes) should always be used as the base of your setup.
A variable set with an inherent order is one that has a clear beginning and end. Days of the
week, order of finish from first to last, numbered chairs, or appointment times all have an
inherent order. A group of girlfriends, countries in Europe, or car models do not. Here is one of
the games from the previous page:
Toy trucks should bring back some
fond memories. In this game, there
are two variable sets: toy-truck
models and assembly lines. The
assembly lines have an inherent
order (1 through 7), so we use them
as the base. Then, our job is to
assign the models to the lines.
Exactly seven toy-truck models—F, G, H, J, K, M, and S—are
assembled on seven assembly lines, exactly one model to a
line. The seven lines are arranged side by side and numbered
consecutively 1 through 7. Assignment of models to lines must
meet the following conditions:
^
1
2
3
4
5
6
7
Building this setup early in the process will allow you to visualize the rules and deductions. Try
to keep your setups as consistently as possible. You will learn through repetition.
A small number of ordering games will be better suited to a
vertical setup (for instance, layers of a cake or floors in a building). When
this happens, just organize the slots vertically.
BP Minotaur:
Over the next four chapters, we will cover the four types of ordering games: (1) Basic ordering,
(2) 1 to 1 ordering, (3) Underbooked/Overbooked ordering, and (4) Tiered ordering.
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World of Ordering /
31
8/basicORDERING
What Is It?
Ordering games will present you with a variety of rules that introduce spatial relationships
between players. The most basic type of ordering principle simply tells you that one player must
come somewhere before or after another player. Basic ordering games only include this type of
relationship.
A dash is used to show that one player must be placed somewhere in front of another player.
Here are some basic ordering principles and the correct diagrams:
L is ranked higher than P.
l - p
K is assembled on a higher-numbered line than M but a
lower-numbered line than G.
m - k - g
h
Gregg joined the law firm before both Hodges and Ivan.
g
i
o
Marquitta’s car is washed after both Orlando’s and Frank’s.
m
f
Basic ordering games will give you a combination of rules like these. Each of the rules should
be represented with the all-powerful dash. However, there is a very important second step. You
must learn how to combine such ordering principles to make deductions.
Basic ordering principles establish that one player
comes before another, but not necessarily immediately before. If
L is ranked higher than P, L could be ranked one, two, or five spots
ahead of P. Don’t assume that they have to be consecutive.
BP Minotaur:
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Ordering Chains
In a basic ordering game, you can generally combine some (or even all) of the rules to build an
ordering chain. This will allow you to see how the rules work together. This strategy will save
valuable time and help avoid mistakes.
In a basic ordering game, try to build an ordering chain involving as many rules as possible.
To illustrate how to build an effective ordering chain, we will use a hypothetical game involving a
classic American television show: the Simpsons. Here’s the intro:
ts
When you see that the studen
d
are called in “consecutively an
one at a time,” you know you
have an ordering game.
Exactly six students at Springfield Elementary
School— Bart, Lisa, Milhouse, Nelson, Ralph, and
Wendell—are each called into Principal Skinner’s
office, consecutively and one at a time, in connection
with the defacement of Superintendant Chalmers’ new
car. The following conditions must apply:
First things first—you have to build a
good setup. There are two variable
sets here: the students, and the order
in which they enter Principal Skinner’s
office. The sequence they’re called in
has an inherent order, so you should
use that as the base of your setup. At
this point, you want to represent the
variables and build your setup.
6s: b l m n r w
1
2
3
4
5
6
Next up, check out the rules:
Note that many players appear in
more than one rule. This is a clear
sign that the rules can be combined.
Instead of dealing with
each of these rules in
isolation, it is much
more helpful to build an
ordering chain. Here is the
step-by-step process.
blueprintprep.com/lsat
Bart and Wendell are both called into the office at some
time before Nelson.
Ralph is called into the office at some time after Wendell.
Lisa is called into the office at some time before Bart.
Milhouse is called into the office at some time after Nelson.
Bart and Wendell are both called into the office at
some time before Nelson.
b
n
w
Basic Ordering /
33
Now, we want to attempt to add the later rules.
Ralph is called into the office at some time after Wendell.
Since Wendell is already part of the chain from the first
rule, we can just add this rule onto the end. Both Ralph
and Nelson now enter after Wendell.
b
n
w
r
Two rules down. Let’s take a look at the next one and see if it can also be added to the same
chain.
Lisa is called into the office at some time before Bart.
Things that we know about Bart: (1) he WILL ride his
skateboard into Principal Skinner’s office, and (2) he is in
front of Nelson. Bart is already part of the chain, so we
can add this rule by placing Lisa in front of Bart.
l - b
n
w
r
This is going well, but there is still one rule to go.
Milhouse is called into the office at some time after Nelson.
Nelson was part of the very first rule. This rule tells
us that Milhouse is called later than Nelson, so we can
add Milhouse into our ordering chain behind Nelson.
l - b
n - m
w
r
That’s an example of how you can combine the rules in a basic ordering game into one ordering
chain. These ordering chains can be a little ugly in the beginning, but they will grow on you like
oddly adorable and diagram-y fungus.
In some games, there will be rules that can’t be combined.
No need to stress - you can just deal with them separately.
Godly Guidance:
Once you build an ordering chain, it’s important to know how to use it. Here are the
rules to keep in mind:
1.
Always Watch the Front and the Rear
On occasion, you will be able to severely limit the options for the first or last slot. If so, you want
to spot this restriction before you hit the questions. Always check to see who could be first and
who could be last.
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Any player that does not
have someone who must be in
front of them could be first.
•
Either Milhouse
or Ralph must be
the last student
into the office.
l - b
w
r
Either Lisa or Wendell
must be the first student
to enter the office.
Same strategy for the rear: Just
look for players without anyone
that must be after them.
l - b
n - m
w
r
Deductions of this sort will be helpful as
you work through the game. Don’t try
to remember them - write them directly
into your setup. That’ll make it much
easier to answer a question that places
Wendell into the third slot—looking at
your sketch, you’ll immediately be able
to see that Lisa has to be first.
2.
•
n - m
l/w
1
r/m
2
3
4
5
6
Stay Within the Lines
Creating an ordering chain will enable you to quickly draw conclusions about the relative positions of
different players. However, it is important to avoid drawing unwarranted conclusions. The general
rule is that you must have a clear relationship between two players to decipher who must come
first. Here are some helpful conclusions that you can draw about the state of Springfield Elementary:
Since you know that Lisa
enters before Bart and
Bart enters before Nelson,
Lisa must enter before
Nelson.
l - b
n - m
w
r
Wendell precedes Nelson,
who precedes Milhouse.
Thus, Wendell must
precede Milhouse.
These types of deductions will be very helpful as you attack the questions. For instance, if an
answer choice states that Nelson enters the office before Lisa, you will immediately know that it
must be false. Or if a question states that Milhouse enters the office fifth, you know that Wendell
must enter before that point.
Life on these games, however, is not all candy and smiles. There are also some tempting invalid
inferences that you must avoid. We’ll explore those on the next page.
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Basic Ordering /
35
If your ordering chain does not directly specify which of two players must come first, don’t make
erroneous conclusions.
between Lisa
There is no definite relationship
that Ralph
and Ralph, so it could be true
.
enters before Lisa, or vice versa
l - b
n - m
w
r
What are you talking about? It totally looks like L is before R.
Bro Tip:
Yes, Broseidon, it does look that way. Also, please stop flexing. Anyway, that is precisely the type of
mistake you must avoid. Don’t fall for visual tricks - stick to the rules. In this ordering chain, the only
person who must enter before Ralph is Wendell, so it could be true that Ralph enters before Lisa.
3.
Know the Limits for Each Player
In basic ordering games, you will be asked a number of questions about the possible placements
of various players. Can Wendell be the second student? Could Milhouse enter fifth? To answer
these questions, you should count the number of players that must come before or after the
player in question. Let’s do two examples - one with Lisa and one with Nelson.
l - b
1
2
n - m 3
w
r
•
There are three students who must
head into the office after Lisa: Bart,
Nelson, and Milhouse.
Since there are three students that must follow Lisa, she can’t be fourth, fifth, or sixth.
The latest that Lisa could enter the office is third.
1
l - b
2
n - m
3
•
w
r
Now we are going in the other direction.
Lisa, Bart, and Wendell are the only three
students who must enter before Nelson.
There are three students that must enter the office before Nelson, so he can’t be
first, second, or third. Sorry, Nelson: The earliest spot possible for you is fourth.
This process can help you identify the most restricted players.
If someone is limited to two or three spots, that can break open the game.
Godly Guidance:
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4.
Watch Out for Randoms
You know that character in horror movies who has concerningly small amounts of dialogue?1 No
one really knows who she is or where she came from. Although she may just be fodder for the
Big Bad Evil within the opening scenes, she’s got that unpredictable look in her eye. There is an
analog to this wild card in Logic Games: the “random.” Randoms are players in a game that have
no restrictions placed on them. If Tall, Dark, and Suspicious is not mentioned in any of the rules,
then you should take note of this fact (normally we just circle the variable). TD&S is very flexible
and that makes her dangerous.
A random is a player that is not mentioned in any of the rules in a game.
Noticing a random in a game can be helpful. The very fact that they have no restrictions makes
them good candidates to pop up in the answer choices to Could Be True questions. Could our
horror movie rando turn into a rampaging fighter at any moment? Well, yeah. Could Tall, Dark and
Suspicious end up in lane 6? If she’s not mentioned in the rules, there’s no reason why she can’t.
Randoms will be an issue in all types of games, but we
figured this was a good place to make the introduction.
Keep an eye out for them at all times.
Up next, we have a drill to help develop your
skills with ordering chains.
1
Will that mild mannered elderly woman turn out to be possessed by a demon, an experienced vampire hunter,
or perhaps just a baker of phenomenal cookies? We just don’t know yet!
blueprintprep.com/lsat
Basic Ordering /
37
Ordering Chain Drill
For each of the following games, construct an appropriate ordering setup. After you read
through the rules, build an ordering chain by combining as many rules as possible. When you
think you have a handle on the game and the rules, go ahead and attempt the questions.
Big Money
A magazine ranks the average salaries for eight affluent types of professionals—astronauts, baristas,
chefs, doctors, entertainers, firefighters, gymnasts, and hairdressers—from highest (first) through
lowest (eighth). There are no ties. The following conditions must apply:
The firefighters rank higher than the astronauts.
The gymnasts rank higher than the hairdressers.
The doctors rank lower than the baristas but higher than the chefs.
Both the doctors and the astronauts rank higher than the gymnasts.
The entertainers rank lower than the astronauts.
1.
What is a complete and accurate list of
all of the professions that could have the
highest average salary?
4. What is the lowest ranking that the
baristas could have among the eight
professions?
2. What is a complete and accurate list of
all of the professions that could have the
lowest average salary?
5. What is a complete and accurate list of all
of the possible rankings for the doctors?
3. What is the highest ranking that the
gymnasts could have among the eight
professions?
6. If the chefs rank fourth, then what must be
the ranking of the astronauts?
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Cool Runnings
At the Winter Olympics, nine countries competed in the four-man bobsled: Jamaica, Kazakhstan,
Lithuania, Madagascar, Nicaragua, Oman, Poland, Qatar, and Romania. The nine countries finish first
through ninth based on their overall time. There are no ties. The top three teams win medals. The
following conditions govern the results:
Poland has a slower time than both Lithuania and Nicaragua.
Lithuania has a faster time than Oman but a slower time than Romania.
Madagascar has a faster time than Qatar.
Poland has a faster time than Jamaica.
1.
What is a complete and accurate list of the
countries that could have the fastest time?
4. If Qatar has the second fastest time, then
what is the best possible finish for Oman?
2. If Poland is the fourth fastest team, then
which teams must win medals?
5. What is the worst possible finish for
Romania among the nine countries?
3. What is a complete and accurate list of the
countries that cannot win a medal?
6. What is a complete and accurate list of
the possible finishing placements for
Kazakhstan?
blueprintprep.com/lsat
Basic Ordering /
39
Ordering Chain Answer Key
Use the following key to check your deductions and your answers. Make sure to go back and
review anything that might have gone wrong along the way.
Big Money
8p: a b c d e f g h
f - a
e
g - h
b/f
1
1.
b - d
2
3
4
5
6
7
8
c
The baristas and the firefighters are the only options for the top spot (B, F).
2. The three professions that could be last are the chefs, hairdressers, and entertainers (C, H,
E).
3. The gymnasts must rank lower than the baristas, doctors, firefighters, and astronauts, so
the highest ranking the gymnasts could have is fifth (5th).
4. The baristas must rank higher than the doctors, chefs, gymnasts, and hairdressers, so the
lowest ranking the baristas could have is fourth (4th).
5. • The doctors only have to rank lower than the baristas, so the doctors could rank as
high as second.
• The doctors have to rank higher than the chefs, gymnasts, and hairdressers, so their
lowest possible ranking is fifth.
• The doctors could rank anywhere between second and fifth (2, 3, 4, 5).
6. • If the chefs rank fourth, the baristas and doctors both must rank in the top three.
• The firefighters rank higher
than any of the remaining
professions, so the firefighters
b d f
must also place in the top
three.
c
a
• The astronauts must rank
higher than the entertainers,
5
1
3
4
6
2
7
gymnasts, and firefighters,
so the astronauts come in at
number five (5th).
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8
Cool Runnings
9c: j k l m n o p q r
r - l
o
p - j
n
1
2
3
4
5
6
7
8
9
m - q
k
In this game, one of the rules cannot be combined with the rest of the chain. Also, Kazakhstan is
not mentioned in any rules, so it’s a random (although notable for being the home of Borat).
1.
Romania, Nicaragua, and Madagascar could each place first according to our chains. But
don’t forget about Kazakhstan, which could place anywhere, including first (R, N, M, K).
2. Romania, Lithuania, and Nicaragua must each be faster than Poland, so they are the top
three if Poland is fourth (R, L, N).
3. Poland and Jamaica are the only countries to have at least three other countries that
must be faster than them, so there are no medals for the Poles or the Jamaicans (P, J).
4. • If Qatar finishes second, then the gold goes to Madagascar.
• Oman must also be slower than both Romania and Lithuania, so the best Oman could
finish is fifth (5th).
5. Romania always beats out Lithuania, Oman, Poland, and Jamaica, so the worst finish for
Romania is fifth (5th).
6. Kazakhstan is random and could finish anywhere from first to worst (1st, 2nd, 3rd, 4th,
5th, 6th, 7th, 8th, 9th).
Lessons we learn from this drill: (1) It pays to be a barista, (2) that movie about the Jamaican
bobsled team was a total fabrication, and (3) ordering chains really help you visualize how the
rules intersect in a basic ordering game.
At this point, we recommend you go get your hands on some basic ordering games. Once you
do a handful, this approach will become very familiar and then you can fly through such games.
When you are ready, we can add some complexity.
blueprintprep.com/lsat
Basic Ordering /
41
9/gamesLOGIC
what if...?
It’s a bummer to stop the momentum at this point. We just got through our first chapter of
game types, but we have to interrupt for a commercial break. In every other type of game you
will face, you might be confronted with an ugly type of rule based on what’s called a conditional
statement.
In the previous type of game, a rule told you that L is delivered before H. That is an absolute
statement - it was true for the entirety of the game. But what if a rule said, “if L is delivered
before H, then K is delivered before M”? This doesn’t imply that L must be delivered before
H, or that K must be delivered before M. But if L is delivered before H, then you know
something else must occur. There’s an important distinction between absolute rules, which
state a fact, and conditional rules, which give a relationship between conditions.
A conditional statement asserts a logical relationship such that satisfying one
condition guarantees that another condition must follow.
Conditional statements are prevalent in many types of
games and all throughout the Logical Reasoning section. A good LSAT
score requires a deep understanding of these statements.
BP Minotaur:
Mastering conditional statements is one of the most difficult skills for students to develop.
When you see an absolute rule, it’s pretty simple. But conditional statements are more
complex. Take the last example—if L is delivered before H, then K is delivered before M. But
what if L isn’t delivered before H? Or what if M is delivered before K? As you might expect,
there are rules associated with such statements, and they are important to memorize.
This chapter is devoted to conditional logic in Logic Games. It’s lengthy, but that is indicative of
its importance. Here’s a look at what’s on tap:
1.
2.
3.
4.
5.
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Sufficient and Necessary Conditions
Valid and Invalid Conditional Inferences
Logically Denotive Words
Conjunctions and Disjunctions
Rules of Negation
y
These are just big, scar
words for concepts that
sily
we are going to make ea
digestible.
blueprintprep.com/lsat
Sufficient or Necessary?
Conditional statements assert the existence of a hypothetical relationship such that if the first
condition is met, then the second must follow.
If you drive a Rolls Royce,
then you are rich.
This statement does not assert that anyone actually
drives a Rolls Royce, or even that anyone is rich. Rather,
it asserts a relationship between driving a Rolls Royce
and being rich.
Conditional statements are always composed of two elements: a sufficient condition and a
necessary condition.
Sufficient Condition [ Necessary Condition
In the previous example, the sufficient condition is driving a Rolls Royce, and the necessary
condition is being rich. The distinction between sufficient and necessary conditions will be
tested repeatedly on the LSAT, so it’s very important to understand the difference.
Sufficient Conditions
Satisfying a sufficient condition is enough to guarantee that a necessary condition will
follow. Nothing else is required. In our previous example, the fact that a person drives a
Rolls Royce is enough to conclude that he or she is rich. No other evidence is needed and no
other evidence can destroy that conclusion. Even if this person also lives in a cardboard box
and eats bargain-brand cat food, you can still conclude that he or she is rich.
Necessary Conditions
A necessary condition is required in order to satisfy a sufficient condition. Without a
necessary condition, the sufficient condition cannot occur. In our previous example, it is a
given that someone is rich if they drive a Rolls Royce. If someone is not rich, then they do
not drive a Rolls Royce.
Do not confuse sufficient and necessary conditions. Being
rich is necessary for someone to drive a Rolls Royce. However, it is not
sufficient. People can be extremely wealthy and choose to drive a BMW,
a Prius, or a camel. They’re rich - a little eccentricity is expected.
BP Minotaur:
blueprintprep.com/lsat
Games Logic /
43
Yeah, I got this one. While drinking a 12 pack is sufficient
to make some bad decisions, it’s certainly not neccessary.
Bro Tip:
Actually, Broseidon, that is precisely correct. Also, try not to drink so many 12 packs;
instead, why not make some gains on that 6 pack above your tail? In Logic Games, you
will be presented with a variety of conditional statements, and it’s important to know what
conclusions you can draw from them. Next, we are going to cover two valid inferences that
will be helpful, and two invalid inferences you must avoid.
The Protagonists
Harry Potter. Ellen Ripley.1 Basically anyone name-dropped in a Disney movie title. People you
want to cheer for, through and through. In life, we love the heroes and heroines. The same is
true with the LSAT. Except on the LSAT, we call them valid inferences.
There are two valid inferences that can be drawn from any conditional statement you confront in
a game.
Valid Affirmation (Satisfying the Sufficient Condition)
The valid affirmation is the most basic inference that can be drawn from a conditional
statement. If a sufficient condition is satisfied, that is always enough to conclude the
necessary condition follows.
If Timmy is at home, then Lassie is also at home.
t
[
l
This rule would be part of a game in which you have to assess which family members are
at home (and hopefully not near any wells). If you know Timmy is at home (satisfying the
sufficient condition), it is guaranteed that Lassie is at home as well.
Satisfying a sufficient condition guarantees that the necessary condition follows.
As you can see, we use an arrow to represent conditional
relationships. Try to avoid any other representations, as it is vital to
quickly and accurately diagram these rules in difficult games.
BP Minotaur:
1
44
If you have no idea who this is, then it’s time to go on a cinetamographic journey through the Alien series.
Though, maybe consider skipping Alien vs Predator – Requiem.
/ Chapter 9
blueprintprep.com/lsat
Contrapositive (Denying the Necessary Condition)
There is a second valid inference that follows from any conditional statement. It’s called the
contrapositive, and it will be your best friend in Logic Games. Think of the contrapositive
as the flip side of the valid affirmation. In a conditional statement, the necessary condition
is required for the sufficient. Thus, if a necessary condition is denied, then the sufficient
condition must be denied as well.
Denying a necessary condition guarantees that a sufficient condition cannot follow.
You don’t realize it, but you use the contrapositive
every day. To make your dog happy, it’s necessary that you take him on
a walk No walk? Prepare for very dramatic doggy sighs.
Godly Guidance:
To understand the contrapositive and how it works, let’s take a look at a rule from a game:
If Pink Floyd performs on day 4, then Led Zeppelin
performs on
day 6.
p4 [ l 6
You might find this rule in a game that involves scheduling a music festival for 70’s psychedelic
rock bands. If Pink Floyd performs on day 4, then Led Zeppelin must perform on day 6. But
there is a second inference. If Led Zeppelin does not perform on day 6 (the necessary condition
is not met), then Pink Floyd cannot perform on day 4 (the sufficient condition can’t follow).
To form the contrapositive, there are two steps:
(1) Switch the sufficient and necessary conditions, and
(2) Negate both conditions.
L6 [ P4
If Led Zeppelin does not perform on day 6, you can immediately conclude that Pink Floyd
doesn’t perform on day 4.
To form the contrapositive, swap the sufficient and necessary conditions, and negate both
conditions. We will cover more complicated rules of negation later, but for now, negating a
condition means ruling it out as a possibility. For instance, the negation of Amal is in seat 3 is
Amal is not in seat 3. The negation of Beatrice is not in seat 5 is Beatrice is in seat 5.
a [ b
B [ A
blueprintprep.com/lsat
For every conditional statement, watch for two things: (1) if the
sufficient condition is affirmed and (2) if the necessary condition
is denied. Valid conclusions follow from both.
Games Logic /
45
Here are more details about how this rule will function in a game. In our example, a clear
conclusion can be drawn if Pink Floyd performs on day 4 (that Led Zeppelin must perform on
day 6). It can be harder to spot the contrapositive. If Led Zeppelin performs on day 1, or day 5,
or any other day besides 6, then you know that Pink Floyd can’t perform on day 4. This can be
easy to miss, so it’s imperative to write out the contrapositive for a visual reminder.
Because the contrapositive is so important, write
it out every time you are given a conditional rule. Every time.
Godly Guidance:
The Antagonists
Emperor Palpatine. Lex Luthor. Grandpa Joe in Charlie and the Chocolate Factory.2 In movies, the
protagonist always comes out on top. But this is real life. On the LSAT, the baddies can easily
win unless you know how to defend against them.
The villains on the LSAT take the form of two very tempting invalid conditional inferences. You
must avoid these like the plague, or like pretty much everyone heavily featured on any reality TV
show. They are very dangerous, and you must stay away.
Converse (Satisfying the Necessary Condition)
The most common logical fallacy on the LSAT is what we call the converse. The converse
occurs when the sufficient and necessary conditions are reversed but not negated.
Do not confuse the conditional arrow
with an equal sign. These relationships don’t go both ways.
Godly Guidance:
This fallacy stems from the distinction between sufficient and necessary conditions.
Satisfying a sufficient condition guarantees that the necessary condition follows, but
satisfying the necessary condition does not guarantee anything.
Satisfying a necessary condition is not enough to conclude that
the sufficient condition must follow.
2
46
Really, Grandpa Joe? You couldn’t possibly leave bed to help out the family until the moment Charlie won you a
trip to Willy Wonka’s Factory? Don’t even get me started on the fizzy lifting drink room.
/ Chapter 9
blueprintprep.com/lsat
Consider the following rule:
If Bigfoot is captured second, the Loch Ness
b2 [
Monster is captured third.
l3
We are now entering the wonderful world of cryptids. This game might have you identify the
order in which the creatures above, as well as Mothman, the Jersey Devil, and literal immortal
Keanu Reeves, are captured. The above rule informs you that if Bigfoot is captured second, then
the Loch Ness Monster must be captured third. However, if the Loch Ness Monster is captured
third, it is a mistake to think Bigfoot must be captured second.
l3 [ b 2
B A D ! W RON G !
As you can see here, the two conditions are reversed but not negated. To form the
contrapositive (a valid inference), you need to both reverse and negate.
This fallacy can be very tempting, and it will be offered to you in many incorrect answer
choices. Stay away.
Satisfying a necessary condition doesn’t guarantee the truth
of the sufficient condition, but it does not preclude it, either. If the Loch
Ness Monster is captured third, Bigfoot could be captured second. It is
just a fallacy to conclude that Bigfoot must be captured second.
BP Minotaur:
Inverse (Denying the Sufficient Condition)
Another common fallacy arises when both of the conditions of a conditional statement are
negated, but the conditions are not reversed. Even if a sufficient condition is not met, that
does not imply the necessary condition cannot be satisfied.
Negating a sufficient condition is not enough to conclude that the
necessary condition will not occur.
Check this out:
If Channing is drinking merlot, then Niles is
drinking
shiraz.
blueprintprep.com/lsat
cm [ ns
Games Logic /
47
This example stems from an infamous Blueprint trip to Napa Valley (names have been changed
to protect the mildly guilty). Here, a group of people are assigned to different wine-tasting
teams. If Channing is sipping on merlot, then Niles must be throwing back the shiraz. However,
don’t make the mistake of thinking that if Channing is not drinking merlot, then Niles cannot be
drinking shiraz.
Cm
[
Ns
STOP! NO GOOD!
Here, the two conditions are negated, but they are not reversed as they are with the
contrapositive. This fallacy, like the converse, will be a tempting answer choice, but
don’t be fooled.
If a sufficient condition is negated, the
necessary condition may or may not follow.
Godly Guidance:
The Real Deal
Now let’s apply these abstract concepts to real logic games. Here is a rule that could be part of
a game dealing with parenting workshops.
If Bianca attends the workshop on Tuesday, then
Kevin must attend on Friday.
bt [ k f
Kf [ B t
The first step is always to diagram
the rule and its contrapositive. If
Bianca attends on Tuesday, then Kevin
must attend on Friday. To form the
contrapositive, reverse both terms and
negate them. So, if Kevin does not go
to the workshop on Friday, then Bianca
cannot attend on Tuesday.
Be sure to watch out for the two common fallacies we just learned. If Kevin goes to the
workshop on Friday, that does not mean that Bianca must attend on Tuesday (converse).
Also, if Bianca does not learn some parenting skills on Tuesday, we cannot conclude that
Kevin cannot attend the workshop on Friday (inverse).
Once you diagram the conditional claim and its
contrapositive, train your eyes to only focus on the sufficient
conditions. These will lead to valid conclusions, while looking for
necessary conditions will only lead to confusion.
BP Minotaur:
48
/ Chapter 9
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The following chart illustrates the conclusions that can be validly drawn from this rule:
What You Know
Conclusion
Bianca attends on Tuesday.
Kevin attends on Friday.
Bianca does not attend on Tuesday.
No conclusion
Kevin attends on Friday.
No conclusion
Kevin does not attend on Friday.
Bianca does not attend on Tuesday.
Let’s do one more example.
If the juggler is not on stage 2, then the sword
swallower is on stage 1.
J2 [ s 1
S1 [ j 2
Step one: Diagram the rule and its
contrapositive. If the juggler is not on
stage 2, the sword swallower must be on
stage 1. We also know that if the sword
swallower isn’t on stage 1, the juggler will
be found on stage 2.
Even though the structure of this rule looks
different, you form the contrapositive with the exact same steps: (1)
switch the sufficient and necessary conditions, and (2) negate both.
Godly Guidance:
Here is the table of valid conclusions from our circus example:
What You Know
Conclusion
The juggler is on stage 2.
No conclusion
The juggler is not on stage 2.
The sword swallower is on stage 1.
The sword swallower is on stage 1.
No conclusion
The sword swallower is not on stage 1.
The juggler is on stage 2.
At this point, you should have a rudimentary grasp of the rules regarding sufficient and
necessary conditions. It’s important because these rules will be the difference between right and
wrong answers. Time for a drill.
blueprintprep.com/lsat
Games Logic /
49
sufficient/necessary drill
This drill is designed to test your understanding of conditional statements. In the table, you’ll
find four different columns. Your mission, if you choose to accept it, is to diagram these
statements and identify when (and what) valid conclusions can be drawn.
1.
Read the conditional rule and create an arrow diagram in the second column.
(Remember to always diagram the contrapositive.)
2. The third column gives you an additional piece of information. This is similar to what you
will find in the middle of a game. Use the fourth column to fill in any valid conclusions
that can be drawn. As always, avoid those ugly fallacies.
Note: In a number of examples, you will not be able to draw any valid conclusions.
If this occurs, write “no conclusion” in the fourth column.
Conditional Rule
50
Arrow Diagram
What You Know
1. If Shonda is selected, then
Esther is selected.
Suzy is selected.
2. If the zoo purchases a panda,
then it also purchases a zebra.
The zoo purchases
a zebra.
3. If Antoine is on TV, then
Bernadette is not on TV.
Antoine is not on
TV.
4. If G is on stage, then H is not.
H is on stage.
5. If Peng does not run the third
leg, then Rita runs the second leg.
Rita runs the
second leg.
6. If X does not survive, then Z
does survive.
X does not survive.
7. If Sly is not on the pink team,
then Ty is not on the pink team.
Ty is on the pink
team.
8. If there is no diamond, there is
no engagement.
There is a diamond.
/ Chapter 9
Conclusion
blueprintprep.com/lsat
Answer Key
Here are the answers to the previous drill. If you committed any mistakes, make sure to feel
very ashamed (or just understand the mistake you made and avoid it next time).
(Esther is selected.)
z (No conclusion)
B (No conclusion)
H (G is not on stage.)
(No conclusion)
z (Z survives.)
Tp (Sly goes pink.)
E (No conclusion)
1.
s [ e
5.
P3 [ r 2
2.
p [
6.
X [
3.
a [
7.
Sp [
4.
g [
8.
D [
Now, young caterpillar, you should feel comfortable with sufficient and necessary conditions, the
twin pillars of LSAT logic. You should also have a basic understanding of the contrapositive and
the two common conditional fallacies (converse and inverse). These are difficult and important
concepts, so you might want to bookmark these pages for later. But there’s more to learn...
indicator words
As you can see from our discussion of valid and invalid inferences, if you can’t correctly identify
sufficient and necessary conditions, then you will have a difficult time mastering games. To make
it even more challenging, conditional rules are not always phrased as if/then statements. But
don’t worry—the following rules will teach you how to diagram the most common expressions of
conditional rules in Logic Games.
Conditional rules are often written in a
convoluted manner. However, you should translate them into
“if/then” statements. This is the simplest form.
Godly Guidance:
There are a number of keywords used to introduce sufficient or necessary conditions.
Hint: You should memorize the following indicator words (just replace the part
of your brain still holding onto the lyrics of the “Friends” theme song).
If (All, Any, Every, When)
“If” is the most common word the LSAT uses to introduce a sufficient condition. The
condition that follows “if” forms the sufficient condition, and the remaining clause forms
the necessary condition. This type of conditional rule is the most straightforward to diagram.
Luckily for you, it is also the most common.
blueprintprep.com/lsat
Games Logic /
51
If there are slurpees at the convenience store, then there is also beef jerky.
s
[
j
v7
[
L5
The Louvre cannot be visited on day 5 if Versailles is visited on day 7.
Be aware that it does not matter whether
“if” introduces the first or second claim in the rule. It is
always the sufficient condition, regardless of where it appears.
Godly Guidance:
The words “all,” “any,” “every,” and “when” also can be used to introduce a sufficient
condition. As with the word “if,” these words are enough to guarantee an outcome. These
rules should be diagrammed in the same way as “if” statements.
All of the students in the Mathletes are also in the Glee club.
m
[
g
Pigs in a blanket are baked on every day that custard is not.
C
[
p
“If” (and similar words) always introduces a sufficient condition.
Before we move on to the next indicator word, it’s time for some practice. You will find some
conditional rules below. Diagram each of them correctly by spotting the keywords. The answer
key can be found at the end of this section (page 55).
52
1.
If Tina is on the wetlands committee, then Raul is on the forest committee.
_ [ _
2.
Jamie must drive on the fourth day if Ken does not drive on the second day.
_ [ _
3.
If disco is played, then reggae is not. _ [ _
4.
The quarterback is in every class that the cheerleader is in. _ [ _
5.
All of the employees that work on Thursday also work on Friday. _ [ _
/ Chapter 9
blueprintprep.com/lsat
Only (if)
One small word can drastically change the meaning of a conditional statement. The word
“only” and the phrase “only if” always introduce a necessary condition. The referent of
“only” (which nearly always immediately follows the word or phrase) forms the necessary
condition, while the other clause forms the sufficient condition.
Kipp performs during the show only if Biff also performs.
k
Only members of team X can serve as the game master.
gm
[
b
[
x
“Only” always introduces a necessary condition.
Now it’s time for you to practice. Just like last time, diagram these conditional rules by
identifying the keywords. Yet again, the answer key is at the end of the section.
1.
Tiagra is a winner only if Salim is a winner.
_ [ _
2.
K is placed in slot 5 only if M is placed in slot 7. _ [ _
3.
Only if the Bruins make the tournament can the Trojans make the tournament.
_ [ _
4.
Only those who get a rose move on to the next round. _ [ _
5.
Gregg places fourth only if Haley does not place first. _ [ _
If and Only If
The phrase “if and only if” is not used commonly in games, but it is important to understand
in case you ever encounter it. Since the phrase “if” introduces a sufficient condition and the
phrase “only if” introduces a necessary condition, the phrase “if and only if” introduces a
condition that is both sufficient and necessary. This type of rule should be represented with
a reciprocal (double-sided) arrow.
Dominique upgrades to a super wash if and only if Charlotte
upgrades to a super wash. blueprintprep.com/lsat
ds \ c s
Games Logic /
53
The contrapositive of this statement is a bit different than other conditional rules. Because
this is a reciprocal relationship, if one condition isn’t met, then neither condition is met. The
best way to interpret this type of rule is that there are really only two possibilities: either both
conditions are met, or neither one is met.
“If and only if” introduces a reciprocal relationship.
Up next? That’s right, more practice. This phrasing is not very common, but here are two
examples for you to diagram. You will notice that the arrow is missing, so you also need to fill in
the appropriate arrow.
1.
Lisa purchases a dalmation if and only if Priya purchases a terrier.
_
_
2.
Marshawn is interviewed on day 4 if, but only if, Lee is interviewed on day 6.
_
_
Unless
The word “unless” can be frightening to diagram, but we will get through it together.
Logically, the word “unless” introduces a necessary condition. However, to diagram one of
these statements, it is much easier to replace “unless” with the phrase “if not”. The term
following “unless” is negated to form the sufficient condition, and the other term forms the
necessary condition. This may sound complicated, so let’s consider the following examples:
The vacuum is not in the closet unless the umbrella is in the closet.
To diagram this statement, replace “unless” with “if not.” Thus,
U [ V
the claim can be restated as follows: If the umbrella is not in the
closet, then the vacuum is not in the closet.
You should practice this maneuver until your eyes begin to bleed (not really, but please
memorize the rule). Let’s try another.
Unless Barnaby performs on stage 3, Cullen must perform on stage 5.
Follow the same steps on this questionable example. Replace
“unless” with “if not” and you are left with the following claim: If
Barnaby does not perform on stage 3, then Cullen must perform
on stage 5. B3 [ c 5
To diagram an unless statement, replace “unless” with the phrase “if not.”
54
/ Chapter 9
blueprintprep.com/lsat
Your turn. Use the rule outlined on the last page to diagram the following conditional rules.
1.
The drums will not be included unless the saxophone is included.
_ [ _
2.
Unless Andre is on the green team, Benji cannot be on the green team. _ [ _
3.
D must be invited unless F is not invited. _ [ _
That brings us to the end of our discussion of conditional keywords. However, make sure to
check this answer key and look over any errors.
“If” statements
1.
2.
3.
tw [ rf4.
K2 [ j45.
c [ q
th [ f
d [ R
“Only” statements
1.
2.
3.
t [ s4.
k5 [ m75.
t [ b
mo [ r
g4 [ H1
“If and only if” statements
1.
ld \ pt2.
m4 \ l6
“Unless” statements
1.
2.
3.
In the third “unless”
example, you have to negate the condition
Ag [ Bg
that F is not invited. Thus, “F is invited”
f [ d
becomes the sufficient condition.
Godly Guidance:
S [ D
If you got the majority of those correct, you are well on your way to becoming a conditional rock
star. Let’s move on to a bigger drill.
blueprintprep.com/lsat
Games Logic /
55
Get Your Diagram On
This drill is designed to test your ability to diagram conditional rules. For each of the following
statements, diagram the sufficient and necessary conditions. Then, diagram the contrapositive.
Hint: You will have to alter some of the arrows.
1.
If Batman is seen at the crime scene, then
Robin will also be present.
7.
_ [ _
_ [ _
_ [ _
2. Mr. T will pity anyone who is a fool.
_ [ _
8.
_ [ _
Conifers are not in the forest if spruces are
not in the forest.
_ [ _
_ [ _
4.
If St. Nick is not on the red team, then the
Easter Bunny must be on the red team.
_ [ _
_ [ _
5.
Only champions from the first round make it
to the Showcase Showdown.
_ [ _
_ [ _
6.
56
The male supermodel will wear a speedo
only if he has thoroughly waxed.
Only a member of the first panel can be the
chairman on the second panel.
_ [ _
_ [ _
3.
Brandon will eat the sandwich only if there
is extra jelly.
_ [ _
9.
Jameer bids on the vacation if, but only if,
Dwight bids on the living room set.
_ [ _
_ [ _
10. Eric will get married if and only if Lyle gets
married.
_ [ _
_ [ _
11. Gertrude cannot win an award unless
Henrietta wins an award.
_ [ _
_ [ _
12. X is selected unless Y is not selected.
_ [ _
_ [ _
_ [ _
_ [ _
/ Chapter 9
blueprintprep.com/lsat
13. Any symptom of pneumonia is also a
symptom of narcolepsy.
20. The Horn Toad Race is the third destination
if the Monster Truck Rally is not third.
_ [ _
_ [ _
_ [ _
_ [ _
14. Only people from France shower irregularly.
21. If brain matter is found at the crime scene,
then fingerprints cannot be.
_ [ _
_ [ _
_ [ _
_ [ _
15. Model 1 wears the purple dress unless model
3 wears the yellow dress.
22. The fourth toy is green only if the sixth toy
is purple.
_ [ _
_ [ _
_ [ _
_ [ _
16. If the USA wins the gold medal, then Russia
wins the bronze.
23. Joey cannot attend the party unless Ross
also attends the party.
_ [ _
_ [ _
_ [ _
_ [ _
17. The turtle is exhibited at the zoo only if the
unicorn is not exhibited.
24. If curling is scheduled for Wednesday, then
skeleton is scheduled for Friday.
_ [ _
_ [ _
_ [ _
_ [ _
18. If the brownie is the sixth course during
dinner, then the tilefish must be the third
course.
25. Jessica is featured in every skit that Katie is
not.
_ [ _
_ [ _
_ [ _
_ [ _
19. Peter is accepted if, but only if, Rachel is
also accepted.
_ [ _
_ [ _
blueprintprep.com/lsat
Games Logic /
57
How’d you do?
b [ r
R [ B
1
“If” introduces a sufficient condition. So
when the caped crusader shows up, his loyal
sidekick will always be there with him. If
Robin is not present, then you know Batman
is nowhere to be found. However, does
Batman also have to follow Robin? No way,
as any self-respecting Christian Bale fan
knows.
2
f [ p
P [ F
“I pity the fool.” Little did you know that Mr.
T is a big fan of the conditional statement.
“Anyone” introduces a sufficient condition, so
being a fool is sufficient to receive some pity.
The contrapositive demonstrates that if Mr. T
shows you no pity, you are not a fool. But do
only fools receive pity from Mr. T? Of course
not: He could also show pity to those with
small biceps and meager jewelry collections.
3
S [ C
c [ s
Remember: No matter where “if” appears
in the sentence, the sufficient condition will
always follow. If spruces are not in the forest,
then conifers are not in the forest. Also, if
conifers are in the forest, then spruces must
be in the forest. But the forest could contain
spruces without conifers.
4
Nr
Br
[
[
br
nr
What does “if” introduce again? Oh yes, a
sufficient condition. If St. Nick is not on the
vaunted red team, then the Easter Bunny
must be on the red team. And if the Easter
58
/ Chapter 9
Bunny is not on the red team, St. Nick must
be. This rule can also be interpreted to mean
that either St. Nick or the Easter Bunny
must always be on the red team. It is also
acceptable for both St. Nick and the Easter
Bunny to be on the red team. Now there’s a
power couple!
5
s [ c
C [ S
“Only” always refers to a necessary condition.
You might recognize this example from a
classic TV show that rewarded contestants
with living room sets and wave runners. It
is necessary for a contestant to be a firstround champion to advance to the Showcase
Showdown. However, it is far from sufficient.
Many first-round champions lose on the wheel
and never make the big showdown.
6
s [ w
W [ S
“Only if” always introduces a necessary
condition. There are many requirements
for a male supermodel to wear a speedo
(spray tanning comes to mind), and waxing is
definitely one of them. Does waxing guarantee
anything? Not even close. There may be other
issues that intervene, such as heat rash or a
surprising bout of shyness. But if a supermodel
does not wax, there will be no speedo.
7
b [ j
J [ B
“Only if” still introduces a necessary condition.
Brandon is apparently only interested in
sandwiches that have extra jelly. If a sandwich
dares to have mere regular amounts of jelly,
Brandon will not be interested. (Don’t even
get him started on non-jelly sandwiches.)
blueprintprep.com/lsat
8
c2 [ m1
M1 [ C2
One more time: “Only” introduces a necessary
condition. In order to become the chairman
on the second panel, a person must have been
on the first panel. So if a person (be it Bob,
Marta, or Laquisha) was not on the first panel,
they cannot be the chairman on the second
panel.
9
jv \ dl
Jv \ D l
“If, but only if” signifies a reciprocal
relationship. Here, we return to bidding on
questionable prizes. This rule means there
are two options: either Jameer bids on the
vacation and Dwight bids on the living room
set, or Jameer does not bid on the vacation
and Dwight does not bid on the living room
set. Both or neither.
10
em \ l m
Em \ L M
“If and only if” also signifies a reciprocal
relationship. Here, the guys are sticking
together. Either both Eric and Lyle are getting
married, or they will both grow old without a
marital partner (bromance4lyfe). Don’t forget:
“If and only if” means we either have both
conditions, or we have neither one.
11
H
g
[
[
G
h
12
“Unless” becomes “if not,” so we know that if
Y is selected, then X must be selected. Also,
if X is not selected, then Y cannot be selected.
Watch those double negatives.
13
blueprintprep.com/lsat
p [ n
N [ P
Not a fun game when you have to deal with
symptoms and diseases, but there is a lesson
here: The word “any” introduces a sufficient
condition. So if coughing or drowsiness or an
ugly rash is a symptom of pneumonia, then it is
also a symptom of narcolepsy—and, of course,
if a symptom is not found with narcolepsy,
then it’s not found with pneumonia. But if
insomnia or explosive diarrhea is a symptom
of narcolepsy, it need not be a symptom of
pneumonia. Good to know.
14
i [ f
F [ I
Back to the world of “only.” Here, we visit
the land of stereotypically baguette-toting
soap haters. If the only people who shower
irregularly are from France, then being from
France is necessary. Does everyone in France
shower irregularly? Well, no, even if some
people think that way. If you aren’t from
France, however, then you shower regularly
(hopefully just about every day).
15
Remember: Always replace “unless” with the
phrase “if not.” This rule can be restated:
If Henrietta does not win an award, then
Gertrude does not win an award. Also, if
Gertrude wins an award (perhaps for most
grandma-ish name), then Henrietta must also
win an award.
y [ x
X [ Y
Y3
P1
[
[
p1
y3
After you replace “unless” with “if not,” this
rule reads: If model 3 does not wear the yellow
dress, then model 1 wears the purple dress.
And, of course, if model 1 does not wear the
purple dress, then model 3 is rocking a yellow
frock. (Yep, we said frock.)
Games Logic /
59
16
ug
Rb
[
[
rb
Ug
Damn straight, Putin! If America brings
home the gold, then Russia earns the
bronze. The contrapositive tells us if Russia
does not win the bronze, then the US will
not win the gold. However, if Russia wins
the bronze, that does not guarantee the US
wins the gold.
17
t
u
[
[
U
T
Is this a hallucinogenic zoo? Unicorns?
What’s next, manticores? “Only if” indicates a
necessary condition, so a turtle exhibit implies
that there is no unicorn exhibit. And a unicorn
exhibit would be clear evidence that there
are no turtles to be found. It is possible to
have neither turtles nor unicorns (boring), but
the zoo never exhibits both. That would be
sensory overload for the children.
20
21
19
p \
P \
r
R
Peter and Rachel are sticking together. If
either one is accepted, then the other one
must be accepted as well. And if Peter or
Rachel is not accepted, then neither are
accepted. In other words, you have to
have both or neither. This relationship is
diagrammed with the reciprocal arrow.
60
/ Chapter 9
h3
m3
b
f
[
[
F
B
Gross. Now you get to play the role of a crime
scene investigator. If you uncover some brain,
then there are no fingerprints. And if you
uncover some fingerprints, don’t expect any
brain matter to be found. This rule means that
you can never find both brain and fingerprints
together. But they’re sure to find some DNA.
That stuff is everywhere.
b6 [ t 3
T3 [ B6
Yummy. Nothing says haute cuisine like
tilefish and brownies. If the brownies are the
sixth course, then the tilefish must be third.
And if tilefish is not third (perhaps it is second
or, gasp, not served at all), then the brownies
cannot be the sixth course.
[
[
Horn Toad Race or Monster Truck Rally?
Tough decision. If either one of these
destinations is not third, then the other one
must be third. This rule is best interpreted
to mean that either the Horn Toad Race or
the Monster Truck Rally must be the third
destination.
22
18
M3
H3
g4
P6
[
[
p6
G4
“Only if” indicates a necessary condition. So if
the fourth toy is green, then the sixth toy must
be purple. Alas, if the sixth toy is not purple,
then the fourth toy cannot be green.
23
R [ J
j [ r
Once you’ve replaced “unless” with “if not,”
the rule tells us if Ross does not attend the
party, then Joey will not attend the party.
This also means that Ross must attend if
Joey attends. But what about Chandler and
Monica? They’re probably making out in the
back room.
blueprintprep.com/lsat
24
cw
Sf
[
[
sf
Cw
In this rule, you are in charge of scheduling
Olympic events. If curling (the definition of
excitement) is on Wednesday, then skeleton
(a really safe activity to pick up) is on
Friday. Also, if skeleton is scheduled for any
day besides Friday, then curling is not on
Wednesday.
25
K
J
[
[
j
k
The word “every” indicates a sufficient
condition. If Katie is not featured in a skit,
then Jessica must be. And if Jessica is not
featured in a skit, then Katie must be. Thus,
if either one of them is not in a skit, then the
other one must be. This means either Katie or
Jessica (or both) must be in every skit.
If diagramming seems slow and arduous at this point, that
is natural. You will speed up with practice. However, if you still have
that uncomfortable feeling (like walking into a dentist’s office), be sure to
review these rules before moving on. It’s going to get more complicated.
BP Minotaur:
At this point, you should feel comfortable with the following:
1. There are only two types of rules in Logic Games: absolute and conditional.
2. A conditional rule doesn’t actually establish anything concrete - rather, it
introduces a relationship between two conditions such that satisfying one
guarantees another.
3. A sufficient condition is enough to guarantee the necessary condition follows.
4. A necessary condition is required for a sufficient condition to follow.
5. There are two valid inferences from any conditional statement: the valid
affirmation (satisfying the sufficient condition) and the contrapositive (denying
the necessary condition).
6. Avoid two common invalid inferences when working with conditional statements:
the converse (satisfying the necessary condition) and the inverse (denying the
sufficient condition).
7. Always diagram conditional rules and their contrapositives.
That is a wrap on the basics. However, you will occasionally be confronted with more
complicated conditional rules. Guess what’s up next?
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And Versus Or
Alien versus Predator. The Yankees versus the Red Sox. Facebook versus common sense.
These are classic battles. “And” versus “or” on the LSAT may not have garnered as much
hype over the years, but the difference between the two is important for Logic Games. These
claims are referred to as conjunctions and disjunctions. Many rules will give you conjunctions or
disjunctions, and you must know how to diagram them.
A conjunction is an “and” statement.
A disjunction is an “or” statement.
Conjunctions and disjunctions can be introduced in a variety of ways. The following chart
outlines the correct way to diagram the most common forms:
Rule
Correct Diagram
Both A and B
a & b
Either A or B
a or b
Not both A and B
A or B
Neither A nor B
A & B
Bro Tip:
“Not both” and
“neither” cause lots
of confusion for
students.
It looks like you switched ‘not both’ and ‘neither.’
Many students think it looks that way. After all, not both A and B has and in it and nor
sounds just like or. But be careful. To satisfy the condition that you don’t have both,
you only have to be lacking one or the other. And to have neither, you can’t have
either one. We will introduce some helpful examples in just a moment.
Enough chit chat. Let’s see this in action. Here are some hypothetical rules:
The fruit salad includes either bananas or papaya.
b or p
According to this rule, either banana or papaya must be included in the fruit salad. You
must have one or the other—or you could have both. It’s important to note that an “or”
statements always allows for the possibility of both.
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Outside our LSAT bubble, when a friend says, “I’d like
filet mignon or a veal cutlet,” we usually take it to mean that they
desire only one of the two options. This is not true on the LSAT.
Unless stated otherwise, an “or” statement allows for both (filet and
cutlet), even though that would be quite a hefty load of meat.
BP Minotaur:
Let’s take a look at a couple more rules.
The squadron cannot include both Maverick and Iceman.
M or I
Obviously, any squadron featuring both Maverick and Iceman would be overflowing with
testosterone and homoeroticism. This rule is commonly misinterpreted to mean that both
Maverick and Iceman are not on the squadron. However, this rule allows either one of them
to make it; it simply rules out the possibility of having both. Thus, the rule should be
diagrammed to show that either Maverick or Iceman does not make the squadron. (It is still
possible that neither one makes the squadron, even though no one would watch such a film.)
Neither Bunion Away nor Cellulite-B-Gone is part of the Fortune 500.
B & C
When a rule says neither, it means that each condition does not happen. This rule informs
you that Bunion Away and Cellulite-B-Gone are both not part of the Fortune 500. Shocking.
Exclusive Disjunctions (But Not Both)
Remember, on the LSAT, an “or” statement allows for both. So if a rule states that Toby or Mary
goes to the party, one or the other must go, but it also could be true that they both go.
Occasionally, however, the test specifies that it must be one or the other and not both. This is
done through the use of the words “but not both” (not very subtle). Here is an example:
Either Swashbuckle or Alestorm, but not both, is in
the top 10 list on the pirate metal charts.
1
1
2
(s or a) & (S or A)
Logically, there are two parts to this
statement: (1) Either Swashbuckle or
Alestorm is topping the charts, and (2)
either Swashbuckle or Alestorm is not
included in the top 10.1 It’s important to
diagram both conditions to distinguish
“but not both” statements from an
inclusive “or.”
We promise, you will not regret looking up Pirate Metal. Sail the LSAT high seas with your new favorite music
genre, me hearties.
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Games Logic /
63
Complex Conditionals
When conditional statements include conjunctions and/or disjunctions, we refer to them as
complex conditionals. We already know the steps used to form the contrapositive of any
conditional statement: (1) Switch the sufficient and necessary conditions, and (2) negate
both conditions. The same rules apply to complex conditionals, although you must be sure to
correctly negate any conjunctions and disjunctions.
To negate a conjunction or disjunction, “and” becomes “or,” and “or” becomes “and.”
As always, some examples will help elucidate this process.
Clearly, something is going down in the
red states. The first step is to diagram
the rule as stated. If the Senator from
Oklahoma gives a speech, then both
the Senator from Texas and the Senator
from Mississippi do not.
Here’s where it gets a bit complex. For the
big guy from Oklahoma to give a speech, it
is necessary that both of the other senators
do not give speeches. Thus, if either the
Senator from Texas or the Senator from
Mississippi gives a speech, then the Senator
from Oklahoma does not give a speech.
That was so much fun, let’s do another.
Gomez must be scheduled for Friday if either
Marquez or Nando is scheduled for Tuesday.
mt or nt [ gf
Gf [ Mt & Nt
1. Flipped the conditions
2. Negated everything
3. Changed “or” to “and”
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If the Senator from Oklahoma gives a speech, then
neither the Senator from Texas nor the Senator
from Mississippi give a speech.
o [ T & M
t or m [ O
1. Flipped the conditions
2. Negated everything
3. Changed “and” to “or”
First, you hopefully spotted the word “if,”
which introduces the sufficient condition.
This rule tells you that if either Marquez
or Nando is scheduled for Tuesday, then
Gomez must be scheduled for Friday.
To form the contrapositive, follow the
same steps as before: Flip the terms,
negate them, and change “or” to “and.”
Since scheduling either Marquez or Nando
for Tuesday is sufficient to guarantee that
Gomez is scheduled for Friday, if Gomez
is not scheduled for Friday, then neither
Marquez nor Nando can be slotted in for
Tuesday.
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One more example! This is a complicated one...
If there is no cranberry sauce, then there must be
either pumpkin pie or apple cobbler, but not both.
C [ (p or a) & (P or A)
To form the contrapositive, you have
to execute the same steps: (1) Flip the
sufficient and necessary conditions, (2)
negate everything, and (3) switch the
operators (and/or).
Mmmm, now this is a tasty
rule. Nothing spells gluttony like
Thanksgiving. This rule is complicated
because it involves an exclusive
disjunction. If there is no cranberry
sauce on the table, then there must be
either pumpkin pie or apple cobbler,
but not both. In other words, there
must be one and not the other. This
should be represented using the
convention discussed earlier.
(P & A) or (p & a) [ c
Contrapositive: If there is neither pumpkin pie nor apple cobbler or if there is
both pumpkin pie and apple cobbler, then there must be cranberry sauce.
Conditional statements with conjunctions and/or disjunctions are among the most challenging
rules you will confront in Logic Games. If you can diagram this tasty, Thanksgiving-inspired
example, then you can diagram anything. Make sure to review these rules often during your
studies.
Next up: a drill to make sure that
everything is clicking.
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Diagramming, Super-Sized
In front of you lies a mix of complicated conditional rules. Diagram each rule and its
contrapositive.
1. If the dolphin is in tank 3, then both the shark and
the whale are in tank 2.
2. The Titans make the playoffs only if the Steelers
or the Jaguars make the playoffs.
3. J cannot be selected if both K and L are selected.
4. If the first and second pregnancy tests are
positive, then the third one is positive as well.
5. If Van takes chemistry, then he takes physics but
not astronomy.
6. If the tarantula or the rattlesnake is in the closet,
then neither little Susie nor her dolly is in the
closet.
7. If it is not the case that both Ben and Leo win an
Oscar, then Will must win an Oscar.
8. If X is selected, then either Y or Z, but not both,
must be selected.
9. Bill is having a good time if he is eating either
funnel cake or turkey legs, but not both.
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How’d it go this time?
Diagram:
Contrapositive:
1
d3 [ s 2 & w 2
S2 or W2 [ D3
If the dolphin is in tank 3, that is sufficient to tell you that both the shark and the whale
are in tank 2. Because both conditions are necessary, if either one does not happen (if
the shark is not in tank 2 or if the whale is not in tank 2), then the dolphin cannot be in
tank 3. And if you cannot find the dolphin in any tank, it’s time to call Ace Ventura: Pet
Detective.
2
Diagram:
Contrapositive:
t [ s or j
S & J [ T
It’s time for the NFL playoffs. “Only if” introduces a necessary condition, so either the
Steelers or the Jaguars must make the playoffs in order for the Titans to make it. Thus, if
both the Steelers and Jaguars do not make the playoffs, then the Titans also do not make
the playoffs.
3
Diagram:
Contrapositive:
k & l [ J
j [ K or L
In this example, selecting both K and L is sufficient to conclude that J cannot be selected.
Thus, if J is selected, then it cannot be true that both K and L are selected (either K or L
cannot be selected). This rule can also be interpreted to mean that K, L, and J cannot all
be selected together. Any two of the variables could be selected, but not all three.
4
Diagram:
Contrapositive:
1p & 2p [ 3p
3p [ 1p or 2p
If the first test is positive, you are allowed to take a second. But if both the first and
second tests come up positive, you know what is coming on number three. Thus, if the
third test is not positive, then either the first or the second (or both) must not be positive.
Note: This is not an effective means of contraception.
5
Diagram:
Contrapositive:
c [ p & A
P or a [ C
This one can be a little confusing. If Van takes chemistry, then Van takes physics but he
does not take astronomy. To form the contrapositive, you still follow the same rules: Flip
the terms, negate all of the conditions, and switch the operator. If Van does not take
physics, or if he does take astronomy, then he cannot take chemistry.
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Games Logic /
67
6
Diagram:
Contrapositive:
t or r
s or d
[
[
S & D
T & R
This closet is more like a haunted house. If either the tarantula or the rattlesnake is found
in the closet, then both little Susie and her dolly are not in the closet. Thus, if either little
Susie or her dolly (or both) are in the closet, then neither the tarantula nor the rattlesnake
is in the closet.
7
Diagram:
Contrapositive:
B or L [ w
W [ b & l
The original claim here can be difficult to decipher. Here, our sufficient condition says, “If
it is not the case that both Ben and Leo win an Oscar.” We have a “not both” statement
which, if you remember from our chart a few pages back, we diagram as not Ben or not
Leo. If this happens, then Will must win (he is, after all, kind of a big deal). And if Will
does not win an Oscar (some people just do not understand the comic genius behind Sex
Panther), then both Ben and Leo must have brought home the shiny trophies.
8
Diagram:
Contrapositive:
x [ (y or z) & (Y or Z)
(Y & Z) or (y & z) [ X
This is an ugly one. Make sure to always take note of the phrase “but not both.” If X is
selected, then either Y or Z must be selected and either Y or Z must not be selected (one
or the other, but not both). The contrapositive would then state that if neither Y nor Z
are selected or if both Y and Z are selected, then X cannot be selected.
9
Diagram:
Contrapositive:
(f or t) & (F or T) [ g
G [ (F + T) or (f + t)
In this example, if either funnel cake or a turkey leg is being eaten by Bill, and either a
funnel cake or a turkey leg is not being eaten by Bill, then Bill is having a good time. And
if he’s not, then one of two things must be true: (1) Bill is sadly bereft of two delicious
festival foods, or (2) Bill has flown too close to the sun and made the forbidden Funnel
Cake Turkey Leg Combo, and he has regrets.
For some students, this drill feels worse than wearing a meat-scented swimsuit in a piranha-filled
river. The good news is that it gets better with practice. Also, such complex rules don’t show up
all the time. But when they do, it’s important to be able to diagram them correctly.
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Transitive Property
There is one last important skill you need to develop: combining conditionals to draw important
deductions. Until now, we have been dealing with conditional rules in isolation, but it is common
to be presented with more than one conditional rule in a game. When this happens, you should
see if any additional deductions can be made.
Let’s check out an example. Pretend that the wonderful people who write the LSAT have been
watching a Star Wars marathon, and they give you the following rules:
If Obi Wan goes to Tatooine, then Jar Jar goes to Tatooine.
If Jar Jar goes to Tatooine, then Yoda does not go to Tatooine.
1.
o [ j
J [ O
2.
j [ Y
y [ J
Welcome to a world of interstellar
intrigue, planetary travel, and also,
regrettably, midichlorions. As we know,
we always want to start by diagramming
each rule.
See how the necessary condition of the first rule
is the same as the sufficient condition of the
second rule? Learn to love that. It means the
rules can be combined.
These two rules can be combined to uncover a helpful
deduction. If Obi Wan goes to Tatooine, then Jar Jar must
go as well. And if Jar Jar goes to Tatooine, then Yoda
cannot go. These two rules tell you that if Obi Wan goes to
Tatooine then Yoda does not. The contrapositive will also be
useful: If Yoda goes to Tatooine, then Obi Wan does not.
o
y
[
[
Y
O
In logic, this is called the transitive property. Whenever the necessary condition of one
statement is the same as the sufficient condition of another statement, they can be combined
to form a transitive conclusion.
Transitive conclusions are commonly the key to answering
questions, so there’s a big payoff when you can combine conditional rules.
Godly Guidance:
Congratulations! You’ve now learned how to diagram and understand conditional statements.
Be sure to review this chapter early and often. Now that we have this stuff in our bag of tricks,
it’s time to jump back to ordering games. The next chapter covers games that will look like the
basic ordering games covered earlier, but the rules will be very different.
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10/1:1ORDERING
What Is It?
The next set of games are similar to the last, but a little bit different.1 We are now going to focus
on 1:1 ordering games. These games will also introduce two variable sets (ice cream scoops and
children, basketball players and shoe sizes). Each player in the game will be assigned to one and
only one slot. The big difference in this chapter will be a variety of new rules.
An ordering game with 1:1 correspondence has one and only one slot for each player.
Assigning seven Xbox controllers to seven brothers is a game with 1:1 correspondence.
Arranging eight sprinters in eight lanes is a game with 1:1 correspondence. If you have six
friends at a party and only two chairs available to sit in, you don’t have 1:1 correspondence
(and hopefully the attendees enjoy musical chairs).
1:1 ordering games are among the most common
types of games on the LSAT. Frequently, though not always, the
first game in a section will be of this type.
BP Minotaur:
Note: As with all ordering games, remember to identify the variable set with the inherent
order (days, height, ranking), and use that variable set as the base. The other
variable set will then be arranged into the ordered slots.
In this chapter, we will introduce a variety of new ordering rules. The setup for 1:1 ordering games
will look very familiar, but your challenge, if you choose to accept it—and you’re reading this book,
so you’ve already made your choice—is to learn to juggle these new rules effectively. Let’s go.
Blocks
Legos. Lincoln Logs. These were the staples of our youth. Before the joys of computers and the
World Wide Web, children used to spend hours constructing empires out of miniature wooden
blocks.2 Finally, all of that practice pays off.
70
1
After writing this sentence, we realized that telling you something is the same, but different, is not very helpful.
Other platitudes that we really enjoy: “It is what it is,” and the classic rejoinder, “Yeah, but still.”
2
Fortunately, the joy of playing with blocks has lived on in Minecraft.
/ Chapter 10
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Blocks are used to represent spatial relationships that are more concrete than those represented
with dashes. When you know exactly where one player is situated in relation to another, use a
block to symbolize this relationship. Here are some examples of rules correctly symbolized as
blocks:
The samurai sword must be placed immediately in front of the crib.
s
c
The family room set is auctioned off immediately after the vacation rental.
v
Jack arrives at the party immediately before Kai but
immediately after Mike.
m
j
f
k
Symbolizing these rules as blocks gives you
an important visual reminder to keep consecutive slots open.
Godly Guidance:
On occasion, blocks will leave empty slots between players. This can easily be incorporated into
the diagram. Here are a few examples:
Exactly one lucky winner spins the big wheel after Betty but before Tina.
The bus tour visits Chattanooga exactly three days after Nashville.
Bro Tip:
_
t
_
_
c
You beefed it on that last one. That’s only
two days after.
While wrong, Broseidon does raise a good
point. You have to be very careful with the
wording that introduces blocks. The last block
does represent that Chattanooga is visited
three days after Nashville. However, this is
synonymous with a rule stating there are two
cities between Chattanooga and Nashville.
blueprintprep.com/lsat
n
b
a
_
_
b
“three spots
after”
“two spots between”
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71
Reversible Blocks
There is one more trick when it comes to blocks. Sometimes, they can go both ways.3 The
previous blocks made it clear which player was in front, but some blocks are reversible. Certain
rules will tell you that two players must be next to each other without defining who comes first.
To represent this, we will place a double-sided arrow over the block.
Here are some examples:
Sigfried and Roy must stand next to each other in line for the buffet.
s
r
Exactly one clown performs in between Bozo and Krusty.
b
_
k
You will grow to love blocks. Since they give a fixed
relationship, you will commonly find that there are only a few possible
placements for a block. This can lead to huge deductions.
Godly Guidance:
Restrictions
In ordering games, you always want to rule out possibilities. For example, if neither Ralph
nor Eduardo can sit in seat 4, there are two less people to worry about in that slot. Rules will
commonly dictate that a player cannot be placed in a certain slot. We can easily represent
these rules by placing a restriction under that slot. Here are some examples:
Delilah cannot be seated in chair 3.
1
2
3
4
5
6
D
Neither Monday nor Friday is a day on which the
cheetah can be wrestled.
m
C
3
72
t
w
r
f
C
Various drafts of this book had inappropriate comments inserted into this footnote, but we’ve all grown as
people since we first started sharing Logic Games wisdom. Progress!
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You can also form restrictions using other types of rules, and they can give you great visual
reminders in a game. Both dashes (which you should remember from basic ordering games)
and blocks can be used to form helpful restrictions. “How?” you ask. Here are some examples:
Sleepy must be in a lower-numbered room than Dopey.
Grumpy must be in the room numbered one lower than Bashful.
1
s - d
g
•
•
2
3
4
D
B
b
5
6
S
G
Since Sleepy must be in a lower-numbered room than Dopey, Sleepy cannot be in room 6,
and Dopey cannot be in room 1.
Since Grumpy must be in the room numbered one lower than Bashful, Grumpy cannot be
in room 6, and Bashful cannot be in room 1.
But wait, there’s more. You should always keep track of your restrictions. When you are able to
make a lot of restrictions about players that cannot go in a certain slot, it is time to start thinking
about who can go into that slot. This can lead to big-time deductions.
For example, pretend you are attempting a 1:1 ordering game with five players­: T, U, V, W, and
X. Here’s an example of how restrictions can lead to a big deduction:
T cannot be first or fifth.
X must be third.
U and V must be in front of W.
u
w
v
•
•
•
•
Not on 5
1
2
T
W
W
x
3
w
4
5
T
U
V
None of these
punks can be
fifth either.
T cannot be first or fifth, so we can make restrictions under those slots.
X gets plugged into the third slot.
Both U and V must come before W, so W cannot be first or second, and both U and V
cannot be fifth.
Here’s the big moment. Since T, U, and V cannot be fifth, and X must be third, the big
deduction is that W must be fifth because it is the only option left.
Before we go any further, it’s time for a drill.
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1:1 Ordering /
73
1:1 ordering drill
Peanut butter is great. Jelly is surely a treat. Put them together, though, and magic happens.
Logic Games aren’t quite as delicious, but the same principle applies. You must learn to use all
of the rules together to form deductions.
Represent the following rules using dashes and blocks.
Then, make as many restrictions as possible.
Note: Each game is a 1:1 ordering game with six players and six slots.
1.
2.
74
Six daredevils on a reality TV show­—Bam, Cam, Frank,
Jane, Stevie, and Weenie—are ranked according to the
number of injuries they suffer from first (most injuries) to
sixth (least injuries). There are no ties.
Stevie has more injuries than Bam and Jane.
Jane ranks immediately ahead of Weenie.
1
2
3
4
5
6
1
2
3
4
5
6
An entirely different TV show features six characters—
Brian, Lois, Meg, Peter, Quagmire, and Stewie. They are
ranked by their coolness factor from first (coolest) to sixth
(least cool). Again, there are no ties.
Peter is ranked third.
Stewie ranks immediately ahead of Quagmire.
Brian is cooler than Lois but less cool than Meg.
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3.
4.
Six animals are arranged from highest (first) to lowest (sixth)
on the food chain. There are no ties. The six animals are an
elephant, a hare, a panther, a snail, a turtle, and a wolf.
The elephant is lower than the hare.
The snail and the hare are separated by exactly one other
animal.
The turtle is neither the highest nor the lowest animal.
The panther is the fourth highest animal.
The wolf is higher than the panther.
1
2
3
4
5
6
1
2
3
4
5
6
Six types of cereal—Cornies, Double-O’s, Eggish, Fantastic,
Gruel, and Hamandeggs­—are part of a consumer survey
that ranks the cereals from most popular (first) through least
popular (sixth). As always in this drill, there are no ties.
Cornies are more popular than Double-O’s and Fantastic.
Gruel is ranked second.
Fantastic is more popular than Hamandeggs.
Eggish and Fantastic are ranked consecutively.
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75
Answer Key
There are two important things to check in this answer key. First, make sure you diagrammed
the rules correctly and combined them whenever possible. Second, check the restrictions to see
if you were able to spot them all.
1
b
s
j
•
•
•
•
•
•
•
w
s
q
m - b - l
•
•
•
•
•
•
76
2
B
J
W
W
3
4
5
6
S
S
S
J
The Jane and Weenie block should be combined into the ordering chain.
Stevie has more injuries than Bam, Jane, and Weenie, so Stevie cannot be ranked fourth,
fifth, or sixth. Stevie must be ranked pretty high.
Bam has fewer injuries than Stevie, so Bam cannot be ranked first.
Jane has fewer injuries than Stevie but more than Weenie, so Jane cannot be ranked first
or sixth.
Weenie has fewer injuries than Stevie and Jane, so Weenie cannot be ranked first or
second.
Cam and Frank are randoms because they aren’t in any rules. No restrictions there.
The first slot is the most restricted. Either Stevie, Cam, or Frank must be ranked first.
2
•
1
m/s
p
1
2
Q
B
L
S
L
3
l/q
4
5
6
Q
M
S
M
B
Stewie must be ranked immediately higher than Quagmire, so Stewie cannot be ranked
second (because Peter is third) or sixth.
Quagmire must be ranked immediately below Stewie, so Quagmire cannot be ranked first
or fourth (because Peter would get in the way again).
Meg ranks higher than Brian and Lois, so Meg can’t be ranked fifth or sixth.
Brian ranks higher than Lois but lower than Meg, so Brian can’t be ranked first or sixth.
Lois ranks lower than Meg and Brian, so Lois can’t be ranked first or second.
The coolest character must be either Meg or Stewie.
The least cool character must be either Quagmire or Lois.
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3
h - e
s
_
h
w - p
•
•
•
•
•
•
d
c
•
•
•
2
T
E
S
H
3
4
5
6
W
T
H
S
W
The elephant is lower than the hare, so the elephant isn’t first and the hare isn’t sixth.
The panther is fourth, and the hare and the snail must be separated by exactly one spot,
so the hare and the snail cannot be second or sixth.
The turtle can’t be first or sixth.
Since the wolf is higher than the panther, the wolf must be no lower than third.
There’s a big deduction about the lowest spot on the food chain. There are restrictions
for four of the six animals, and the panther also can’t be sixth. The only player left is the
elephant, so the elephant is lowest on the food chain (shocking).
Once we know E must be last, and knowing that P is already 4th, once we’ve restricted S
and H from 2, that leaves only T or W to fill that slot.
4
•
•
1
e
p
t/w
e
f
-
h
c
g
1
2
D
E
F
H
d/h
3
4
5
6
C
H
C
D
H
C
C
E
F
The first, third, and fourth rules can all be combined into a powerful ordering chain.
Cornies are more popular than Double-O’s, Eggish, Fantastic, and Hamandeggs. Since
Gruel is second, Cornies must be the most popular.
The block with Eggish and Fantastic is more popular than Hamandeggs, so neither
Eggish nor Fantastic can be the least popular cereal. The block must be placed third and
fourth, or fourth and fifth.
Double-O’s can’t be ranked fourth because there would be no possible placement for the
block.
Hamandeggs is less popular than Cornies, Gruel, Eggish, and Fantastic. The only cereal
Hamandeggs could beat out is Double-O’s, so Hamandeggs is either fifth or sixth.
That drill became increasingly difficult with each new example. By now, however, you should be
grasping how these new ordering rules work together.
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1:1 Ordering /
77
At this point, you should rate your confidence with the previous rules as “strong to very strong.”
But that’s not all. Say hello to more new rules...
Divisions
Can’t we all just get along? Unfortunately, no. There are times when you just have to keep
people away from each other. Republicans and Democrats. One spy and that other spy. Eagles
fans and... everyone else.4 Some rules in games perform the same function. Most commonly,
they state that two players cannot be next to each other. We call this type of rule a division.
Here are a couple examples:
The ham cannot be served immediately before the matzah.
h
The second
example is
reversible, but
the first is
not.
Rush and Obama cannot be seated next to each other.
r
BP Minotaur:
m
o
Divisions are much less common than blocks.
Options
Games are all about figuring out your options. There are some rules that will specify that a
certain slot must be assigned to one of two players. When this happens, you should scream for
joy (figuratively, of course; you are not allowed to scream during the actual exam). Only two
players can possibly fill a slot, and we represent this by writing an option in that slot. Here’s an
option in action:
b/c
Either Balthazar or Cryptonite must be assigned to space shuttle N.
l
m
n
o
p
Options can also be used to represent helpful deductions. Pretend you are doing a 1:1 ordering
game that involves scheduling the performances for five acrobats­—Alibaba, Barbie, Coinstar,
Deuteronomy, and Elephantitis—from first through fifth. Check out the following rules and how
we can make an option in our setup to represent a deduction:
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Barbie must perform fourth.
Both Coinstar and Deuteronomy must
perform after Elephantitis.
<
Only two options left.
a/e
c
1
d
C
D
e
•
b
2
3
5
4
Barbie must perform fourth. Coinstar and Deuteronomy cannot perform first since
they must follow Elephantitis. These restrictions only leave two options for the first
performance: Alibaba and Elephantitis. This can be plugged right into the setup.
Linked Options
Linked options are a frequently-used variant of normal options. If you know that two players
must fill two specific slots, but you don’t know exactly who fills each one, you should represent
this situation with linked options.
Here is a quick example to show you how this works. Let’s play with five acrobats again, but
now the performers are named Vendetta, Wilma, Xavier, Yolanda, and Zane.
Xavier must perform second.
Vendetta must perform fourth.
Vendetta must perform after both Yolanda and Zane.
Y or Z must fill both the
first and third spots.
y
v
y/z
x
z/y
v
w
1
2
3
4
5
z
•
•
Since both Yolanda and Zane must precede Vendetta, and there are only two available
spots that precede her, Yolanda and Zane must fill those two slots. However, it is not
clear whether Yolanda goes in spot 1 and Zane goes in spot 3, or vice versa.
Once you fill in slots 1 and 3 with linked options, it is easy to spot an important deduction:
Wilma must fill the last slot.
Linked options allow you to visually represent that two
slots are reserved for two players. Otherwise, it would be easy to make a
mistake and think another player could be assigned to one of the slots.
Godly Guidance:
blueprintprep.com/lsat
1:1 Ordering /
79
Arches
Some rules will restrict a certain player to only two possible slots. For instance, the big money
must be behind door number 1 or door number 2. These rules will be important because they
place such a strong restriction on one of the players. Instead of writing this rule off to the side
and possibly forgetting about it, we want to represent such rules directly in our setup. We can
do this by making arches to show that a player only has two options.
Here are two examples for your viewing pleasure:
j
Juan must be assigned to week 3 or week 5.
1
3
2
5
4
6
d
Divine must stand at the front or the back of the line.
1
2
3
4
5
6
7
That’s all, folks. To master 1:1 ordering games, you simply have to learn how to use each of these
types of rules. Here’s a quick overview of the rules that we have covered so far:
1. Dashes - A is before B.
2. Blocks - A is immediately before B.
3. Restrictions - A is not in slot 4.
4. Divisions - A is not next to B.
5. Options - A or B is in slot 3.
6. Arches - A is in slot 1 or slot 6.
Your next task is to learn how to use these wonderful tools together. There is a drill on the next
page to help you do exactly that. Get in there.
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1:1 Ordering Drill
This drill is designed to test your budding knowledge of ordering rules. For each of the following
games, build an appropriate ordering setup, represent the rules, and try to make as many
deductions as possible (mainly, try to combine rules and note restrictions). When you feel ready,
try to answer the questions that follow. Game on.
Game #1: Cast of Characters
Exactly seven TV personalities—Alf, Beetlejuice, Chuck Norris, Donatello (from the Teenage Mutant
Ninja Turtles), Mr. Ed, Fantasia, and Gonzo—all attend an awards show. The characters arrive only
once and one at a time. The order for the arrival is governed by the following conditions:
Either Chuck Norris or Donatello must be the fourth character to arrive.
Fantasia arrives earlier than Gonzo.
Donatello must arrive either immediately before or immediately after Alf.
Mr. Ed must arrive immediately before Beetlejuice.
1.
If Alf arrives second, then when must
Chuck Norris arrive?
2. If Gonzo arrives second, then when could
Chuck Norris arrive?
Game #2: Eligible Bachelors
A magazine ranks the top six bachelors in the world. The finalists are Boyega, Idris, Jungkook, Lil
Nas, Styles, and Zendaya. There are no ties. The following restrictions govern the final results:
Styles ranks lower than Lil Nas X.
Idris either ranks first or third.
Lil Nas X ranks exactly three spots lower than Jungkook.
1.
What is the complete and accurate list of
the possible rankings for Lil Nas?
blueprintprep.com/lsat
2. If Styles is not the lowest ranking
bachelor, then what is Idris’s ranking?
1:1 Ordering /
81
Game #3: College
A university student has a busy week ahead. Between Monday and Friday, he must go grocery
shopping, play video games, organize his DVD collection, play in a beer pong tournament, and do
homework. The student performs exactly one task each day. The following rules must apply:
The student does not go grocery shopping on Monday, Wednesday, or Friday.
The student must play video games before he plays beer pong.
At least one activity must be performed in between the days he does homework and organizes his
DVDs.
1.
What is the complete and accurate list of
activities the student could perform on
Monday?
2. If the student goes grocery shopping
in between playing video games and
playing beer pong, what activities could
the student perform on Wednesday?
Game #4: The Big Game
A NFL sportswriter visits the training camps of seven different NFL teams on seven consecutive days.
The writer will visit one team on each day. The teams visited are the Arizona Cougars, Baltimore
Raptors, Chicago Beavers, Denver Baboons, Green Bay Packrats, Indianapolis Caterpillars, and
Jacksonville Jarheads. The visits must conform to the following conditions:
Chicago is visited before Indianapolis.
Jacksonville is visited on the first or last day.
If Baltimore is visited on the third day, then Arizona is visited on the seventh day.
Denver is visited before Baltimore or before Green Bay, but not both.
1.
82
Which teams cannot be visited on the
first day?
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2. If the writer visits Baltimore on the third
day, what is the complete and accurate
list of the days she could visit Denver?
blueprintprep.com/lsat
Game #5: Happy Birthday
On a recent episode of Super Spoiled Sweet Sixteen, a Beverly Hills teen opened six birthday presents.
The presents were opened consecutively and one at a time. The six presents were a Porsche, a Rolex,
a servant, tennis lessons, an actual unicorn, and a yacht. The following rules govern the order in which
the presents were opened:
The Rolex is opened before both the Porsche and the tennis lessons.
The tennis lessons are opened before the unicorn.
If the servant is opened before the yacht, then the yacht is opened before the tennis lessons.
1.
Among the six presents, what is the
latest the Rolex could be opened?
2. If the servant is opened first and the
Porsche is opened third, then which
present must be opened fourth?
Game #6: Busy Week
Jake must schedule one date each night this week. Seven lucky ladies—Gwen, Harriet, Ivanna, Jackie,
Krista, Lucy, and Mindy—will go on a date with Jake on a different night, from Sunday through
Saturday. The schedule is consistent with the following:
Ivanna must be scheduled for Thursday.
Krista must be scheduled for an earlier day than Ivanna.
If Mindy is scheduled for Monday, then Jackie must be scheduled for Wednesday.
There must be exactly one day between Jake’s dates with Lucy and Ivanna.
Gwen and Jackie must be scheduled for consecutive days.
1.
If Mindy is scheduled for Monday, then
which lucky lady is scheduled for Friday?
blueprintprep.com/lsat
2. If Gwen is scheduled for a later day than
Ivanna, then what is the complete and
accurate list of the days that Jake could
schedule his date with Mindy?
1:1 Ordering /
83
Check it out
Here are the answers for the previous drill. Make sure you represented all of the rules correctly
and are starting to spot deductions. Review anything you missed.
Game #1: Cast of Characters
7c: a b c d e f g
f - g
c/d
d
a
1
G
B
e
•
•
1.
•
•
5
4
6
F
E
B
E
7
b
Since Fantasia arrives before Gonzo, Fantasia cannot be the last character to arrive and
Gonzo cannot be the first character to arrive.
Mr. Ed must arrive immediately before Beetlejuice, so Mr. Ed cannot arrive last and
Beetlejuice cannot arrive first. Also, since either Chuck Norris or Donatello must arrive
fourth, Mr. Ed cannot arrive third, and Beetlejuice cannot arrive fifth.
Fourth
If Alf arrives second, then Donatello must arrive first or third.
Since Donatello cannot arrive fourth, Chuck Norris must arrive fourth. (Hide the women
and children.)
2. Third, Fifth, Seventh
• If Gonzo arrives second, then Fantasia
f
arrives first.
• Chuck Norris can’t arrive fourth
1
because there would not be enough
room for both blocks, so Donatello
f
must arrive fourth.
1
• If Alf arrives third, Chuck Norris could
arrive fifth or seventh (to allow space
for the block).
• If Alf arrives fifth, Chuck Norris must arrive third.
84
3
2
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g
a
d
2
3
4
5
6
7
g
c
d
a
e
b
2
3
4
5
6
7
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Game #2: Eligible Bachelors
6b: b i j l s z
j
_
_
l
i
-
s
j
b/z
i
l
1
2
3
4
5
6
b/z
l
s
4
5
6
j
1
2
3
This game is a good example of the ambiguous wording that can
be dangerous in Logic Games. Here, ranking lower does not correspond to lower
numbers. Rather, slot 1 is the highest rank, and slot 6 is the lowest rank.
BP Minotaur:
•
•
•
1.
•
In this game, there is a huge block that includes both Jungkook and Lil Nas. In addition,
you know that Styles must be placed somewhere after the block. This combination
could lead to tons of restrictions. However, because there are so many places that these
players cannot be placed, it becomes more helpful to think about where they can be
placed. The block with Jungkook and Lil Nas has only two possible placements: first and
fourth, or second and fifth.
If Jungkook is ranked first and Lil Nas is fourth, then Idris must be third. In addition,
because Styles must rank lower than Lil Nas (fifth or sixth), you should add an option for
either Boyega or Zendaya in the second slot.
If Jungkook is ranked second and Lil Nas is fifth, then Styles must be ranked sixth. Since
Idris must be ranked first or third, the fourth spot must be assigned to either Boyega or
Zendaya, leading to an option.
Fourth, Fifth
Since the Jungkook/Lil Nas block only has two possible placements (above), we deduced
that Lil Nas must either be ranked fourth or fifth.
2. Third
• If Jungkook is ranked second, then Styles must be ranked last. Thus, if Styles is not
ranked last, then Jungkook must be ranked first.
• If Jungkook is ranked first, then Lil Nas must be ranked fourth and Idris is ranked third.
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1:1 Ordering /
85
Game #3: College
g
5a: g v d b h
v - b
m
h
•
•
•
1.
•
d
G
B
t
w
G
r
f
G
V
Since the student cannot go grocery shopping on Monday, Wednesday, or Friday, grocery
shopping must occur on Tuesday or Thursday.
The video games must come before beer pong, so the student cannot play video games
on Friday, and he cannot play beer pong on Monday (not a good way to start the week).
Since there must be at least one activity in between homework and organizing DVDs, that
rule should be represented as a division.
Video Games, Homework, Organizing DVDs
The student can’t go grocery shopping or play beer pong on Monday, but the other three
options are acceptable because no other rules prevent them from going on Monday.
2. Homework, Organizing DVDs
• If the student goes grocery shopping in between the days he plays video games and
plays beer pong, he still could go grocery shopping on Tuesday or Thursday.
• If the student goes grocery shopping on
Tuesday, then he must play video games on
Monday. Homework and organizing DVDs can’t
v - g - b
be done on consecutive days, so there should
be linked options for these two activities on
Wednesday and Friday. Thursday looks like a
d/h
v
h/d
b
g
great day for playing beer pong.
• If the student goes grocery shopping on
f
m
w
r
t
Thursday, then he must play beer pong on
Friday. Just like in the first situation, homework
and organizing DVDs form linked options, this
b
h/d
d/h
g
v
time on Monday and Wednesday. Playing video
games is slotted in for Tuesday.
f
m
w
r
t
• The only possible activities for Wednesday are
homework and organizing DVDs.
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Game #4: The Big Game
7c: a b c d g i j
j
c - i
•
•
•
b3 [ a 7 [ j 1
A7 [ B3
1
b/g - d - g/b
I
D
2
3
4
5
6
7
C
D
Since Chicago is visited before Indianapolis, Chicago cannot be visited on the last day,
and Indianapolis cannot be visited on the first day.
If Baltimore is visited on the third day, then Arizona is visited on the seventh day, which
then means Jacksonville has to be visited on the first day. Also, if Arizona is not visited
on the seventh day, then Baltimore cannot be visited on the third day (contrapositive).
The last rule says that Denver must be visited before either Baltimore or Green Bay, but
not both. Therefore, Denver must be visited before one of the cities and after the other—
in other words, Denver is between them. We represent this rule as an ordering chain with
linked options. From this chain, we see that Denver cannot be visited on the first day or
the last day.
1.
•
•
Denver, Indianapolis
Indianapolis can’t be visited on the first day because it comes after Chicago.
Denver must be visited after either Baltimore or Green Bay, so it also can’t be visited on
the first day.
2.
•
•
•
Fourth, Fifth
If Baltimore is on the third day, then Arizona is on the seventh day.
Since the slot for the last day has been filled, Jacksonville must be visited on the first day.
Denver must be visited after
Baltimore, but before Green Bay,
j
b
c
a
so Denver can’t be visited on the
second day or the sixth day.
5
1
3
4
6
2
7
Indianapolis must be visited after
Chicago, so Chicago is the only
D
D
G
option remaining for the second
G
day.
I
The Denver visit could take place
on the fourth day or the fifth day.
•
•
blueprintprep.com/lsat
1:1 Ordering /
87
Game #5: Happy Birthday
6p: p r s t u y
p
r
t - u
s - y [ y - t
t - y [ y - s
•
•
•
•
•
1
2
P
T
U
U
3
4
5
6
R
R
R
T
Y
The Rolex must be opened before the Porsche, tennis lessons, and the unicorn, so the
Rolex cannot be opened fourth, fifth, or sixth.
The Porsche must be opened after the Rolex, so the Porsche cannot be opened first.
The tennis lessons must be opened after the Rolex but before the unicorn, so the tennis
lessons cannot be opened first or last.
The unicorn must be opened after the Rolex and the tennis lessons, so the unicorn cannot
be opened first or second.
The last rule states that if the servant is opened before the yacht, then the yacht is
opened before the tennis lessons. It is also important to form the contrapositive: If the
tennis lessons are opened before the yacht (negation of the necessary condition), then
the yacht must be opened before the servant (negation of the sufficient condition). This
rule implies that the yacht must be opened before the tennis lessons or the servant, or
both, so the yacht cannot be opened sixth.
In 1:1 ordering games, there are no ties. If A is not in
front of B, then it must be behind, and vice versa. Keep this in mind
when you are negating conditions to form the contrapositive.
BP Minotaur:
1.
Third (The Porsche, tennis lessons, and unicorn must be opened after the Rolex.)
2. Yacht
• If the servant is opened first, then it must be opened before the yacht. Thus, the yacht is
opened before the tennis lessons.
• The Rolex must be opened second (before
t
s
p
y
u
r
the Porsche). According to the altered
ordering chain, the yacht is fourth, the tennis
5
1
3
4
6
2
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lessons are fifth, and the unicorn is last.
Game #6: Busy Week
7l: g h i j k l m
l
k - i
mm [ jw
Jw [ M m
g
•
•
1.
•
•
•
•
•
i
s
m
t
w
r
f
s
K
K
j
Since Ivanna is on Thursday, and Krista must be scheduled before Ivanna, Krista cannot
be the date for Friday or Saturday.
Since Ivanna must be on Thursday and there is exactly one date between Ivanna and
Lucy, Lucy must be on either Tuesday or Saturday (an arch).
Harriet
If Mindy is on Monday, then Jackie is on Wednesday.
Gwen and Jackie are on consecutive days, so since Ivanna is on Thursday, Gwen is on
Tuesday.
Lucy can’t be on Tuesday, so she
k
g
j
h
i
m
gets the hot date on Saturday.
Krista must be scheduled before
r
s
t
w
f
m
Ivanna, so Krista is on Monday.
Friday goes to Harriet.
2. Sunday, Wednesday
• Gwen and Jackie form linked options for Friday and Saturday.
• Lucy can’t be on Saturday, so she
l
must be on Tuesday.
• Since Jackie isn’t on Wednesday,
s
t
m
Mindy can’t be on Monday.
• Mindy’s only options left are
M
Sunday and Wednesday.
i
w
r
l
s
g/j j/g
f
s
That’s a great drill to develop your ordering skills. It’s almost time to jump into actual 1:1 ordering
games, but there’s one more important point to cover.
blueprintprep.com/lsat
1:1 Ordering /
89
all rules are not created equal
When you throw a party, there are some guests that you really need to keep an eye on, whether
for good reasons (cute, charming guy) or not-so-good reasons (sloppy drunk who likes to break
things). The same principle can be applied to Logic Games. Not all rules are created equal.
When you work through a game, it will commonly be the case that you will keep reverting back
to one or two rules, while the others are more like wallflowers.
Staring at an ugly setup with six or seven equally unattractive rules can be quite overwhelming.
However, true games gurus can spot the important rules early, and thus have a good idea of
where to start the work on each question. There are two types of rules in ordering games that
tend to be the most helpful: block and arches.
j
b
_
t
1. Blocks are great because they take
up a lot of space. In that sense,
they are like a group of 12 at a
McDonalds - hard to find room.
2. Arches put a strong restriction on
one of the players. This is like a
vegetarian at a burger shack - not
many options available.
When you are struggling to find deductions or to work through
a question, it is a good idea to always look for blocks and arches.
BP Minotaur:
As we work through more ordering games, we will introduce lots of advanced strategies. But
you will find that we will return to these rules over and over again.
That wraps up our summary of 1:1 ordering games. It’s crucial that you practice a number of
these games so the strategies can sink in. They are one of the more common types of games,
so make sure you get a lot of practice. We recommend doing at least 6-8 until you feel pretty
comfortable. Best of luck!
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11/under/overBOOKED
What Is It?
Up to this point in our adventure, we have dealt exclusively with ordering games that have a
property called 1:1 correspondence. Eight clowns and eight stages. Seven donkeys and seven
lanes. Six contestants and six chairs. Everything fits nicely. However, the LSAT is not always so
nice. Many ordering games do not have 1:1 correspondence between the number of players
and the number of slots.
These games commonly show
up in two forms. Here is an
example of the first:
The Rodriguez parents are out of town from Monday
night through Friday night. Each night, one of the three
older siblings—Carla, Debra, or Ephram—must stay
home to watch their newborn sister.
In this game, there are three players (the siblings) that must fill the five slots (Monday
through Friday). This game has fewer players than slots.
An underbooked ordering game has fewer players than slots.
And here is an example of the second:
Nine students—A, B, C, D, E, F, G, H, and I—each
must give an oral report in history class on a historical
figure of their choosing over a span of six weeks, week
1 through week 6.
This one goes the other way.
Now, there are actually nine
players (students) and only six
slots (weeks). This game has
more players than slots.
An overbooked ordering game has more players than slots.
Underbooked and overbooked ordering games add a level of complexity since not everything
fits very nicely. However, we will show you how to handle this fresh new nonsense. As we move
into more complex games, there will be more factors to juggle. The previous games have been
solely concerned with the question of who goes where, but these new games will introduce
questions related to how many times players can appear or how many players can be assigned
to each slot.
blueprintprep.com/lsat
Under/Overbooked Ordering /
91
Underbooked Ordering
As always, your first task is to identify what type of game you are staring at. As of this moment,
we are adding a second step to this process.
Step 1: Does the game involve ordering? Grouping? Both?
Step 2: What is the ratio of players to slots? 1:1? Underbooked? Overbooked?
Here’s how it works: You will read a very familiar-sounding ordering game, but then
you will notice a twist. There are too many players. There aren’t enough players. It is
important to notice this hurdle, because then it is time to jump into action.1
Always read the introduction slowly. Missing a
feature of a game will spell disaster down the road.
BP Minotaur:
When you recognize that you are grappling with an underbooked ordering game, there are
normally two ways the game can be structured. Here is an example of the first:
Each of five people—Alfonso, Babar, Calvin,
Demar, and Ernie—graduated from high school in
a different one of seven years: 1992 through 1998.
This game is underbooked because you
have to order five students in seven years.
Each person will only fill one slot, so this
game will end with some empty slots. For
instance, it might be the case that no one
graduated in 1996.
More frequently, however, you will be given a game that is more similar to the one on the
previous page. Remember the Rodriguez family?
The Rodriguez parents are out of town from Monday
night through Friday night. Each night, one of the
three older siblings—Carla, Debra, or Ephram—must
stay home to watch their newborn sister.
In this game, you can’t have any empty
slots. The newborn would break into the
liquor cabinet, turn off Safe Search, and
never be the same. Thus, some of the
siblings must watch the newborn on more
than one night.
In underbooked ordering games, either (1) some slots will remain unoccupied, or
(2) some players will fill multiple slots.
1
92
This surprise and change in direction is akin to real life situations: (1) You are speeding along the freeway when
you see blinking lights and the cone zone up ahead; or (2) You are having a nice night with your partner when
they hit you with the “so, we need to talk about us”. No time for indecision; you must react.
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New Rules
Most of the rules in underbooked ordering games will be identical to those we have already
covered. You will continue to be confronted with basic ordering principles, blocks, divisions,
arches, and Megatrons (that last one isn’t real, but it would be awesome if it were).
There are, however, a few additions. There can now either be (1) empty spots or (2) players that
go more than once, and this allows them to offer some additional types of rules.
Let’s take a look at the new rules.
If you are working through a game in which some
slots are going to be unoccupied, the new rules will
relate to which slots can or cannot remain empty.
Let’s use our old high school graduation game as
an example.
These will be incredibly
important rules, and they should
be represented directly into
your setup. Here is the correct
representation:
No one graduated in 1995.
One of the students graduated in 1993.
x
92
93
94
95
96
97
98
If you have a game in which players can fill more than one slot, the rules can be more varied (and
complicated). You will generally find restrictions on the number of slots one or more players can
fill.
Check out some rules:
Each of the older siblings must watch the newborn at
least once.
Ephram must watch the newborn on more nights than
Carla.
min = 1
e > c
Sometimes you have to do a little bit of
math to figure out how many times each player can appear.
Godly Guidance:
blueprintprep.com/lsat
Under/Overbooked Ordering /
93
It’s go time, team. Underbooked and overbooked ordering games can be tricky, so it’s very
important to get some practice. Go forth and practice 3-4 of each type. Then let’s move on to
the next type of ordering game in the following chapter.
Go get ‘em!
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12/tieredORDERING
What Is It?
In the first couple chapters of ordering games, we have developed a deep relationship with
games that have two variable sets: parcels and delivery times; dresses and hangers; saxophonists
and auditions. We are now departing from that comfort zone.
Many ordering games will present you with more than two variable sets.
Some games feature up to four or five!
When you have to order more than two variable sets, the best way to organize the information
is with different tiers in your setup. It’s crucial that you continue to identify and use the variable
set with an inherent order as the base of your setup. Here are the correct steps to build a good
tiered ordering setup:
1.
Always identify the basic process in the game. Watch out for the common
phrases that indicate an ordering game (consecutive, order, sequential).
2. Identify the variable set with an inherent order (days of the week, rankings,
time slots), and use that variable set as the base of your setup.
3. New step: Build a tier for each additional variable set.
Here’s an example, in real time:
During a span of five weekdays—
Monday through Friday—five
rooms in a house must be cleaned,
one room per day. The rooms in
question are the parlor, a restroom,
the saloon, a TV room, and the
unicorn stable. Five people—
Vivica, Wilma, Xena, Yavar, and
Zela—must each be assigned
to clean one of the rooms. The
following conditions govern the
cleaning assignments:
1. We’re tasked with making a cleaning schedule,
assigning rooms and people to days.
2. The days of the week have an inherent order and
should be used as the base.
3. There should be two tiers for the other two
variable sets: rooms and people.
p:
r:
1
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2
3
4
5
Tiered Ordering /
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The goal for your setup is to create something in which you
can easily visualize any rule they throw in your direction. Thus, it’s very
important to build the appropriate number of tiers.
BP Minotaur:
When you are doing games, you never want to force yourself to remember things. Ever been to
the grocery store without a list? You probably returned with cereal but no milk, or meat but no
bread. Sucks. Trust us, you have enough to think about when you are taking the LSAT. Make
sure to nicely organize all of the information by creating tiers.
The setups for tiered ordering games will all look very similar. However, these games are
introduced in a couple of different ways. Let’s take a look.
Different Categories
There are ordering games in which the players belong to different categories (boys and girls; 7th
graders and 8th graders; right-handed or left-handed; boxers or briefs). When this occurs, it is
best to form a tiered ordering setup. There should be one tier for the player and another tier for
the category to which that player belongs. Consider the following game:
At a pet store, exactly four puppies- Bubba,
Chucky, Ducky, and Eddie—and three kittensMindy, Nina, and Oprah—are displayed in seven
consecutive cages along the display wall. Each
cage holds only one animal.
This game sounds pretty similar to a 1:1
ordering game. However, the players
are split into two categories: puppies
and kittens. Our setup needs to be
able to incorporate this information.
C’mon, get good. We already know which ones are dogs
and which ones are cats, we don’t need a second tier.
Bro Tip:
Broseidon, that’s a common reaction by students, and many set this game up with
only one tier. However, imagine you were given the following rules in this game:
A puppy is displayed in cage 5.
A kitten must be displayed in either cage 2 or cage 6,
but not both.
Bubba is displayed in between two kittens.
These rules would be very hard to visualize
and work into the setup if we did not have
tiers. It’s much easier to visualize these
rules if you have a second tier to track the
categories (puppies and kittens).
When the players in an ordering game belong to different categories, always
form a second tier for the categories. Always.
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Here’s the appropriate
setup for this game. The
animal’s name is placed
in the bottom tier and
whether the animal is a
puppy or kitten occupies
the top tier. Very cute.
p/k:
n:
1
3
2
4
5
6
7
On to the next version of tiered ordering.
Players with Characteristics
A slightly different type of game will ask you to order a set of players and also track a certain
characteristic of each one. In these games, it is best to have a tier for the player (children,
for example) and each characteristic that is introduced (tall or short; green eyes or blue eyes;
favorite brand of cereal). Here is an example:
Over the span of one month, Juliette reads seven
novels: Abigail, Beauty and the Beefcake, Chesapeake
Children, Dances with Dunces, Edward Scissorfeet,
Frank-’n’-stein, and George and the Grasslands.
Some of these novels are romances and some are
action-adventures. Juliette reads the seven novels
consecutively.
r/a:
n:
1
2
3
4
5
6
7
The basic process in this
game is to order the books
according to when Juliette
reads them. However, we
also have to track whether
each book is a romance
(probably Edward
Scissorfeet) or an actionadventure (most likely
Dances with Dunces). We
need two tiers, and our
setup should resemble the
beautiful setup you see to
the left.
But wait, there’s more. This setup can actually grow larger. Check this one out:
The top five contestants in a talent competition are V,
W, X, Y, and Z. Each contestant performed one of the
following during the talent portion of the show: baton
twirling, gymnastics, singing, dancing, or magic. During
the competition, each contestant wore one of the following
colors: red, blue, silver, gold, and violet. The final ranking
of the contestants must meet the following conditions:
blueprintprep.com/lsat
Everyone loves a talent
competition. And the winner is...
our tiered setup. On this one, we
have to determine the ranking of
the contestants. However, we also
have to track the talent each one
performs and the color of their
outfit.
Tiered Ordering /
97
For this game, we need a setup with
three tiers: one for the contestant,
one for his or her impressive talent,
and one for the color of his or her
outfit.
o:
t:
c:
They could add another characteristic
(such as hair color), but that can be
easily incorporated as well.
1
2
3
4
5
Independent Variable Sets
The third and final version of tiered ordering occurs when you are presented with two (or more)
independent variable sets that must be ordered. The setup will look identical to the previous
games, but each tier is now used for a different variable set.
As always, here’s an example:
In each of the next six weeks, the students in a college
philosophy course will be assigned to read a work by
one of three ancient philosophers—Socrates, Plato,
and Aristotle—and a work by one of five modern
philosophers—Hobbes, Descartes, Locke, Kant, and Frege.
a:
In this game, the students
have to read two works each
week. Thus, we have to order
the assigned works from the
ancient philosophers and
the assigned works from the
modern philosophers (which are
independent variable sets). This
means you should build a tier
for each one.
m:
1
2
3
4
5
6
That’s a summary of the common features found in tiered ordering games. The first crucial step
in each game is to build the correct setup. With that in mind, we have prepared a beautiful drill
to help you hone your skills at setting up tiered ordering games.
Good luck...
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Tiered Ordering Setup Drill
For each of the following situations, read over the introduction and build the correct setup.
Remember, your setup should allow you to easily organize all of the variable sets.
1.
An editor of a magazine reviews six articles
consecutively. Each of the articles is either a news
story or an opinion piece.
2.
3.
Lily is sick and stays home from school on Tuesday.
She watches six television shows during the course of
the day, each one starting after the last one finishes.
Each show is either on NBC, CBS, or ABC. Also,
each show is either a sitcom or a drama.
4.
5.
A television talk show airs five shows during a certain
week, from Monday through Friday. On each show,
one of five activists is interviewed and the host gives a
final thought on one of five topics.
There are five body builders who compete in the Mister
Universe competition. The competitors are each ranked
on three different criteria: biceps, triceps, and oil
application. There are no ties in any category.
Mistress Laser reads the fortune of six troubled souls
over the span of two days. She has three consecutive
appointments on the first day and three consecutive
appointments on the second day. Each client
receives either a positive or negative fortune from the
powerful Mistress Laser.
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Tiered Ordering /
99
does yours Look Like This?
1
n/o:
a:
1
2
2
3
4
5
6
On each day, there is both an
activist and a captivating final
thought. We need to build a setup
with two tiers.
ft:
tm:
m
3
t
w
r
f
s/d:
n:
s:
1
4
2
3
4
5
b:
t:
o:
1
5
2
3
4
5
p/n:
a:
1
100
In this one, the editor reviews six
articles consecutively. The second
tier is built to track whether each
article is a news story or an opinion
piece.
/ Chapter 12
2
6
Poor Lily is sick. We have to
order the shows, keep track of the
network on which they air, and
figure out whether each show is
a sitcom or a drama. That means
three tiers. Feel better, Lily.
In this one, we get to deal with
oiled up, steroid-filled bodybuilders.
This one is different because the
same variable set (bodybuilders)
is being ordered three times. So
we need a tier for each of the three
criteria, and the competitors will be
placed into their appropriate rank
on each tier.
Even though the appointments are
separated into only two days, there
is a sequence of six appointments.
The second tier is for whether each
fortune is positive or negative.
blueprintprep.com/lsat
New Rules?
No. Well, not really. Most of the rules on tiered ordering games are identical to those already
covered (dashes, blocks, divisions, arches, options). However, mixed in with the usual suspects
will be some rules that might appear to be new. These are really just slight alterations to our
good old rules. For instance, you might get some intriguing new blocks due to the increased
size of our setup.
Suppose we were doing an ordering game with two
tiers, and we are confronted with this rule. It gives
us a concrete spatial relationship, so we symbolize
it with a block.
Luke must sit in between two girls.
The goal is to create
a block that looks
exactly as it will
when inserted into
your setup. Here,
you would have Luke
flanked by a girl on
both sides (lucky
guy).
g
_
l
g
b/g:
s:
1
2
3
4
5
When you represent these “new” blocks in a tiered ordering game, you might have flashbacks to
a certain video game called Tetris. Once again, your childhood experiences pay off big time in
games.1
Final Pre-Game Comments
As you have probably noticed, the setups for tiered ordering games can be pretty intimidating.
You will commonly have 10, 12, or more slots in your setup. On less complex games, working
through a number of hypotheticals can be an effective way to attack a game. But that’s a
dangerous approach on tiered ordering games. Drawing hypotheticals with 12 slots could easily
take you deep into your golden years.
This means that it is very important to search out deductions. We know we harp on deductions
in all types of games, but they are even more crucial on tiered ordering games. There will always
be big deductions to simplify these games. Yes, always. So make sure to spend a little extra
time breaking down the rules and looking for deductions.
1
The piece shown on this page was unequivocally one of the best pieces in Tetris, only rivaled by the highscoring long and straight piece. And the award for most annoying piece goes to the little guys, the ones where
you could never tell whether the piece was pointing right or left. Still brings back bad memories.
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101
Stop! Don’t even think about moving on to the next chapter until you get some practice. It’s time
to go fight it out with some tiered ordering games. In addition, this is the final type of ordering
game. So it wouldn’t be a bad idea to do some more mixed practice on all types of ordering
games. Make sure you feel very comfortable before moving on because a lot changes in the next
chapter...
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13/helloGROUPING
Part Deux
Welcome to the second act, also known as the world of grouping games. Just when you were
getting comfortable with ordering games, we go and switch it up on you. Remember, the basic
Blueprint strategy relies on classifying games according to two basic processes: ordering and
grouping.
Grouping games are neither more challenging nor less
challenging as a whole than ordering games. Students are generally
split on which game type they find to be more difficult.
BP Minotaur:
Grouping games present an entirely new challenge. Ordering games are centrally concerned
with spatial relationships. Who goes in slot 5? How early can the horseshoe crab appear? Can
Baz and Wayne be next to each other? Your mind has been filled with thoughts about the
relative positions of the players in a game for some time now. As of this chapter, all of those
concerns fade into the background (they will be back later). Grouping games challenge you
to assign players to different teams. The important questions will now center around whether
players can or cannot be selected together.
Can Charles be assigned to the green team?
Which ingredients can’t be included in the same recipe?
If Pengpeng is in the ceramics class, can Hrishi be in the painting class?
How many squirrels can be selected?
In ordering games, your job was to line things up. Now, your focus is on making teams.
Our strategy for grouping games will be very similar to ordering games. First, we will
learn to represent and interpret all of the rules. Then we will work through the different
permutations of grouping games. And our focus the whole time will be on spotting
common and powerful deductions.
Grouping games are nearly as common as ordering
games, and you can bet you will see at least one on your LSAT.
Godly Guidance:
blueprintprep.com/lsat
Hello Grouping /
103
Picking Teams
Every grouping game involves selecting players for a group or assigning players to different
groups. You might be selecting friends to invite to a party, or fish for an aquarium. You might be
picking squads for a cheerleading competition, or assigning plumbers to different work teams.
But the basic process remains the same: grouping.
Each of the following is an example of a grouping game:
Each of two boats, boat 1 and boat 2, will be assigned exactly
four people. Exactly eight people, three adults—F, G, and H—and
five children—V, W, X, Y, and Z—must be assigned to the boats
according to the following conditions:
A panel of five scientists will be formed. The panelists will
be selected from among three botanists—F, G, and H—three
chemists—K, L, and M—and three zoologists—P, Q, and R.
Selection is governed by the following conditions:
Each of five students—Hubert, Lori, Paul, Regina, and Sharon—
will visit exactly one of three cities—Montreal, Toronto, or
Vancouver—for the month of March, according to the following
conditions:
Five children—F, G, H, J, and K—and four adults—Q, R S, and
T—are planning a canoeing trip. The canoeists will be divided
into three groups—groups 1, 2, and 3—of three canoeists each,
according to the following conditions:
To prepare for fieldwork, exactly four different researchers—a
geologist, a historian, a linguist, and a paleontologist—will learn
at least one and at most three of four languages—Rundi, Swahili,
Tigrinya, and Yoruba. They must learn the languages according to
the following specifications:
Note the wording that introduces grouping games.
Rather than referring to “consecutive” or “adjacent” positions,
these games “assign” or “divide” the players.
BP Minotaur:
Just like ordering games, the actual subject matter of grouping games doesn’t matter at all.1
Now that you know what a grouping game will sound like, it’s time to talk strategy.
1
104
No need to book a trip to Canada, buy a canoe, or find a Yoruban dictionary. None of that will help you much
on the LSAT (or possibly at all).
/ Chapter 13
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The Setup
Building a consistent setup is a key step in approaching any game. If you build a different
setup for each game, it will be hard to recognize their repetitive nature. In every grouping
game, you will have a set of players (students, chairs, toys, power tools) that is being assigned
to groups (classes, rooms, cabinets, hardware stores). There could be one group, two groups,
three groups, or more. However, there will always be one variable set that is being assigned to
another.
The groups should always form the base of your setup. Arrange the groups
vertically and then insert players into the groups.
Consider the following game:
Five children—F, G, H, J, and K—and four adults—Q, R S, and
T—are planning a canoeing trip. The canoeists will be divided
into three groups—groups 1, 2, and 3—of three canoeists each,
according to the following conditions:
1:
2:
3:
In this game, it’s time
for an amazing canoe
trip! (Excitement greatly
exaggerated.) There are a total
of nine people (five children and
four adults). These lovely folks
are being assigned to three
different groups. The groups (1,
2, and 3) should form the base
of your setup. An appropriate
setup for this game would look
very similar to the one drawn
to the left. Now, it will be easy
to visualize which people are
together and how many people
are in each group.
Don’t overlook the setup phase of any game. When you have the correct setup, visualizing the
game will be easy, and deductions will come early and often. A bad setup can doom you to a
painful section and LSAT mediocrity.
Students commonly try to build a grid to organize grouping
games. Grids have numerous flaws and should always be avoided. Attacking
a grouping game with a grid setup is like going to war with a squirt gun.
Godly Guidance:
There are some elements that are important to note in grouping games. When you first
recognize a grouping game, noticing some salient features will help you determine your strategy.
Get ready to discuss the three big ones.
blueprintprep.com/lsat
Hello Grouping /
105
To investigate the subtleties of grouping games, we will use a set of eight students. Let’s call
them Alf, Babak, Chuckford, Delta, Ebenezer, Farrah, Gary, and Harry (in proper alphabetical
order). That’s quite a crew.
In each grouping game, your basic approach will be informed by the answer to each of the
following three questions. These features will also foreshadow the types of deductions you are
likely to uncover.
One Group or Multiple Groups?
The first distinction that must be made is based on the number of groups being formed. This
distinction can drastically change how you build your setup and how the rules in a game
function.
In some games, you will only be
selecting one group. Certain
players will be chosen and others
will be left behind.
Eight students are trying out for a high school softball team.
There are exactly five spots available on the team, so a coach
must select five of the eight students to fill the roster spots.
In this game, the task is to select five of the eight students. There is only one group being
selected: the students that make the softball team. Many grouping games will ask you to
select some members of a larger group. You might have to select some friends to be part of a
wedding, or some types of cookies for a cookie jar, or some actors to be on stage during a play,
but the common feature is that you are just selecting one group.
At Blueprint, we call these In and Out grouping games. The name is designed to remind you
of the basic task in the game. Some players are being selected and others aren’t. The rules
and deductions will focus on the players that are selected, but it’s also important to track
those that are not selected.
To track all of the players, we will
build a setup with two groups: an
In group (for the players that are
selected) and an Out group (for the
players that don’t make the cut).
Our setup for the game above
would look like this:
in:
out:
The majority of questions in a game like this one will
focus on the players that are selected. But important deductions
will arise from knowing who isn’t selected.
BP Minotaur:
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As you can imagine, the rules
for In and Out games will place
restrictions on which players
can, must, or cannot be selected
together. Here are some rules you
should expect to see:
Chuckford and Ebenezer cannot both make the team.
If Farrah makes the team, then Gary also makes the
team.
In other grouping games, you will be challenged to separate players into multiple groups. Red
team or blue team? Good or evil? Tall, grande, or venti? In the previous game, only some of
the players made the team. In these games, everyone makes a team - your job is to figure out
which one.
Here’s an example. In this game, the
students are being assigned to three
distinct groups (team X, team Y, and
team Z). You will run into games that
include two, three, four, or even more
groups.
Eight students are separated into three different teams
to compete in a trivia challenge. The teams will be
named team X, team Y, and team Z. Each student must
be assigned to one of the teams, and each team must be
assigned at least two students.
These are called multiple-group grouping games.
The first big change is your setup. Rather
than having an In group and an Out group,
your setup now must reflect the different
groups. And just because we like to
remind you about things over and over
and over again, always use the groups as
the base of your setup.
x:
y:
z:
The rules in a game like this will also be slightly different. Rather than principles about which
players can and cannot be selected, the rules will focus on the players that can, must, or cannot
be assigned to each team.
Some rules will be general
principles that are applicable to
every group, and other rules will
focus on just one of the groups.
Here are a couple of examples:
If Alf is assigned to team Z, then Babak must be
assigned to team Y.
Ebenezer and Harry cannot be assigned to the same
team.
The distinction between In and Out grouping
games and those with multiple groups is so fundamental that we
will cover these games in separate chapters.
BP Minotaur:
blueprintprep.com/lsat
Hello Grouping /
107
Stable or Unstable Groups?
In all grouping games, it’s important to watch for restrictions placed on the sizes of the groups.
Some games will define exactly how many players are in each group, and other games will
place little or no restrictions on the sizes of the groups. To put it simply, sometimes you will
know that the red team has four members, and other times you won’t know how many members
it has.
Here is an example taken from the
high pressure world of competitive
spelling.1 In this game, it is
established that each group has
four players.
Two four-person teams, the Polygons and the
Quadrilaterals, will be selected for a spelling bee. The
teams will be selected from a group of eight students.
Each student will be assigned to only one team.
A game in which we know the exact size of each group is called a stable grouping game. The
sizes of the groups remain stable throughout the game and do not fluctuate. With all of the
moving pieces in games, it’s nice to know that at least one thing isn’t going to change.
Your setup should always reflect
any information that you are given
about the groups. In this one, we
can insert four slots for each of the
two teams. Here is an effective
setup for this game:
p:
q:
Groups can be the same size or different sizes, but you
can reflect either in your setup. In a stable grouping game, important
deductions will occur when you run out of spots in one of the groups.
Godly Guidance:
A stable grouping game specifies how many players are in each group.
There will, of course, be other grouping games in which you will not be furnished with this
information. Some games will only put partial restrictions (at least two, at most four) on the
sizes of the groups. Other, even more vague games will place no restrictions on the group
sizes at all. This doesn’t mean the game is more difficult. We just need to use a slightly different
approach. Check out the example on the next page.
1
108
If you haven’t had the pleasure of watching the national spelling bee on ESPN8, “The Ocho”, we recommend it.
/ Chapter 13
blueprintprep.com/lsat
A chef is creating a new main dish for a special
dinner party. She must include some of the following
eight ingredients in her new dish.
in:
out:
First, notice that this is an In and Out
grouping game. A chef must select
some ingredients and not others. It is
not clear, however, how many ingredients
are included. There could be just one
ingredient (a relatively unimpressive dish),
three ingredients, or possibly all eight
ingredients. Any and all restrictions should
be represented in your setup. In this case,
however, there’s not much to work with.
All we know is that there must be at least
one ingredient in the In group.
But you know that not all of the ingredients are in the dish,
so you can toooootally put some slots in the Out group, too.
Bro Tip:
Actually, that’s not the case. The setup to this game states that “some” of the ingredients
are included in the dish. The chef might decide to just throw all of the ingredients
together and see what happens.2 The rules in this game will likely rule out that possibility
(by stating, for example, that two ingredients cannot both be included), but there are
grouping games in which some groups can be empty.
This is called an unstable grouping game. This does not refer to your mindset while taking the
LSAT; rather, it refers to the fact that the group sizes can change during the game. There might
be four ingredients included in the dish on one question and six ingredients on the next. It’s
important to think about the range of possibilities for each group.
This game has almost no restrictions, but other games will place
partial restrictions on the sizes of the groups. For instance, the chef could use
“at least three” or “at most five” ingredients. Your setup should always adjust
to these restrictions by placing the correct number of slots in each group.
BP Minotaur:
An unstable grouping game does not specify exactly how many players are in each group.
Two questions down, one to go...
2
The word “some” can mean “all” on the LSAT. If you’re told that “some” of the people at a party drank mojitos
(not an example you are likely to deal with on the LSAT), it could be true that everyone enjoyed the minty goodness. This comes up much more often in Logical Reasoning, but it’s worth noting here.
blueprintprep.com/lsat
Hello Grouping /
109
Categories or No Categories?
The last distinction which will prove to be important in grouping games relates to the actual
players in the game. In most games, you will be presented with a set of interchangeable players
that don’t come from different categories.
In this one, we see our familiar
eight students. This game has
four distinct groups, and each one
is assigned two players. There
is nothing that distinguishes one
player from the next (other than
their fascinating names). Thus, you
can just write out the variables.
Eight students­—Alf, Babak, Chuckford, Delta,
Ebenezer, Farrah, Gary, and Harry—will be assigned
to four different teams for the upcoming sack race. Each
team will be assigned two of the eight students and each
student will be assigned to only one team.
8s: a b c d e f g h
In other grouping games, the players will actually come from different categories. Males and
females. Tall and short. Spicy, tart, and sweet. Irish, German, and French. When this occurs, it is
important to note this early on because it adds a level of complexity to any game.
Here is an example of a game
in which the players come from
different categories. This is an In
and Out grouping game. It’s a little
unstable because you are selecting
either five or six of the eight
students. The new characteristic
is that the players come from
different categories (freshmen,
sophomores, and juniors). This
needs to be part of your setup
when you are symbolizing the
variable sets.
There are eight students campaigning for positions in
student government. Three of the students—Alf, Babak,
and Chuckford—are freshmen, three students—Delta,
Ebenezer, and Farrah—are sophomores, and two
students—Gary and Harry—are juniors. Either five or
six of the eight students will be elected.
3f: a b c
3s: d e f
2j: g h
When a game introduces different categories, you can expect different types of rules to pop up.
There will be the normal rules about players that can or cannot be selected together, but there
will also be restrictions about how many players can be selected from each category.
In this game, you will have to track
(1) which players are elected, and (2)
how many freshmen, sophomores, and
juniors are elected. Here are a few of the
different rules that you could encounter:
If Farrah is not elected, then Delta must be elected.
At least one student from each class must be elected.
There must be more sophomores elected than either
freshmen or juniors.
Next up is a drill to make sure you got it.
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blueprintprep.com/lsat
Grouping Game Drill
This drill is designed to reinforce the grouping distinctions we just covered. For each one of the
following games, circle (1) whether the game is selecting just one group or multiple groups, (2)
whether the group sizes are stable or unstable, and (3) whether the players come from different
categories or not. Then, use that information to build the appropriate setup.
1. A college student is packing for a semester
abroad. Her suitcase is filling up quickly and
she can fit no more than five of the following
seven items—camera, deodorant, fanny pack,
mascara, passport, toothbrush, and visor. Her
selection must accord with the following:
One Group
Stable
No Categories
Multiple Groups One Group
Unstable
Stable
Categories
No Categories
2. Seven employees of Stigmata Corp—Abigail,
Benji, Candace, Duane, Ernie, Fergie, and
Glinda—are each assigned to one new project.
One employee is assigned to the Mars project,
three are assigned to the Pluto project, and
three are assigned to the Venus project. The
following must obtain:
One Group
Stable
No Categories
3. Five boys—Javier, Kyle, Laird, Matt, and
Nin—and four girls—Ophelia, Paula, Robin,
and Sally—are divided according to their
reading abilities. Each person is classified as
remedial, intermediate, or advanced, according
to the following:
4. A circus act will include exactly five animals.
The animals must be chosen from among three
lions—F, G, and H, three tigers—J, K, and L,
and four bears—W, X, Y, and Z. The selection
must be consistent with the follow restrictions:
One Group
Multiple Groups Stable
Unstable
No Categories
Categories
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Multiple Groups
Unstable
Categories
Multiple Groups
Unstable
Categories
Hello Grouping /
111
Grouping Game Drill Answer Key
Here’s what your setups should look like, along with an explanation. If you missed anything,
make sure to look back and review the important features of each game.
1.
Pack the Fanny Pack?
•
•
•
7i: c d f m p t v
This is an In and Out grouping game. Our
student must pick some items to be packed and
must leave others behind (hopefully not the
deodorant).
The group sizes are unstable, although you should
put two slots in the Out group since you know
she can only take a maximum of five items.
There are no categories.
in:
out:
7e: a b c d e f g
2.
Planetary Alignment...
•
•
•
3.
m:
There are three separate groups in this one - Mars,
Pluto, and Venus.
The group sizes are stable, even though the
groups are different sizes.
There are no categories.
p:
v:
Center for Reading Good
•
•
•
4.
•
•
•
a:
This game also has three distinct groups
which are the three different reading levels.
The group sizes are completely undetermined,
so this game is unstable.
There are two different categories in this one males and females.
5m: j k l m n
4f: o p r s
Lions, Tigers, and Bears. Oh my!
3l: f g h
3t: j k l
4b: w x y z
This is an In and Out game - you are
selecting one set of animals for the act.
Exactly five animals are selected, so this
is a stable grouping game.
There are three different categories.
i:
r:
in:
out:
That wraps up our introduction to grouping games. This might seem to be a lot to think
about when you are attacking a game. That’s because it is. But these distinctions will become
automatic with some good practice. Speaking of good practice, let’s keep moving.
112
/ Chapter 13
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14/theBIGfour
Grouping Relationships
Before we actually attack grouping games, it’s important to check out the rules. In ordering
games, there were some common rules we kept seeing over and over again. The same will be
true in grouping games. So we have to make sure to understand (1) how to represent the rules
and (2) how to use them to spot deductions.
The rules in grouping games are even less original
than they were in ordering games. There are only so many ways
that you can say, two players can’t be on the same team,
Godly Guidance:
In ordering games, you will run into a conditional rule every now and then (if J is in spot
3, then K must be in spot 5). However, they are more of an afterthought to the blocks,
arches and options that make up most of the rules in for those games. In grouping
games, conditional rules play a much more prominent role. In fact, grouping games are
based entirely on rules that restrict which players can be selected or assigned together.
These restrictions are generally introduced with conditional rules.1
Here is a medley of rules you
might see in a grouping game.
These are all conditional rules.
Some games will present you
with five or six of these bad boys,
so it’s crucial to understand how
they work.
If A is selected, then B is also selected.
C and D cannot both be on team X.
E cannot be in the first class unless F is in the second class.
If G is uncovered at the site, then neither H nor J is
uncovered at the site.
Here’s the great news: Each of these rules (and all the others just like them) can be simplified. It
might seem that grouping games introduce a huge number of different relationships. But that’s
not the case. Not even close. In fact, every single conditional rule you encounter in a grouping
game can be broken down into one of four basic grouping relationships.
Four distinct grouping relationships dominate the rules in grouping games.
1
If you are already getting nervous at the mere mention of conditional rules, or if you start to feel nervous about
these rules at any time, go back and review the chapter on conditional statements (Chapter 9, Games Logic).
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The Big Four /
113
Now it’s time to take a look at the big four. Through years of teaching the LSAT, we at Blueprint
came to notice that teaching the big four grouping relationships works much better with an
extended story attached. So we are going under the sea for an ocean adventure! Bet you never
realized the secrets to LSAT success can be found through a story about the ocean, huh?
Warning: This story is definitely not based on any other stories about undersea creatures and
their ocean-crossing, son-rescuing adventures. Any similarities are entirely coincidental.
We need a few ocean creatures to tell our touching relationship story. Let’s start with a clownfish
and a royal tang.
Stage 1: Tag-Along
A number of grouping rules will establish that one player always follows another player. This is
appropriately called the tag-along phase of the relationship.
Time for our analogy. Here is where our ocean adventure begins. Our clownfish, who we’ll call Marvin, is not
a very adventure prone chap. However, a series of mishaps and a very unethical diving dentist have forced
Marvin to leave his comfy home. He encounters a Royal Tang, Rory, who knows where he needs to go. So Marvin follows Rory everywhere. If you see the royal tang, our clownfish fellow is sure to follow. Now, does that
mean that our royal tang follows our clownfish? Not so much. At least not yet.
Here’s the basic form of this rule in a grouping game: If one player is assigned to a certain
group, then another player must also be assigned to that group. We call this the tag along
phase to emphasize the fact that one player follows another, but it does not necessarily go both
ways. Here are examples of grouping rules that introduce this relationship:
If Rory performs at the concert, then Marvin must also
perform.
r [ m
M [ R
This rule would be part of an In and Out
grouping game. If Rory performs at the
concert, then Marvin must also perform.
But it could be true that Marvin performs
and Rory does not.2 Remember to always
write out the contrapositive. If Marvin
doesn’t perform, then neither does Rory.
Here is another example with new participants. This one would originate from a game with
multiple groups.
Even though this game about assigning
If Sita is assigned to the traffic committee, then
people to various committees isn’t the same
Bobby is also assigned to the traffic committee.
type of game as our In and Out undersea
example, they both have very similar-looking
tag-along rules.
2
114
Though we suspect Marvin isn’t as inclined to whale-song-performances as Rory is.
/ Chapter 14
blueprintprep.com/lsat
Once again, we want to diagram the conditional rule
and its contrapositive. If Sita is assigned to traffic, then
Bobby follows along. And if Bobby is not assigned to
traffic, then neither is Sita.
Bro Tip:
st [ b t
Bt [ S t
That sure looks like they have to be together, if you know
what I mean.
It sure does, Broseidon, but please stop high fiving yourself. That is a very common mistake,
and one that’s important to avoid. If Bobby is assigned to the traffic committee, we have no
information about Sita. She could be assigned to the traffic committee, but she could also be
assigned to another committee (like, say, the crime-fighting committee). With a simple tagalong relationship, don’t assume that the two players must be together.
It’s also possible for one person to be very popular and have two tag-alongs. But even when a
rule involves more than two players, it’s important to recognize the basic relationship.
If Samuel attends the review session, then both
Beatriz and Raj will also attend.
s [ b + r
B or R [ S
Looks like Samuel’s a darn good study
buddy. This rule includes three players,
but the principles are very similar to the
previous rules. If Samuel heads to the
review session, then both Beatriz and Raj
are sure to follow. If either Beatriz or Raj
doesn’t show up for the review session,
then Samuel must not be there.
Remember the flaws we discussed earlier.
If Beatriz or Raj attends, that doesn’t mean Samuel must attend.
Even if both Beatriz or Raj attend, Samuel might choose to skip it.
And if Samuel doesn’t attend, that doesn’t give us any information either.
BP Minotaur:
That wraps up the first stage of our relationship. Whether we’re talking about Marv, Bobby,
or Beatriz and Raj, we’ve got followers who we know to expect to tag-along if our leader is
attending. But where can our fishy friends go from here?
Stage 2: Must Be Together (Besties)
Grouping rules will often tell us that two players must always be assigned to the same group.
Sometimes, you can’t have one without the other.3
3
Please refrain from making any “awww” noises. Feelings have no place on the LSAT.
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The Big Four /
115
Woohoo! Here’s the happy part of our story. Rory realizes that when she’s with Marv, she’s able to do things
she’s never been able to do before! Her power level is now over 90004 - or at least, she can remember things!
Now they’re both deeply invested in the partnership, and they’re friends (maybe even best friends), so they’re
always together.
In grouping games, some rules will establish that two players must always be together. This
introduces a reciprocal relationship in which the players can never be separated. Here are
some examples of the besties relationship.
Rory visits the jellyfish if, but only if, Marvin also
visits the jellyfish.
r
\
m
As soon as you know that either Rory
or Marvin visits the jellyfish, it’s safe to
conclude they both do so. Let’s hope our
aquatic allies avoid those tentacles! This
relationship should be diagrammed with
the reciprocal (double-sided) arrow.
Just like every other conditional rule, this one has a
contrapositive. If either Rory or Marvin visits the jellyfish, the other
one must. Also, if either Rory or Marvin choose to avoid the jellies, then
the other one avoids them too. Here’s the simplest way to interpret a
rule like this one: You either get both of them, or you get neither one.
Godly Guidance:
`
This type of rule is much more common in games where players are being sorted into multiple
groups. Here comes an example.
Mater and Lightning attend the same monster truck
rally.
m
\
l
In this one, Mater and Lightning are part
of a friend group choosing which monster
truck rally to attend (always a tough
choice). Mater and Lightning likely got
matching racing stripes for the occasion,
so we have to keep them together. The
rule should again be symbolized with the
reciprocal arrow.
These BFFs will help you with deductions. You will
often find that there are not many groups that have two open spots.
Godly Guidance:
Did you ever think that games could be so wholesome? Make sure to never confuse the tagalong relationship with besties. Tag-along goes one way. Besties are reciprocal.
4
116
Little known fact: Undersea creatures love vintage memes.
/ Chapter 14
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That brings an end to our second grouping relationship. But here is where things go terribly
wrong. As with most relationships, there are some rocky patches—how could we enjoy the
resolution without the heroes’ darkest hour? And, well, let’s just say that a storm is brewing...
Stage 3: Cannot Be Together (Hate)
The third type of rule in grouping games will specify that two players cannot be selected or
assigned to a group together. You must keep them separate.
At this point, things start to fall apart. Between terse interactions with sharks, chats with whales, scary
anglerfish and other ocean dwellers, Marvin’s stress levels have never been higher.Marvin’s frustration turns
to outright anger, and our fishies split up. It gets a lot more serious when our unethical diver dives in again
and snatches up Rory. As Marvin continues his quest to find his family, Rory is now stuck in a tiny fish tank
miles away. Now Marvin and Rory are trapped far apart, in the “hate” phase.5
In grouping games, rules will very commonly give you combinations of players that cannot be
together. This type of rule will pop up when you are selecting one group or assigning players to
multiple groups. Below are a few examples.
The hate relationship is the most common one
in grouping games. So many bad feelings, such a shame.
BP Minotaur:
Marvin and Rory cannot both be in the fish tank.
m ] r
This would be an In and Out game set in
a tiny waiting room fish tank. Rory and
Marvin are not getting along at this point,
so they cannot both be in the tank.6 To
represent this relationship, we will negate
the reciprocal arrow used for the besties
relationship.
Now... here comes a little twist. This rule states that Rory and Marvin cannot be together, which
we correctly recognized as a hate relationship. However, grouping games can introduce the
same exact relationship in a couple of different ways. Let’s say they gave you this rule instead:
If Rory is in the fish tank, then Marvin is not.
r [ M
m [ R
r ] m
This rules tells us that if Rory is in, then
Marvin is out. The contrapositive tells you
if Marvin is in the tank, then Rory gets to
swim free. What does that mean? They
can’t be together, either in or out of the
fish tank. This rule is synonymous with the
first one, so diagram it the same way.
5
Never fear, hate phases in children’s movies don’t tend to last forever.
6
Not to mention, that tank is already pretty dang crowded. Don’t overstock your fish tanks!
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The Big Four /
117
With some practice, you will learn to spot
different versions of the same relationship automatically.
Godly Guidance:
Just like you can sometimes have more than one follower, you can also have more than
one hater—a fact many celebrities unfortunately know all too well. A breakup, contract
dispute, or flopped launch happens and haters abound. Ouch. Grouping games will
commonly express that one person must stay away from two others. Check it out:
If Kanye appears on stage, then neither Jay-Z nor
Drake appears on stage.
k [ J + D
j or d [ K
k ] j
k ] d
In the original diagram, if Kanye appears,
then Jay-Z does not appear and Drake
does not appear. The contrapositive tells
us that if either Jay-Z or Drake appears,
then Kanye won’t show his face on stage.
This complicated conditional rule can also
be simplified. In this situation, Kanye is
now “hated” by both Jay-Z and Drake.7
It will be much easier to deal with two
hate relationships than the original, ugly
conditional rule.
So far, all of the examples we’ve talked about would stem from games in which some players
were being selected and others were left behind (In and Out grouping). The hate relationship
also occurs frequently in games with multiple groups. Consider this rule from a game in which
players are assigned to different committees:
Ahmed and Sven cannot be assigned to the same
committee.
a ] s
It’s a different type of game, but this
is definitely the same kind of hate
relationship. Whether there are two, three,
or seven committees in this game, we’ve
given a relationship where members hate
each other, and we must keep them apart.
There are other permutations of the hate relationship that are more complex, but we will cover
those when we get into the specific game types. For now, just know that there’s going to be a
lot of hate flying around, and you have to be able to spot it.
It would seem that this is clearly the end of the road for Marvin and Rory. After that argument
and separation, what could possibly come next?
Well, this is where it gets really complicated... turns out Rory found the exact fish
Marvinwas looking for! Looks like time to team up again and look after the kid!
7
118
Note that real life is complicated. Logic games, in their own way, are blessedly simple.
/ Chapter 14
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Stage 4: At Least One (Caretaking)
We knew they’d get through it! Rory has found lost little Beemo and now Marvin, Rory, and
Beemo are a happy crew. How does this relate to grouping games? You see, Beemo is still a kid,
so someone needs to be around to watch him. Someone always has to be there in case more
dentists with nets and terrifying nieces go for a dive. The same relationship pops up in grouping
games. It will sometimes be asserted that at least one of two players must always be selected.
In the conclusion of our analogy, we’re left with a very happy ending. Beemo has been found, and Marvin and
Rory decide to take care of the little guy together. Beemo definitely needs someone to keep an eye on him, so
either Marvin or Rory must be with him at all times. Welcome to parenthood.
The caretaking/at least one relationship is almost always introduced indirectly. It is your job to
simplify the rules and get to the basic relationship, just like we did with the hate relationship.
If Marvin does not get invited to the club, then Rory
does get invited to the club.
M [ r
R [ m
m or v
This rule would be part of an In and
Out grouping game in which you must
determine which lucky fish get to join a
cool group.8 If Marvin doesn’t get invited
to the club, then Rory must. And, if Rory
does not get invited to the club, then
Marvin must. Thus, if either one of them
does not receive an invitation, then the
other one does. This rule can be simplified
to state that either Rory or Marvin must
always be invited to the club.
Remember that “or” statements are always inclusive.
Either Rory or Marvin must get invited, but it’s possible that they both do.
Godly Guidance:
In games that involve multiple groups, you can also be confronted with rules that introduce a
similar relationship. Check this one out, from a hypothetical game about a fashion show.
If Heidi does not wear green, then Nina must wear
green.
Hg [ ng
Ng [ hg
8
hg or ng
Nina has to rock some green if Heidi does
not. Also, if Nina does not wear green,
then Heidi must wear green. Note that the
structure of this rule is similar to the first
example. If one condition is not met, then
another condition must be. This rule can
be simplified to state that at least one of
Heidi and Nina must wear green.
Fish are Friends, Not Food Club, to be exact.
blueprintprep.com/lsat
The Big Four /
119
The caretaking phase of the relationship is less common than the others. However, make sure to
pay close attention when it pops up. Since this type of rule establishes that one of two options
must always be met, it will be important in nearly every question that follows.
It’s been quite a ride, but that concludes our modern day aquatic adventure. Best of luck to
Rory and Marv. We loved, we cried, we knew there would be an inevitable sequel. What more
could you ask for? Here is a quick overview of the big four relationships. This shows you the
possibilities that are allowed and those that are outlawed.
tag-along:
a [ b
besties:
a \ b
hate:
a ] b
caretaking:
a or b
a + b
a + B
A + b
A + B
















Believe it or not, these four basic relationships will be the basis for all grouping games. If
you understand these relationships, you will have a great foundation to help you conquer any
grouping game the LSAT throws at you. Remember, this is just an introduction. There are
numerous drills and games waiting for you in the following chapters.
Now that we have covered the basics of grouping games, it’s time to jump in. The next four
chapters will be dedicated to the four common types of grouping games:
1. In and Out Grouping
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/ Chapter 14
2. Two Groups
3. More Groups
4. Profiling
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15/INandOUT
What Is It?
In and Out grouping games will present you with a variety of challenges. You might have to
select which students get elected for student government, or which animals get to ride on
the ark, or which appliances are purchased. However, these games all have one defining
characteristic in common: They require you to select some members from a larger group.
Since you are only selecting members for one group, In and Out
games are the most basic form of grouping. However, basic does not entail easy.
BP Minotaur:
In and Out games only require the formation of one group, namely the players that are selected.
However, it’s also vital to track the players that are not selected. Thus, our setup will always
include a spot for both the players that are In and those that are Out.
Here is a quick example of how to build the appropriate setup for an In and Out game:
The vice president of Synergy Corporation reviews
seven different budget proposals. She will approve
exactly four of the seven proposals, in accordance with
the following restrictions:
in:
out:
In this game, your basic task is to
determine which of the budget
proposals are approved. So we are
dealing with an In and Out grouping
game. In the setup, you want to build an
In group for the four proposals that are
selected and an Out group for the three
that don’t make the cut.
Let’s review some of the other grouping
elements that we covered in the last two
chapters.
Are the group sizes stable or unstable?
It is very important to note whether an In and Out game is stable or unstable. When you read
the introduction to the game, make sure to notice any restrictions given. How many players
are selected?
blueprintprep.com/lsat
In and Out Grouping /
121
Some games will define exactly how many players are selected, other games will give you
loose restrictions, and some evil games will say next to nothing. Here are some examples:
A new scene for a television show is being filmed.
It will feature five of the following eight actors.
in:
This is a stable grouping game. The scene
must feature exactly five actors, and three
actors are not selected. This should be
reflected in your setup.1
out:
A new scene for a television show is being filmed. It
will feature some of the following eight actors.
This game is different because it’s not clear how many
actors are featured in the scene. It could be one, two, or
all eight at this point. This is an unstable grouping game.
All you get is one slot in the In group. (At least it’s not a
weird French film about an inanimate object.)
in:
out:
This distinction will help inform your approach.
With a stable game, you want to watch for situations that
would violate the group sizes. With an unstable game, it’s all
about the rules since the setup is so open.
Godly Guidance:
So now you know what to watch out for when you are building the setup for an In and Out
game. However, a large part of your success depends on your ability to interpret the rules.
Rules (Tag-Along/Must Be Together/Can’t Be Together/At Least One)
In and Out grouping games will present you with a combination of conditional rules. It will
boil down to your understanding of our big four grouping relationships. The subtle distinctions
between the rules will spell the difference between success and failure. That’s right, your
future relies on being able to distinguish whether Ashleigh and Brayden must always be
together, or whether you can have Brayden without Ashleigh. With that in mind, it’s time to
review.
1
122
Watch the distinction between “exactly” and “at least” on the LSAT. When a person claims that they had exactly
two drinks before driving, that is entirely different than if they claim to have had at least two drinks. Confusing
those two claims can ruin an entire game (or city block). Don’t confuse the two, and don’t drink and drive.
/ Chapter 15
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Here’s the plan: We are going to outline each of the relationships again and then insert a
quick quiz to make sure you have a deep understanding of each one. For this exercise, we are
throwing a party. It’s a pretty cool party, so some people are invited and others aren’t.
Stage 1: Tag-Along
In the first relationship, if one player is selected, then another player must be selected. Here
are some examples and the correct diagrams:
a [ b
If Alfonso is invited, then Buddha is also invited.
B [ A
c [ d
Cable is invited only if Dennis is invited.
D [ C
E [ F
If Edward is not invited, Foulad is not invited.
f [ e
Note: On the last example, you have to form the contrapositive to see that this rule introduces
the same relationship. The rule could have stated, “If Foulad is invited, then Edward is
invited,” and it would have been identical in meaning.
Note how important it is to diagram the rules correctly (“if”
versus “only if”). Make sure to review the correct way to diagram each claim.
BP Minotaur:
When a rule introduces the follower relationship, it’s important to recognize this doesn’t imply
the players must be together. One player brings along another, but the second player could be
selected alone.
Now it’s your turn. Diagram the following rule and then answer the questions that follow.
If George is invited to the party, then Hercules is
also invited.
1.
Can George be invited without
Hercules?
Yes
No
[
2. Can Hercules be invited without
George?
[
3. If George is not invited, does Hercules
get invited?
blueprintprep.com/lsat
Yes
Yes
No
No
Maybe
In and Out Grouping /
123
Here’s how the rule should be diagrammed:
Nope. George cannot be invited without Hercules. Anytime
you invite George, Hercules is always sure to follow.
2. Yep. You definitely could have Hercules without George. If
Hercules is invited, George may or may not be invited.
3. Maybe. If George isn’t invited, we don’t know anything
about our boy Hercules.
1.
g [ h
H [ G
Stage 2: Must Be Together
In and Out games are not big on besties. It is very rare for them to tell you that two players
must be selected together. Thus, be careful when concluding that two players must be selected
together if it isn’t explicitly stated.
The most common way for a besties relationship to be introduced in an In and Out
grouping game is with the phrase “if and only if,” or “if but only if.”
Here’s a quick example:
Ivan is invited to the party if and only if Jerome is
invited to the party.
i
\
j
This wording tells you that Ivan is invited
if Jerome is invited. And Ivan is invited
only if Jerome is invited. Therefore,
Jerome being invited is both sufficient
and necessary for Ivan to be invited. This
should be represented with a reciprocal
arrow.
There’s a basic and more helpful interpretation of this rule. Only two possibilities exist for these
players: Either (1) they are both selected or (2) neither one is selected. According to this rule,
Ivan and Jerome are both In, or they are both Out.
Stage 3: Can’t Be Together
The final two relationships are undoubtedly the most important to understand in these games.
First up is the hate relationship. This is the most common rule in all grouping games, including In
and Out games. It establishes that two players cannot both be selected.
Kendra and Leonardo cannot both be invited to
the party.
k ] l
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/ Chapter 15
This is the most basic version of the hate
relationship. They just flat out tell you
that Kendra and Leonardo cannot both be
invited. We heard it was an ugly breakup,
something to do with his secret past as a
Teenage Mutant Ninja Turtle.
blueprintprep.com/lsat
However, the same relationship can be introduced in a sneakier manner. Check this one:
If Kendra is invited, then Leonardo is not.
If Leonardo is invited, then Kendra is not.
So they can’t both be invited. Wait just a
second - that’s exactly the same as the last
rule! And since they mean the same thing,
you want to represent them in the same
exact way.
If Kendra is invited, then Leonardo is not invited.
k [ L
k ] l
l [ K
Bro Tip:
So, basically, one of them is invited and one is a loser
who doesn’t party?
Actually, no. This rule restricts both of the players from being selected at the same time, but
there’s no problem with selecting neither one. At least one of them must be Out, but both of
them also could be Out. According to this rule, three possibilities exist:
(1)
(2)
(3)
Kendra is invited and Leonardo is not.
Leonardo is invited and Kendra is not.
Neither Kendra nor Leonardo is invited.
Don’t forget that both of
them could be Out.
Visually, it’s easy to see this type of rule and think that two players cannot be together anywhere
(they can’t be In together and they can’t be Out together). But that would be a mistake.
Since an In and Out game really only involves selecting one group, and most (if not all) of the
questions will relate to the In group, our rules focus on the In group. You can’t select both
players, but it’s acceptable to select neither.
When dealing with an In and Out game, the hate relationship means that
both players cannot be In, but they both can certainly be Out.
Time for another drill. Same idea - diagram the rule and answer the questions.
1.
If Marco is invited, then Nala is not invited.
Can both Marco and Nala be invited?
Yes
No
2. Can neither Marco nor Nala be invited?
Yes
No
3. If Marco is not invited, is Nala invited?
Yes
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No
Maybe
In and Out Grouping /
125
We’re sure you aced it, but just in case:
Nope. This rule implies that Marco and Nala can never both
be invited.
2. Yep. There’s no problem at all with them both getting the
cold shoulder. They could both be Out.
3. Maybe. If Nala is Out, then Marco could be In or Out.
1.
m ] n
The feeling of hate commonly spreads in these games. It’s important to simplify rules so you can
identify the basic relationship. Rules will commonly assert that selecting one player means that
neither one of two other players can be selected.
Note the form of this rule - if one person
is selected, then someone else cannot be.
But now there are two haters. If Oprah
is invited, then Phil cannot be invited. In
addition, if Phil is invited, then Oprah is
not. So Oprah and Phil hate each other.
But wait, there’s more! If Oprah is invited,
then Quentin cannot be. Also, if Quentin
is invited, then Oprah is not. So Oprah
and Quentin also hate each other. After
all of that work, you can simplify the rule
to state that Oprah and Phil cannot both
be invited, and Oprah and Quentin cannot
both be invited.
If Oprah is invited, then neither Phil nor Quentin is
invited.
o [ P + Q
p or q [ O
o ] p
o ] q
Once you split this rule into two separate hate relationships, they function exactly the same as
any other hate relationship. Remember, they both cannot be selected, but the two participants
(Oprah and Quentin, for example) can both be Out.
And yet another drill...
If Suzette is invited, then neither T-Bone nor
Unicorn is invited.
1.
Can Suzette and Unicorn be invited?
Yes
No
2. Can all three of them not be invited?
Yes
No
3. Can T-Bone and Unicorn both be
invited?
Yes
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No
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One more time:
Nope. Suzette and Unicorn cannot both be invited. For the
record, Suzette and T-Bone also cannot both be invited.
2. Yep. The rule only prevents people from being invited
together. Inviting no one is an easy way to avoid problems.
3. Yep. T-Bone and Unicorn can both be invited as long as
Suzette is not. This rule doesn’t give you any relationship
between T-Bone and Unicorn.
1.
s ] t
s ] u
Stage 4: At Least One
The last relationship is another tricky one, and it must be simplified. Rules will commonly claim if
one player is not selected, then another player must be. There’s a much easier way to interpret
these rules: At least one of the two players must be selected.
If Viola is not invited, then Wilbert is invited.
V [ w
W [ v
Bro Tip:
v or w
If Viola is not invited, then Wilbert is. If
Wilbert is not invited, then Viola is. In
other words, if either one of them is Out,
the other one must be In. There is no
chance of getting by without either Viola
or Wilbert. So we simplify this rule to
state that either Viola or Wilbert must
be invited.
I get it - so one of them is In and the other is Out.
No, no, and no. You have to avoid that mistake. The At Least One relationship asserts that at
least one of two players must be selected. But it’s totally acceptable for both of them to be
selected. Just like the hate relationship, there are three possibilities for this rule:
(1)
(2)
(3)
Viola is not invited and Wilbert is invited.
Wilbert is not invited and Viola is invited.
Both Viola and Wilbert are invited.
“Or” always allows
for both.
When you deal with one of these rules, picture the words “or both” at the end.
When dealing with an In and Out game, the baby relationship means that at least one
of the players must be selected, and it’s acceptable for both to be selected.
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In and Out Grouping /
127
One last drill for you...
1.
Can Xan be invited without Yolanda?
Yes
If Xan is not invited, then Yolanda is invited.
No
2. Can both Xan and Yolanda be invited?
Yes
No
3. If Yolanda is invited, is Xan invited?
Yes
No
Maybe
As you’re getting started, you can write each
rule out and then simplify it. However, as you progress towards
pantheon status, you will want to immediately simplify each rule.
Godly Guidance:
And the winners are:
Yep. At least one of them must be invited, but Xan could be
invited without Yolanda, and vice versa.
2. Yep. At least one must be invited, but both could be.
3. Maybe. As soon as Yolanda is invited, then the rule is
satisfied. Xan could then go either way.
1.
x or y
We have one last hint with the caretaker relationship. Since this rule establishes that at least one
of two players must always be selected, it’s generally helpful to insert this into your setup. You
don’t want to forget that one of these players always has to be part of the In group. Here’s how
this would work for the last rule:
If Xan is not invited, then Yolanda is invited.
in:
x or y
out:
x/y
As soon as you know that either Xan
or Yolanda must be selected, throw
an option into the In group. When
later questions ask for a complete and
accurate list of those people that are
invited, or for the minimum number
of people that must be invited, this
option is an easy way to remember this
important rule.
Alrighty, now you should have a basic understanding of the four relationships and how they
function with an In and Out grouping game. It’s time for a drill that will really challenge you.
Yep, it’s that thing staring at you from the other page. Get in there.
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In and Out rules Drill
This drill is designed to test your ability to understand and simplify conditional rules. Check
out the following game. Then, diagram each rule (and its contrapositive). Whenever possible
(almost always), try to simplify the rule into one of the big four grouping relationships.
When making dishes, a famous chef includes some of the
following ingredients in each dish—alfalfa sprouts, beets,
carrots, duck, eggs, feta cheese, garlic, horseradish, iceberg
lettuce, jicama, kalamata olives, lentils, mango, nutella,
oregano, parsley, and quail­—according to the following:
This is a classic In and Out
game - some ingredients are
included and others are not.
1.
If a dish includes jicama, then it also
includes oregano.
7.
If quail is in a recipe, then neither oregano
nor kalamata olives is included.
2.
Any dish that includes horseradish does not
include parsley.
8.
If garlic is not included in a recipe, then
beets must be included.
3.
Feta cheese is included in any recipe that
includes alfalfa sprouts.
9.
If a recipe does not include both horseradish
and iceberg lettuce, then it must include both
beets and carrots.
4.
Mango is included in a recipe if, but only if,
nutella is included.
10.
If parsley is included in a recipe, then lentils
cannot be included.
If garlic is in a recipe, then both duck and
eggs must be included.
11.
If alfalfa sprouts are not in a recipe, then feta
cheese must be included but garlic is not.
Beets are not included in a recipe if both
carrots and lentils are included.
12.
Nutella is included in every recipe that
mango is not.
5.
6.
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In and Out Grouping /
129
Answer Key
1.
j [ o
O [ J
5.
If jicama is included, then oregano
must be included. And if oregano is
not, then jicama cannot be included.
However, you could select oregano
without jicama. This is follower, not
love.
2.
h ] p
Garlic, duck, and eggs? Tasty. If garlic
is included, then both duck and eggs
must be in the recipe. Thus, if either
duck or eggs is not included, then
there will be no garlic.
6.
If horseradish is selected, then parsley
cannot be. If parsley is included,
then there is no horseradish. This is
the hate relationship. You can never
include both horseradish and parsley.
Remember, a recipe could include
neither ingredient.
3.
a [ f
F [ A
7.
q ] o
q ] k
This rule gives you a lot of hate. If
quail is in a recipe, then oregano is
out and kalamata olives are out. Thus,
if either one is included, then quail
cannot be included. This can be
simplified to two hate rules: quail and
oregano cannot both be selected; and
quail and kalamata olives cannot both
be selected.
m \ n
“If, but only if” introduces a reciprocal
relationship. Either both mango and
nutella are included in a recipe, or
neither one is included.
c & l [ B
b [ C or L
“If” introduces the sufficient condition,
even when it is buried in the end of
a rule. If both carrots and lentils are
included, then there are no beets. So
if beets are in a recipe, then the chef
cannot include both carrots and lentils
(at least one is left out).
The word “any” introduces a sufficient
condition. So alfalfa sprouts is
sufficient to guarantee feta cheese.
However, this does not mean that you
must select both. Feta cheese could
be in a recipe that lacks alfalfa sprouts.
4.
g [ d & e
D or E [ G
8.
g or b
If there is no garlic, you must have
beets; if there are no beets, then there
better be some garlic. This is the
caretaker phase of the relationship.
Either garlic or beets (or both) must
always be included.
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9.
H or I [ b & c
B or C [ h & i
This one is tough. Remember that “not
both” translates to an “or” statement,
but with both terms negated. If either
horseradish or iceberg lettuce is not
included, then both beets and carrots
must be included; and if either beets
or carrots are not included, then both
horseradish and iceberg lettuce must
be in a recipe. This rule could also
be simplified: Every recipe must have
either both beets and carrots or both
horseradish and iceberg lettuce (or
three of the ingredients, or even all
four).
10.
n or m
If mango is not included in a recipe,
then nutella must be included. And
if the chef chooses not to include
nutella in a recipe, then mango must be
included. This is the baby relationship
yet again. If either ingredient is not
included, then the other one must be.
Thus, either nutella or mango (or both)
must be included in every recipe.
Sweet. If that drill went well, it’s time to
move on. If you struggled with some of
those examples, make sure to go back and
examine Chapter 4 and the beginning of
this chapter.
p ] l
Back to hate. If parsley is included in a
recipe, then lentils cannot be included.
And if lentils are included, then parsley
must be left out. So no recipe can
include both parsley and lentils. You
could have parsley, or you could have
lentils, or you could have neither one,
but it’s impossible to have both.
11.
12.
So that takes care of individual rules.
However, from our study of ordering
games, you already know that the powerful
deductions come from combining rules.
Next up: Let’s see how these ugly
rules play together to form powerful
deductions.
A [ f & G
F or g [ a
This rule is pretty complex. If alfalfa
sprouts are not in a recipe, then feta
cheese must be included but garlic
is not. To form the contrapositive,
just flip the sufficient and necessary
conditions, negate all conditions, and
swap the “and” to an “or.” Thus, if feta
cheese is not in a recipe or if garlic is in
a recipe, then alfalfa sprouts must be in
the recipe.
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131
follow the arrows
When you are doing an In and Out grouping game, you will be given a number of conditional
rules. It’s very important to look for transitive conclusions.1 These deductions will save lots of
time and make the questions much easier. Let’s return to our raging party and check out a few
examples.
If Leon is invited, then Mathias is invited.
If Mathias is invited, then Nena is not invited.
l [ m [ N
n [ M [ L
l ] n
If Pattie is invited, then Santa is also invited.
Tania is not invited only if Pattie is invited.
T [ p [ s
S [ P [ t
s or t
Always diagram the original conditional
rule first. If Leon is invited, then Mathias
is invited. And if Mathias is invited, then
Nena is not. Thus, if Leon is invited,
then Nena is not. Also, if Nena is invited,
then Leon is not. Look at that, we just
discovered a hate relationship. Leon and
Nena can’t both be invited. As you move
through the game, you can immediately
eliminate any answer choice that has both
Leon and Nena on the invite list.
In this one, anytime that Pattie is invited,
Santa must be invited (must be an ugly
Christmas sweater party). Also, if Tania is
not invited, then Pattie must be invited. If
you put the rules together, you can see
that if Tania is not invited, then Santa must
be invited. And Tania is invited if Santa is
not. By gosh, we just found a baby. Either
Santa or Tania (or both) must always
be invited. If an answer choice includes
neither one, it’s out.
In the second example, you can see that the order of
the rules doesn’t matter. Just make sure to never flip around an arrow.
Godly Guidance:
On the next page, you will see a drill that’s designed to help you spot these helpful deductions.
1
132
We discussed the transitive property briefly at the end of Chapter 11. It might be a good idea to go back and
review. It’s also a good idea to use the term “transitive property” in front of anyone you want to impress.
/ Chapter 15
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in and out deduction drill
For each of the following games, use the introduction to build the correct setup. Work slowly
through the rules. Represent each rule correctly, and simplify whenever possible. Finally, try to
combine the rules to find those big-time deductions.
Game 1: Buff You Up
A bodybuilder does four of the following types
of exercises during one day’s workout—bench
press, crunches, dead lifts, jumping jacks, lunges,
push-ups, and squats. She chooses the exercises
according to the following:
If she doesn’t do lunges, then she does squats.
If she does push-ups, then she does bench press.
If she does bench press, then she does crunches.
If she does dead lifts, then she doesn’t do lunges.
1.
If she does dead lifts, what
other exercises must she do?
2. If she does push-ups, then what
exercises cannot be done?
Game 2: Splash of Color
An interior designer is selecting colors for the
interior of a house. He must choose from the
following colors: aqua, beige, chartreuse, devilish
red, eggplant, and fuschia. The selection of colors
must conform to the following:
If he chooses eggplant, then he does not choose
chartreuse.
If he chooses either fuschia or devilish red, then
he chooses eggplant.
If he does not choose aqua, then he does choose
beige.
He does not choose aqua unless he chooses
chartreuse.
1.
If he chooses fuschia, what
other colors must be chosen?
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2. If he chooses aqua, then what
colors cannot be chosen?
In and Out Grouping /
133
answer key
Game 1: Buff You Up
1. l or s
d [ L [ s
S [ l [ D
2. p [ b
B [ P
p [ b [ c
1.
Squats, Crunches
•
If she does dead lifts, then
she cannot do lunges.
If she does not do lunges,
she must do squats.
If she didn’t do crunches,
she could do neither
bench press nor push-ups
which would overfill our
Out group, so she must do
crunches.
•
•
C [ B [ P
3. b [ c
C [ B
in:
4. d ] l
l/s
2. Dead Lifts, Jumping Jacks
out:
•
•
If she does push-ups, she
must do bench press and
crunches.
The fourth exercise must
be lunges or squats, so
dead lifts and jumping
jacks cannot be included.
1.
Eggplant, Beige
•
If fuschia is chosen, then
so is eggplant.
If eggplant is chosen, then
chartreuse is not.
If there’s no chartreuse,
there’s no aqua.
No aqua? Say yes to beige.
Game 2: Splash of Color
1. e ] c
3. a or b
2. f or d [ e
4. C [ A
E [ F + D
a [ c
•
•
f or d [ e [ C [ A [ b
•
B [ a [ c [ E [ F + D
2. Eggplant, Fuschcia,
Devilish Red
•
•
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If aqua is chosen, then
chartreuse is chosen.
If chartreuse is chosen,
then eggplant, fuschia,
and devilish red are not.
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Wow - that’s a lot to cover. This is not only a new game type. This is the second big type of
game - grouping - as well. It would be smart to go back and review everything covered in the
past few chapters. Then it’s time to practice. Go yonder and make sure to practice some in and
out grouping games. We recommend working through at least 5-6 games at this point. Make
sure to focus on the common types of rules and simplifying those grouping relationships.
Once you wrap up, let’s keep moving!
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In and Out Grouping /
135
16/TWOgroups
this way or that way
From this point on, we are going to be attacking grouping games that include two or more
groups. Rather than selecting who makes the team as we did in the last chapter, now we
must deduce to which team players are assigned. This is one of the basic distinctions that we
introduced when we first discussed grouping games.
We are going to start off by discussing games that have two distinct groups. Turns out, they
are pretty similar to In and Out grouping games. Rather than forming an In group and an Out
group, now you might have a red team and a blue team, or classroom 1 and classroom 2, or gold
stars and silver stars. But many of the rules and deductions will function in a similar fashion.
Other games will assign players to three, four, or even
five groups, but such games will be covered in later chapters.
BP Minotaur:
Let’s walk through the best way to set these games up and approach the rules.
the setup
The setup for games with two distinct
groups is going to look nearly identical
to In and Out games. Make sure to
label the groups with the appropriate
group names. Here’s a quick example:
Stable or Unstable?
Just like we did in the last chapter, it’s
important to track whether these games are
stable or unstable. Both types are common.
Eight local parents will be assigned to two four-person
neighborhood watch committees—the nighthawks and
the watchbirds. Each parent is assigned to one of the
committees. The assignment must be consistent with the
following conditions:
n:
w:
The game above specifies the size of each group (four), so it’s stable. But a game could just tell
you that each committee has at least two members, or even give you no restrictions at all.
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the rules
It’s all about the big four, just like before. (That was not an intentional rhyming scheme.) Games
with two distinct groups continue to center around conditional rules. It’s crucial to simplify the
rules and understand the basic relationship between the players. When you do so, you will find
that the relationships are very similar to In and Out grouping games. You get a little following,
a little partnership, a little hate, maybe even a kid to watch now and then. However, there are
slight differences in how the rules function (due to the different nature of the game).
Before we look at the specific rules, there’s one principle to cover. When you are assigning
players to one of two groups, you can simplify a lot of rules. When there are only two
options, if you aren’t in one group, you must be in the other. Check out this example:
If Cleopatra is assigned to team 1, then Demetrius is
assigned to team 2.
c1 [ d2
Unhelpful contrapositive:
D2 [ C1
Simplified version:
d1 [ c 2
Assume you are doing a game in which
the players are assigned to team 1
or team 2. The original rule is easy
enough to diagram. The contrapositive
of that statement is, “If Demetrius is
not assigned to team 2, then Cleopatra
is not assigned to team 1.” But that
complicates the issue. If Demetrius
is not assigned to team 2, then he is
assigned to team 1. If Cleopatra is not
assigned to team 1, she is assigned to
team 2. Thus, the contrapositive can
be simplified to state, “If Demetrius is
assigned to team 1, then Cleopatra is
assigned to team 2.” Much better.
Simplifying the contrapositive doesn’t change anything
at all. You are writing the exact same relationship in a more helpful way.
Godly Guidance:
Let’s walk through the different relationships in a game with two groups. For these rules,
assume that you are doing a game with just two groups: team 1 and team 2.
Tag-Along
The tagging along continues in these games. If one player is assigned to a team, then someone
else follows along. Kinda creepy. Check out the example on the next page.
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Two Groups /
137
If Kilowatt is assigned to team 2, then Lynly is
assigned to team 2.
k2 [ l 2
l1 [ k 1
Bro Tip:
If Kilowatt is assigned to team 2, then
Lynly is assigned to team 2. So Lynly is
the follower. Also, if Lynly is assigned
to team 1 (not team 2), then Kilowatt
is assigned to team 1 (not team 2).
So Kilowatt also does some tagging
along. As always, stay away from the
conditional fallacies. What do we know
if Lynly is on team 2? Nada.
I get it, those two are partners, so they have to be together.
Fist bumps for everyone!
Nope. It can be tempting to draw that conclusion, but it’s important to avoid that
mistake. If Kilowatt is on team 2, then Lynly is on team 2. And if Lynly is on team 1, then
Kilowatt is on team 1. So there is a good chance that they will be together on some
questions, but Lynly could be on team 2 if Kilowatt is on team 1. It’s possible for them to
be apart (sad, but true).
Must Be Together
For all of you romantics out there, we are still going to see some affection and partnership.
Many rules will assert that two players must be assigned to the same team.
Zenas and Yavar are assigned to the same team.
z \ y
Now that’s a cute couple - Zenas and
Yavar. According to this rule, they
must be together, so they are besties.
They must both be assigned to team 1
or both be assigned to team 2.
Since there are only two options for these
players, this is a good place to search for deductions.
Godly Guidance:
Cannot Be Together
Then, it all goes south. A very common rule in these games will establish that two players
cannot be assigned to the same team. We’ve entered a world of hate.
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Jacqueline and Henry cannot be assigned to the
same team.
j ] h
Jacqueline and Henry can never be
assigned to the same team due to
their intense hatred for each other. We
represent this rule in a similar fashion to In
and Out grouping games.
When we were working through In and Out grouping
games, two players in a hate relationship couldn’t both be selected.
But it was acceptable for neither one to be selected. In a game
with multiple groups, this rule should be interpreted to mean that
the two players cannot be together in any group.
BP Minotaur:
That’s an important point. Even though the rules look identical, they work in a slightly different
fashion depending on what type of game you are doing.
Here’s the cool part. When you are doing a grouping game with two groups,
the hate relationship is pure gold. You have two groups, and now there are two
players that cannot be together. Rather than keeping this rule off to the side, it
should immediately be inserted into the setup as linked options.
<
1:
j/h
2:
h/j
If you have two groups and
they give you a hate relationship, make linked
options in your setup. This will make it much
easier to make further deductions.
Godly Guidance:
To recap, this rule asserts that two players cannot be together in any group. It’s best to visualize
this relationship by forming linked options in the two groups. There is, however, a more limited
version of the hate relationship. It’s an important one to simplify. Take a look.
If Gertrude is assigned to team 2, then Fonzi is
assigned to team 1.
g2 [ f1
f2 [ g1
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The first step is to make sure to simplify
the contrapositive. If Gertrude is on team
2, then Fonzi is on team 1. This also tells
us that if Fonzi is not on team 1 (or, more
simply, if he is on team 2), then Gertrude
is not on team 2 (she is on team 1). But
wait, you can even go a little farther...
Two Groups /
139
Bro Tip:
So they totally hate each other - like me and leg day.
Not exactly. It might appear that good old Gertrude and Fonzi can never be together,
but take a closer look at the rule. If Gertrude is on team 2, then Fonzi can’t be on
team 2. And if Fonzi is on team 2, then Gertrude is not on team 2. But what if they
were both assigned to team 1? Any problems with that? Nope.
This rule establishes that Gertrude and
Fonzi can’t both be assigned to team 2.
Either one of them could be on team 2
without the other, or they could both be
assigned to team 1. We can represent
this with a variation on the classic hate
relationship.
g2 [ f1
f2 [ g1
g2 ] f2
A complicated game could present you with a medley of
these rules. Staring at four or five rules coupled with contrapositives
can be overwhelming. Make sure to work through the rules slowly so you
can simplify each relationship to its most basic form.
BP Minotaur:
Now for some active learning. Rules such as the one above can make or break a game, so let’s
make sure you got it down. For this drill, continue to assume that everyone is assigned to either
team 1 or team 2.
Challenge: In the space provided, represent the rule and try to simplify the diagram.
When you are ready, attempt the questions that follow.
If Rusty is assigned to team 1, then Krusty is
assigned to team 2.
1.
If Krusty is assigned to team 1, which
team is Rusty assigned to?
1
2
2. Could both Rusty and Krusty be
assigned to team 1?
Yes
No
3. Could both Rusty and Krusty be
assigned to team 2?
Yes
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/ Chapter 16
No
blueprintprep.com/lsat
Here’s the proper diagram for this rule:
2. This one comes straight from the contrapositive.
If Krusty is on 1, Rusty is on 2.
2. Nope. The simplified version of this rule tells you
that it’s impossible for both Krusty and Rusty to be
assigned to team 1.
3. Yes. There’s no problem with both Rusty and Krusty
hanging out together on team 2.
1.
r1 [ k2
k1 [ r 2
r1 ] k1
Just one more relationship...
At Least One
The caretaker relationship will not show up in grouping games with two groups, so don’t worry
about watching over little responsibilities for now. These rules will return, however, in grouping
games with more than two groups.
You will still confront situations where at least one of two
players must be assigned to a team. For example, the rule above states
that Rusty and Krusty cannot both be assigned to team 1. That implies
that either Rusty or Krusty (or both) must be assigned to team 2.
BP Minotaur:
That concludes our introduction to grouping games with two groups. We have a crazy idea - go
try some! Go through the first couple games slowly and make sure you read slowly through the
setup and the rules. As you get more comfortable, you will begin to see the repeating rules and
deductions. Best of luck!
Of course, there’s no rule that says a grouping game can only have two groups. Guess what’s up
next?!?
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Two Groups /
141
17/MOREgroups
Lots of options
In the last chapter, you could hang out in one group, or you had to hang out in the other. But
that was all - there were only two options for each player. Now, our setup is going to grow as
we are presented with games including three, four, or even five distinct groups. Rather than
just choosing between the red and blue teams, we might have to choose between the red, blue,
green, orange, purple, aqua, mauve, and chartreuse teams. Yikes.
There is really just one fundamental change between earlier grouping games and the games to
follow in this chapter. Our shortcuts go away. First, if you weren’t in, you had to be out. Then,
if you weren’t in group 1, you had to be in group 2. If Miyauchi didn’t show up on the finance
committee, he sure as hell was going to be found on the incentives committee. But no longer.
Take a look at this game and the
appropriate setup that should
be built. Now, imagine you are
working through this game and you
find out that Tyrell, the cute little
parakeet, is not in cage B. What
does that mean? Well, Tyrell could
be in cage A or cage C.
Eight parakeets­—Sam, Tyrell, Uptown, Velvet, Waxter,
Xena, Yanni, and Zander—are housed in three separate
cages—A, B, and C­—at an estate. Each parakeet is housed
in only one cage. Each cage must house at least two of the
parakeets, according to the following conditions:
From this example, you can see that
it will be harder to simplify rules in
games with more than two groups.
We will have to search elsewhere for
deductions.
a:
b:
c:
Check out this rule as an example:
If Sam is housed in cage C, then Waxter is housed in
cage A.
sc [ wa
Wa [ S c
Sure, Waxter is housed in cage A when Sam is
housed in cage C. That’s the easy part. But the
contrapositive can’t be simplified:
If Waxter is not housed in cage A (if he is in either B or C), then Sam cannot be
housed in cage C (he must be in either A or B).
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Underbooked? Overbooked?
It’s important to always keep your eyes on the ratio of players to slots. Some grouping games
will present you with more players than available slots, others with less. Check out the following
examples:
Each of three cities—Grantsville, Hollytown, and Iceburg—
will be awarded grants in exactly two of the following areas:
parks, roads, schools, theaters, or waterways. Each grant
must be awarded to at least one of the cities. The following
must obtain:
For this game, your setup shouldn’t change much. The
three cities should be used as the base, and there are
two slots next to each one for the grants awarded. But
wait, check your math... That’s right, there are six slots.
And only five grants.
5a: p r s t w
g:
h:
i:
Say hello to an underbooked grouping game. It’s important to note at this point that one
grant will be assigned to two of the cities. Deductions will surely follow.
Nine children—A, B, C, D, E, F, G, H, and I—will be
separated into four two-person teams for a sack race. Each
child can be assigned to only one team. The following
conditions govern the assignment of children to teams:
t1:
t2:
t3:
Now we are dealing with four groups. But if each group
only has two slots, only eight children make the four
teams. What happens to the ninth child? Well, probably
lots of crying, humiliation, and psychotherapy later in life.
But for the purposes of this game, it’s overbooked, so
we need an additional group to keep track of the child
that has to sit out the sack race. So very sad.
t4:
out:
The fundamentals that you have learned over the last few chapters will continue to be helpful
when working through these games. There are more groups, but that doesn’t change most of
the basic grouping operations. Go ahead and find some games with lots of groups. Show those
games who’s boss!
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Three or More Groups /
143
18/PROFILING
everything is unstable
Just when you thought there couldn’t be any other way to create a grouping game, they throw
one more twist at you. This chapter marks our last type of grouping games: Profiling.
Profiling games look a little scary at first, but students
tend to enjoy them if they grasp the strategy for attacking them.
BP Minotaur:
It’s very important to spot profiling games because the strategy will diverge somewhat
from other grouping games. So the first thing to discuss is what characteristics you
should look for to determine you are up against a profiling game.
Players and Groups are Unstable
As noted in previous chapters, it’s important to track whether variable sets are stable or
unstable. How many players are on the red team? How many ingredients are in the appetizer
recipe? How many pieces of furniture can Maria help move? When you know the answer to one
of these questions, the game is stable. When you don’t, it’s unstable.
In a profiling game, both variable sets are unstable. So there will be two important
characteristics in these games:
1. Players will be assigned to at least one group (rather than exactly one).
2. The number of players assigned to each group will be unknown.
Students commonly confuse unstable grouping games and
profiling games. The difference is that players can now be assigned to
more than one group, rather than just one. Watch for games in which
players are assigned to “at least one” group.
BP Minotaur:
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Let’s take a look at an example.
Four different community centers­—Coneydale, Deadwood,
Evergreen, and Feildheim­—each offer at least one of the
following youth programs: origami, painting, squash,
tennis, and weaving. Each program is offered by at least
one community center. The following conditions govern the
assignment of programs to community centers:
In this game, your job is to
assign programs to the different
community centers. There are
some keywords, so you have to
check both variable sets to see
what restrictions are in place.
Each community center must offer at least one program, but they could offer
more. For example, Deadwood might offer one, two, or four different programs.
2. Each program must be offered by at least one community center, but they could
be offered by more. For example, weaving might be available at one, two, or all
four community centers.
1.
One of these characteristics alone does not entail a profiling game. But when you have both of
these characteristics, it’s profiling time.
Now let’s talk strategy.
Slow Down the Setup
As you know by now, we are big proponents of constructing an effective setup early in the
process so you can visualize how the rules function in a game. However, profiling games are the
exception. Because both groups are unstable in a profiling game, it’s possible to use either
variable set as the base of your setup.
In the game above, you could use the
community centers as the base and
plug in the programs that they offer
(setup #1 to the right). Alternatively,
you could use the programs as the
base of your setup and plug in the
community centers that offer them
(setup #2).
c:
o:
d:
p:
e:
s:
f:
t:
This comes with a big caveat. While it’s
possible to make it through a game with
either setup, there’s always one that will
make your life much easier.
#1
w:
#2
On the next page, we will walk you through the strategy
to ensure the best setup for a profiling game.
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Profiling /
145
Step 1: Identify a Profiling Game
As we discussed a few moments ago, the first step is to recognize that you are staring at a
profiling game. How? Test the sizes of the groups. If both groups are unstable, then you know
you have a profiling game.
Step 2: Check out the rules
Once you realize you are doing a profiling game, you know that two different setups are possible
for the game. Don’t rush and simply choose one of the setups randomly. You want to do a little
research and see which setup will be more helpful for the next 10 stressful minutes of your life.
Where might you find clues about the best way to visualize the game? The rules, of course.
The rules in a profiling game provide helpful hints in building the most effective setup.
The big challenge in a profiling game is that the sizes of the groups are up in the air. You don’t
know much, and that can be uncomfortable. Your task is to take back the power (take that,
LSAT). As you will see very soon, the important deductions in these games will stem from
limiting the sizes of the groups. If you can decipher that a community center offers exactly two
programs, or that tennis is offered by a maximum of two community centers, then you will have
some very valuable pieces of information.
When you read through the rules in a profiling game, identify which variable set
faces more restrictions. Always use that variable set as the base of your setup.
Let’s use our previous game
as an example. Say you
glance down and you see
this set of rules staring back
at you.
Which variable set should
you use as the base of your
setup?
Deadwood offers exactly two programs.
Fieldheim offers tennis and at most one other program.
Coneydale offers more programs than Fieldheim.
Evergreen cannot offer both squash and
weaving.
Try to visualize...
The community centers! The rules all place restrictions on how many programs the
community centers can offer, so it will be much easier to visualize if you use the
centers as the base of your setup.
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Now, pretend we are in an alternate
universe. There are flying cars, dragons
with goatees, and an entirely different
set of rules. Take a look at this
alternate set of rules. Which variable
set do you think should be used as the
base of your setup?
Origami is offered by more of the community centers
than weaving.
Squash is offered by only one of the community
centers.
Tennis is offered by at least two community centers.
Hopefully, you are now visualizing the programs as your base. Working from there will be
much easier since the rules place restrictions on the programs. It’s easier to assign the
centers to the programs in this situation.
Games will give you some rules that favor each of the
two possible setups, but the majority of rules will point you in one direction.
Godly Guidance:
Step 3: Work slowly through the rules
We always urge you to work slowly through the rules and look for interrelationships, but this
is of the utmost importance with profiling games. The important deductions won’t arise from
one all-important rule, but rather from a compilation of the rules. Thus, it’s crucial to test the
significance of each rule thoroughly.
When you are looking for deductions in a profiling game, remember: They start with all of the
power.1 You are given very little. You don’t know how many times the players appear, and
you don’t know the sizes of the groups. Your challenge is to take back the power. You can
accomplish this by limiting the sizes of the groups.
The important deductions in a profiling game will be
based on limiting the sizes of the groups.
The real deal!
To illustrate, let’s do some excerpts
from an actual profiling game. This
is the infamous fancy cars game
from October 2001. Check out
the introduction and identify the
elements that make this a profiling
game.
1
A showroom contains exactly six new cars—T, V, W, X, Y,
and Z—each equipped with at least one of the following
three options: power windows, leather interior, and sunroof.
No car has any other options. The following conditions must
apply:
“They” refers to the people who write these freaking games. We always picture them with horns and a spiked
collar, but feel free to make up your own mental picture.
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Profiling /
147
It’s clear that we are doing a grouping game with two variable sets - cars and options.2 Let’s
check both variable sets to see if we have a profiling game.
1.
Do we know how many options are assigned to each car? Nope. Car V, for instance,
might have just one option or all three (big time).
2. Do we know how many cars have each option? Not so much. Leather might be
found in two cars or four cars.
Clearly, we have a profiling game. But before we build a setup, we need to check out the
rules and see which variable set to use for our base. Remember, it’s all about visualization
and limiting the sizes of the groups.
V has power windows and a sunroof.
W has power windows and leather interior.
W and Y have no options in common.
X has more options than W.
V and Z have exactly one option in common.
T has fewer options than Z.
Check out the rules to this game. Which
variable set should be used as the base of
your setup?
It seems like the cars are the clear winner
in this one. Nearly every rule limits the
options assigned to each car.
Now that you have your setup, it’s time to actually
jump into the rules. We are going to highlight a
couple rules to illustrate the types of deductions
that will be key in such a game. Take a look at these
three rules together. Think for a moment about the
impact they have on the cars involved. Remember,
the key is to limit the number of options that are
possible for each car.
t:
v:
w:
x:
y:
V has power windows and a sunroof.
W has power windows and leather interior.
W and Y have no options in common.
X has
more options
than and
W. leather interior.
W has
power
windows
V andYZhave
have exactly
one option
in common.
W and
no options
in common.
T has fewer options than Z.
X has more options than W.
148
z:
Here’s an overview of the deductions
that can be drawn from this
combination of rules:
•
W has power windows and leather interior, but note that the rule doesn’t tell us if these
are the only options in W. Plug in the two options, but we still want to leave open the
possibility that W could also have a sunroof.
2
The LSAT tends to date itself once in a while. Power windows? That’s a big option on these cars? Wonder if
they also offer a cassette player?
/ Chapter 18
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•
•
•
•
The next rule states that W and Y have no
options in common. Since W already has
power windows and leather interior, Y can’t
have either of those options.
Y has to have something, so Y must have a
sunroof.
Since W and Y have no options in common, W
can’t have a sunroof. Thus, both W and Y are
completely determined.
The third rule states that X has more options
than W. Since W has exactly two options,
X must have all three options. X is totally
pimped out.
t:
v:
w:
p
l
x:
p
l
y:
s
s
z:
It’s important to have conventions to track the
sizes of the groups. Only put a slot when you know there has to
be a variable there (for example, the minimum is two) and use a
vertical line to limit the maximum size of a group.
Godly Guidance:
Isn’t that beautiful? Using just those three rules, we completely determined three of the six cars.
The deductions in a profiling game build and build into a glorious final product. It’s common to
completely determine a number of groups before jumping into the questions.
Here’s a quick recap of the important features covered in this introduction:
1.
In a profiling game, both variable sets are unstable. The players can be assigned to
more than one group, and the group sizes are unstable. Watch for the phrase “at least
one” in the introduction to denote that you have a profiling game.
2. It’s possible to set up a profiling game using either variable set as the base, but one
is always preferable in visualizing the game. To get some clues about the best setup,
quickly read over the rules. Form your setup using the variable set with the most
restrictions on it.
3. Work through the rules very slowly on a profiling game. The deductions will build on
each other, so make sure to review rules as you uncover deductions.
4. The most important deductions will flow from limiting the sizes of the groups. Always
test whether each rule limits how many players could be assigned to each group.
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Profiling /
149
Well, enough chat for now. Time to give is a shot! Go find a profiling game and work through
it slowly. Focus on how you would identify the type of game on test day. Then read slowly
through each rule and build deductions as you go. You got this!
When you feel confident with profiling games, it’s time to keep moving along in our journey. We
know what ordering games look like, and we know how to ace grouping games. But now it’s
time to put it all in a blender and see what happens. Get excited!
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19/COMBOgames
put it together
You might have sensed this coming. Somewhere, the people that write this darn test are sitting
in a dark room, thinking of ways to screw with prospective law students like you while cackling
maniacally. They’ve run out of ordering games. Students have finally started to grasp grouping
games. But they can’t let you off that easily. Logic Games are supposed to terrorize students,
and they need a new weapon. What do they do? They put them together.
Combo games involve both ordering and grouping elements.
This is, of course, analogous to real life. You learn one skill, you learn another skill, but doing
them together can add a degree of difficulty. Walking and chewing gum. Texting and
driving. Going to college and maintaining your dignity. Examples abound.
Combo games are less common than either ordering games
or grouping games. But they tend to be difficult, so ready yourself.
BP Minotaur:
Before we enter the land of combo games, there are a few action items we need to discuss.
New Games, Old Rules
Before you quiver at the mention of combo games, there’s some good news: The rules that you
are going to face won’t be new to you at all!
Combo games include ordering elements. You will see dashes, blocks, arches, and all of that
good stuff. They also include grouping elements, so you can expect a variety of grouping
relationships. But you already know how to deal with all of that stuff.
Some rules will combine ordering and grouping. For
example, “If Jubin and Rubin are on the same team, then Jubin
performs before Rubin.” But that’s as close to “new” as you will see.
Godly Guidance:
blueprintprep.com/lsat
Combo Games /
151
This should be comforting because you have tons of practice with both ordering and grouping
rules. It will be a new challenge to deal with them at the same time, but the vast majority of the
rules will sound familiar.
Order of Operations
One mental obstacle in a combo game is that you will feel like you are juggling a lot of rules and
restrictions. And you are. This necessitates a good plan of attack. There’s one basic principle
to keep in mind when working through a combo game: Always work with the grouping
elements of a game ahead of the ordering rules.
In a combo game, work through the grouping rules before the ordering rules.
The reason for this is rather simple, if you think about it. In a combo game, you have to make
teams and order the players on those teams. But before you worry about the relative order
of the players on a team, you need to know who’s on the team. In other words, you have to
organize the groups before you try to figure out the order.
Here’s a quick example. Say you
are doing this game involving a
sack race. This is a classic combo
game because you have two
teams, and each one is ordered
from first to fourth.
At a family reunion, two teams (blue and gold) are
organized for a sack race from among eight family
members­—Grandpa Joe, Grandma Jane, Uncle Bob, Auntie
Marie, Cousin Sal, Cousin Theo, Sister Nina, and random
guy Hank. Each team will have four members and there
will be four consecutive legs to the race.
Now, pretend you have the following
partial set of rules for the game:
b:
Uncle Bob runs an earlier leg of the race than Cousin
Theo.
Uncle Bob and Grandma Jane are on the same team.
Grandma Jane and Sister Nina are on different teams.
g:
1
2
3
4
If you are working through a question on this game, it will be much easier to work with the
grouping elements before the ordering elements. For instance, if you are told that Sister
Nina runs the second leg on the gold team, what else do you know?
•
•
152
If you look at the first ordering restriction, you are left with nothing. Bummer.
If you start with the grouping rules, you could deduce that Grandma Jane is on the blue
team with Uncle Bob. Then you are in good shape to start thinking about the ordering
rules.
/ Chapter 19
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common combo games
Combo games come in a few different varieties. Essentially, the makers of the test can combine
any type of ordering with any type of grouping. However, there are three types of combo games
that pop up more frequently than the rest.
1.
In and Out with Rankings
In and Out games involve selecting some players from a larger group. They are brutal in nature
because some players are simply left out in the cold. On occasion, they get even more fierce.
Not only are some players left behind, but you have to rank the players that are selected.
In this game, you have to select five
of eight children, a typical process
in an In and Out grouping game.
However, once the five winners
are selected, they must be ranked
according to ability. So it’s not
enough to know that Nantucket will
be competing in the tournament;
you also have to know that he is
ranked fourth.
Five of the following eight children—Klein, Lena,
Magdalena, Nantucket, Ophelia, Peter, Quasar, and Randy—
will be selected for the debate tournament. The children
that are selected will be ranked according to ability from
first (best) to fifth (worst) according to the following:
in:
In and Out combo games will involve
complex ordering rules based on players
being selected (if Quasar and Randy are
selected, then Quasar is ranked higher
than Randy).
2.
1
2
4
3
5
out:
Making a Schedule
Arranging a schedule is pretty common in Logic Games - Monday through Friday, for example.
However, life gets busy. There are times when you have to do more than one thing in a single
day, and this is when you might enter the land of combo games.
Doctor Divya must schedule appointments with ten
different patients—A, B, C, D, E, F, G, H, I, and J—
during one week, from Monday through Friday. Each
day, she sees one patient in the morning and one
patient in the afternoon. Her schedule conforms to the
following conditions:
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m:
a:
m
t
w
r
f
Combo Games /
153
In this game, you have to determine both (1) what day a patient has an appointment, and (2)
whether that appointment is in the morning or the afternoon.
To the right, you can see some
possible rules. You could be
confronted with grouping principles
(the first rule) or ordering principles
(the second rule).
If patient B is scheduled for the morning, then patient D
is scheduled for the afternoon.
Patient C’s appointment is before patient F’s.
That just looks like one of those tiered ordering
deals from a few chapters back, borrrrrrring.
Bro Tip:
That’s an astute observation. The setup to some combo games is actually identical to tiered
ordering games. However, there’s an important distinction. In a tiered ordering game, one
variable set (cars, for example) goes on one tier and another variable set (drivers) goes on the
other tier. In a combo game like the one above, you only have one variable set, so each player
could end up in any slot. This introduces a grouping element into the game.
3.
Relay Race
The third common type of combo game is
similar to the sack race introduced a couple
pages ago. Essentially, two (or more) teams
are formed, and the members of the team
have some order assigned.
b:
g:
1
2
3
4
And now, we’re off. It’s time to flex those ordering and grouping muscles that have been
developed throughout this book.
There are some fascinating challenges waiting for you in the index at the end of the book. Look
up some combo games and get moving. Since combo games are tricky and come in lots of
shapes and sizes, we want you to practice 6-8 games. If you can work through combo games,
you are well on your way to a beautiful LSAT score!
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20/NEITHER?!?
what the...
Yes, we did tell you that Logic Games are all about ordering and grouping. And we weren’t lying.
Well, okay, we were. But just a little bit. Here’s the bad news: Every once in a while, a game pops
up that involves a task that is neither ordering nor grouping.
These games are very rare. They occur, on average, only once every two or three years. But, just
like the Boy Scouts, you always want to be prepared. You wouldn’t want to be surprised by one
of these little devils.
“Neither” games involve neither ordering nor grouping.
We aren’t going to spend much time covering these games. In fact, we aren’t actually going
to do any of them. Rather, we will provide you with an overview of the types of neither games
you might confront. But this should be interpreted by you as a reflection of the small amount
of study time that you should devote to these oddball games. Don’t freak out about this stuff.
Neither games introduce some form of novel gimmick. But once you get the gimmick, you can
easily do any Neither game.
Some of the Neither game types haven’t appeared
on the LSAT since 1995. That is quite some time ago. Coolio
and TLC were sitting at the top of the musical charts.
BP Minotaur:
common neither games
There are four types of Neither games that have popped up over the years:
characteristic grid, mapping, cyclical, and operation.
Of the four, characteristic grid
games are by far the most common.
Godly Guidance:
blueprintprep.com/lsat
Neither Games /
155
1.
Characteristic Grid
Characteristic grid games do not venture very far from ordering and grouping games. However,
the challenge is slightly different. In an ordering or grouping game, you are arranging a set
of variables. You might be arranging them from tallest to shortest, or separating them on
to different basketball teams. In a characteristic grid game, on the other hand, you aren’t
arranging a set of variables at all. Rather, you are assigning characteristics to a set of
variables. Rather than arranging six people, you have to determine who is tall and who is short.
Here’s an example from the
December 2006 LSAT. This one
is a classic. You get to choose a
costume for a clown. (We told
you that the LSAT was great
training for your future legal
career.) As you can see, there’s
no ordering and no grouping
here.
Your job is to determine the
pattern (solid or plaid) and
color combination for the
clown’s jacket and overalls.
(This is not a joke. This is a real
game. Stop laughing.)
A clown will select a costume consisting of two pieces and
no others: a jacket and overalls. One piece of the costume
will be entirely one color, and the other piece will be plaid.
Selection is subject to the following restrictions:
If the jacket is plaid, then there must be exactly three
colors in it.
If the overalls are plaid, then there must be exactly two
colors in them.
The jacket and overalls must have exactly one color in
common.
Green, red, and violet are the only colors that can be in
the jacket.
Red, violet, and yellow are the only colors that can be
in the overalls.
In characteristic grid games, your setup will often look eerily similar to ordering or tiered
ordering games. In addition, the rules will include a lot of restrictions on color combinations
(two reds can’t be next to each other) and conditional rules. By this point, those types of
principles should be no problem for you at all.
2.
Mapping
Mapping games involve... drum roll, please... mapping. These games will make you reminisce
about kindergarten. You’ll literally be playing ‘connect the dots’ all over again.
When you do a mapping game,
they will sometimes provide
you with a map. If not, it’s
advisable to draw your own
map. No need to apprentice
with a cartographer - a simple
arrangement of dots will work.
156
/ Chapter 20
Each nonstop flight offered by Zephyr Airlines departs
from one and arrives at another of five cities: Honolulu,
Montreal, Philadelphia, Toronto, and Vancouver. Any two
cities are said to be connected with each other if Zephyr
offers nonstop flights between them. Each city is connected
with at least one other city. The following conditions govern
Zephyr’s nonstop flights:
blueprintprep.com/lsat
In the game on the previous page (from
October 2003), you have to determine the
flight plan for Zephyr Airlines (almost as bad a
name as Flyhigh). In other words, you have to
connect a bunch of dots to figure out between
which cities they offer flights.
Mapping games have appeared infrequently
over the years. Many of the deductions are
similar to ordering and grouping games. For
instance, you might use a conditional rule to
ascertain that a city must be connected to
one of two other cities, but not both.
3.
Cyclical
Things go in cycles. Bell bottoms are really cool for a time. Then wearing them subjects you
to substantial social humiliation. Then they are all the rage again. This doesn’t happen often in
Logic Games, but it has popped up in the past. A cyclical game tests your ability to figure out a
pattern. This pattern determines how the variables appear in each cycle. The nice thing about a
pattern is that it doesn’t change.
To the right, you can gaze
at a cyclical game from
December 1994. In this one,
clans participate in a harvest
ceremony. The participation
takes place in cycles. Your task
is to (1) figure out the structure
of a cycle (seven days? five
years?), and then (2) uncover
the pattern of participation in
that cycle.
For instance, in this game, it’s
important to note that every
clan not participating in the
first year must participate in the
second and fifth years.
The population of a small country is organized into five
clans—N, O, P, S, and T. Each year exactly three of the
five clans participate in the annual harvest ceremonies. The
rules specifying the order of participation of the clans in the
ceremonies are as follows:
Each clan must participate at least once in any two
consecutive years.
No clan participates for three consecutive years.
Participation takes place in cycles, with each cycle
ending when each of the five clans has participated
three times. Only then does a new cycle begin.
No clan participates more than three times within any
cycle.
Easy hint for spotting a cyclical game:
Look for the word “cycle.” It’s a dead give-away.
Godly Guidance:
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4.
Operation
Nope - this does not refer to the magical board game in which one had to skillfully remove a
patient’s funny bone. Sorry to say it, but LSAT operation games aren’t quite that exciting.
Most ordering and grouping games challenge you to figure out the arrangement of players. Who
is in spot 6? Who’s the captain of the squash team? In an operation game, that’s all done. They
tell you exactly how the players are arranged. For example, they will tell you that Hilda is ranked
first, Ivan is ranked second, and Jamal is ranked third. That might sound easy, but don’t get too
excited. An operation game then challenges you to apply different operations to the original
arrangement. So it’s great that Hilda starts out ranked first, but what could she be ranked after
a couple rounds? That’s the challenge.
In this beauty from October 1995,
we sign up for a tennis league.
As you can see, the initial ranking
is provided. However, the ranking
will be shaken up as the games
proceed. (We are pulling for M she’s got an amazing backhand.)
Within a tennis league each of five teams occupies one of
five positions, numbered 1 through 5 in order of rank, with
number 1 as the highest position. The teams are initially in
the order R, J, S, M, L, with R in position 1. Teams change
positions only when a lower-positioned team defeats a
higher-positioned team. The rules are as follows:
Operation games introduce very random situations. It’s helpful to prefigure the results that
could occur after a few rounds have passed. Where could L be ranked after two rounds of
games? Could R make it all the way to number 1?
That wraps up our quick overview of Neither games. Other LSAT companies and their inferior
books will freak you out by stressing the importance of these games. We choose not to do that.
We want you to spend your valuable time focusing on the material that is most likely to appear
on your LSAT.
The chances of your LSAT score being ruined by a terribly difficult Neither game are
about the same as you getting hit by a tidal wave in the next year. Not gonna happen.
Feel free to do a little practice so you feel comfortable. But make sure to focus on ordering and
grouping.
Up next...
We are taking your game to the next level. In the following chapters, we will cover two advanced
strategies that can be used to really master Logic Games. Athena will be happy.
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21/PLAYtheNUMBERS
Math?!?!
We know, we know. You aren’t here to talk about numbers, and you surely aren’t here to
do math. In fact, law school is probably on the horizon because math (and related physical
sciences) never came naturally to you.
Time for some bad news. To really ace the games on the LSAT, you have to do a little math. But
don’t go searching for a new career. We aren’t talking about calculus, or even geometry. The
LSAT sticks to basic arithmetic. Addition and subtraction. Maybe a little multiplication, but you
can always simplify that to addition if you please.1
What is it?
As you have seen over the last several hundred pages, some games fit very nicely. If you have
seven children sitting in seven consecutive chairs, that’s great. If you have eight politicians
separated into two four-person teams, that’s excellent.
However, games don’t always have such a natural structure. Gotta schedule seven dates over a
span of five days? That’s complicated. Have to put eight animals into three cages of different
sizes? Not so nice. Need to choose five films to show in class, and there are three different
types of films from which to choose? Sounds more complex.
There is, however, an excellent technique to handle these situations. It’s called Playing the
Numbers. This process will help you handle the numerical aspect of Logic Games.
Playing the Numbers is a process that can be used to simplify the numerical part of a game.
Remember the game about airline stops? Or alphabet
soup? How about the monkeys and pandas? Or even the roommates
and their mailbox? In each of those games, we informally touched
on this process. However, it’s time to define exactly when to play the
numbers and how to do it successfully.
BP Minotaur:
1
You know that trick. If you have to multiply four times three, you can just add four plus four plus four. Genius.
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the three steps
There are three basic steps involved in this process. Way back when we were introducing
games, we stressed the importance of making games a linear process. To conquer a game, you
want to practice the same steps every time. The same rule applies to playing the numbers.
Let’s walk through this, one step at a time.
Step 1: Recognize the Challenge
You don’t have to think about playing the numbers in every game. Actually, there are only a few
types of games that require this advanced strategy. The first step is to recognize when you are
faced with a game that might require you to play the numbers.
How do you know? Good news - there are only three types of games in which you have to
think about playing the numbers. Here are the big three:
1. Underbooked or Overbooked Games
1:1 games are nice. Everything fits nicely - you have one and only one slot for each variable. But
underbooked games involve variables that can occur more than once. And overbooked ordering
games give you slots that can be assigned more than one player. All of a sudden you are dealing
with questions about how many.
How many times can Randy appear?
How many workshops can be offered on Wednesday?
Here’s an example of an underbooked ordering game:
A traveling circus makes seven consecutive stops during a
tour. Each stop is in one of the following cities: Wichita,
Sioux Falls, Boise, and Cheyenne. The circus visits
each city at least once during the tour. The following
conditions must follow:
In this ordering game, the task is
to determine which city the circus
heads to for each of the seven
consecutive stops. However, there
are only four cities. So the circus
is definitely headed to some cities
more than once.
How many times does the circus go to Boise? Does the circus visit Cheyenne more times
than Sioux Falls? What is the maximum number of trips the circus could make to Wichita?
These questions will be answered by playing the numbers.
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2. Players from Different Categories
Some games present you with a bland cast of characters from which to choose. But other
games give you a list of players from different categories. Rather than just having eight students
with odd, alphabetically-ordered names, you might have eight students: three freshmen, two
sophomores, and three juniors. When this happens, you might face questions about how many
players can be chosen from each category.
Can you select three juniors?
Could you have more monkeys than raccoons?
Here’s an example of a grouping game with different categories:
Five food products must be chosen for a lab test. The
products must be chosen from three dairy products (milk,
cheese, and yogurt), four meats (chicken, lamb, turkey,
and veal), and three desserts (cake, ice cream, and apple
pie). The following conditions govern the selection:
Since you have to select five of
the ten food products, this is an In
and Out grouping game. The food
products come from three different
categories - dairy products, meats,
and desserts. It’s key to track how
many products are chosen from
each of the three categories.
How many dairy products must be selected? Could more than two desserts be selected?
Which category could have the most products selected? After you play the numbers, you
will uncover the answers to these important questions.
Different categories are presented most often
in grouping games (In and Out grouping games are the most
common). However, this can occur in ordering games as well.
BP Minotaur:
3. Unstable Grouping Games
When you know how many players are assigned to a group, that’s comforting. You get to make
a set number of slots and take a deep breath. But when they don’t define the number of players
in each group, that’s scary. You have to think about how many there could be.
How many diplomats could visit Bangladesh?
What is the minimum number of players on the gold team?
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Here’s an example of an unstable grouping game:
There are three different science courses offered during
fourth period at the local high school: biology, chemistry,
and physics. Eight students—Zander, Yolena, Xade,
Wendy, Vanda, Umeko, Taylor, and Shiba—must each
choose to take one of the courses, according to the
following conditions:
In this grouping game, eight players
are separated into three groups.
It’s far from clear, however, how
many students choose each one
of the courses. Not only will it be
important to track who takes what
course, but questions will also
relate to how many students take
each course.
What is the minimum number of students taking chemistry? If three students take physics,
how many students take biology? If you play the numbers correctly, the answers to these
questions will be at your fingertips.
That’s the first step. You have to keep a watch out for games in which playing the numbers will
be helpful. It’s not a guarantee that you will play the numbers in any of these game types, but
it’s a strong possibility.
Step 2: Look for Principles of Distribution
After identifying a game in which it might help to play the numbers, you need to watch for clues
that it’s going to be helpful. Luckily, they will give you lots of them. You just have to notice
these helpful hints.
A hint to play the numbers comes
in the form of a principle of
distribution. Most rules in games
revolve around who goes where.
You have seen a ton of rules that
look like those to the right.
Most rules in games give
restrictions on who goes where
(which slot of which group).
The circus stops in Boise at some point after any stops
that it makes in Cheyenne.
If the circus stops in Sioux Falls second, then it stops in
Wichita sixth.
Chicken and ice cream cannot both be selected.
If apple pie is not selected, then cheese must be selected.
Xade does not take physics.
Zander takes chemistry unless Umeko takes biology.
A principle of distribution, however, will sound different. It won’t relate to the placement of the
variables at all. Rather, it will restrict the distribution of variables. It won’t tell you that Johnny
appears on day 4; it will tell you that no contestant can appear on more than two days. It won’t
tell you that Ralph is assigned to the green squadron; it will tell you that the green squadron
must have at least as many members as the fuschia squadron.
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A principle of distribution restricts the numbers in a game:
(1) how many times a variable can appear, (2) how many variables can be
selected from a category, or (3) how many players can be assigned to a group.
Principles of distribution will sound different depending on the type of game you are attempting.
Let’s use our previous games to look at some examples.
In the underbooked ordering game, a circus had
to make seven stops in four different cities during
a tour. Clearly, this requires more than one stop
in some of the cities. Here are some principles of
distribution that would govern how many stops
could be made in each of the cities:
Exactly one dairy product is tested.
At most two desserts can be tested.
If more than one meat is tested, then
only one dessert is tested.
The circus makes a maximum of three
stops in any city.
The circus makes more stops in Boise
than Wichita.
In the second game about various food
products, five winners had to be chosen from
ten contestants. The challenge is to discern how
many variables could be chosen from each of
three different categories. To the left are some
principles of distribution you could see.
The third game sends you back to school. Eight
students must be assigned to one of three science
classes. But the groups are entirely unstable.
You will likely encounter principles of distribution
restricting how many students take each class.
At least one student takes each course.
Exactly twice as many students take
chemistry as physics.
That’s step two. You might have noticed that you haven’t actually done much up to this point.
The first step is just to recognize the type of game, and the second step is to watch out for
principles of distribution. But don’t get lazy - step three is when it’s time for action.
Step 3: Do the Math
It’s time to work out the numbers. At this point, you have a grasp on the basic challenge in the
game, and you know the restrictions governing the different distributions. It’s time to crunch the
numbers.
When you play the numbers, always distribute the larger variable set into the
smaller variable set (for example, spread out eight players among the five days).
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When you play the numbers, follow these three easy steps to make sure that you identify all
possible distributions.
1. Start with the most extreme distribution (use the maximum or minimum).
2. Take from the biggest set and give variables to the smaller sets.
3. When you reach the most equal distribution, you are done.
Let’s see how this works in real time. Pretend you are attempting this game. Outlined are the
introduction and a couple rules. Here’s a step-by-step analysis of the correct approach:
Step 1: Recognize the challenge
This is an overbooked ordering
game. There are nine players
(acrobats) that must be distributed
over six slots (acts). This means we
might have to play the numbers.
Over the course of six consecutive acts (numbered first
through sixth), exactly nine acrobats—A, B, C, D, E, F, G,
H, and J—must perform. The performances are governed
by the following conditions:
At least one acrobats must perform during each act.
No more than three acrobats can perform during any
act.
Step 2: Look for principles of
distribution
Both rules should catch your eye - they are principles of distribution. Rather than telling you
when an acrobat does or doesn’t perform, they put restrictions on how many monkeys can
perform during each act.
Step 3: Do the math
•
•
•
First, start with the most extreme distribution. Since there is a maximum of three
acrobats, that’s a good way to start. One act could have three acrobats, another act
could have two acrobats, and the other four acts would then have just one acrobat.
Lame.
Next, you want to take one acrobat
from the biggest group and give
it to one of the smaller ones. You
could also have three acts with two
3
2
1
1
1
1
= 9
acrobats each, and three with just
one acrobat.
2
2
2
1
1
1
= 9
Since the second distribution is the
most equal way to distribute the
acrobats, you are done. Sweet.
That’s the process. You now have isolated the two possible distributions in this game.
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Make sure you understand the function of playing
the numbers: to tell us the possible distributions. Here, it tells us
the two ways to distribute the acrobats over the six acts. However,
I caution against going too far. We still don’t know which acts
feature multiple acrobats.
BP Minotaur:
Let’s do another example - a grouping game this time.
Step 1: Recognize the challenge
A chef is preparing a dinner that will have three courses—
appetizer, entree, and dessert. The chef will use six
different spices: basil, cayenne pepper, coriander, paprika,
sage, and thyme. Each spice is used in exactly one of the
three courses. The following must obtain:
Each course must include at least one of the spices.
Here, we have a grouping game.
There are six players (spices) and
three groups (courses). But the
game is totally unstable - it’s not
clear how many spices are in each
course. It might be time to play the
numbers.
Step 2: Look for principles of distribution
The first rule is a principle of distribution. A simple one, but a principle of distribution
nonetheless. It specifies that each course must include at least one of the spices.
Step 3: Do the math
•
•
•
First, start with the most extreme distribution. Since
each course must have at least one spice, the most
spices that one dish could feature is four. The other
two dishes would be left with one lonely spice.
Next, you want to borrow from the biggest group.
You could also have a dish with three spices, one with
two, and the third dish with only one spice.
The third possibility is that all three dishes include
two spices. This is the most equal distribution, so
we’re done.
4
1
1
= 6
3
2
1
= 6
2
2
2
= 6
These distributions will help you in two big ways.
First, they will eliminate wrong answer choices where the math
doesn’t match up. Second, they will give you a head start on
making hypotheticals for conditional questions.
Godly Guidance:
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165
There’s one more example to cover. This one is slightly different. In the first two examples, you
were given general principles of distribution that applied to each slot or group. In other games,
you will find principles that are specific to one slot, or to one group. When this happens, you
should play the numbers for the specific slots or groups.
Here’s an example. Note how the process changes slightly.
Step 1: Recognize the challenge
You should recognize this one as
an In and Out grouping game - six
of ten sports are selected. But the
sports are pulled from different
categories. Might be time to play
the numbers for how many can be
selected from each.
Step 2: Look for principles of
distribution
Six sports will receive funding from the Olympic
committee. The six must be selected from four summer
events (basketball, swimming, track and field, and
volleyball), three winter events (bobsled, curling, and
skeleton), and three experimental events (bungee jumping,
kite surfing, and sandboarding). The selection must accord
with the following:
Exactly two winter events are selected.
At least as many summer events as experimental
events must be selected.
Boom. Both rules are principles of distribution. Note: Since the principles of distribution give
restrictions on the specific categories, our approach should change. Rather than testing the
general limits of the game, we can test the limits for each category.
Step 3: Do the math
•
•
•
The winter events are always set to two,
which is nice. The most extreme distribution
would include all four summer events and no
experimental events.
Working towards the most equal distribution,
three summer events and one experimental
event could be selected.
The most equal distribution would be two
events from each category, which is also
possible.
s
w
e
4
2
0
= 6
3
2
1
= 6
2
2
2
= 6
Don’t always assume each group must have
at least one. Unless otherwise stated, zero is an option.
Godly Guidance:
That’s an overview of how to play the numbers, but now you get to practice on your own.
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play the numbers drill
Here we go. This drill is designed to develop your math skills. Well, at least to the point where
it will help you on the LSAT. For each of the following games, use the setup and rules to
determine the possible distributions. The first few examples will provide you with a template.
After that, it’s up to you.
1.
Chuck has to wear pants on each day of a five-day work
week: Monday through Friday. He has three different
types of pants from which to choose—corduroys,
jeans, and khakis. His wardrobe is constrained by the
following:
Chuck must wear each type of pants at least once.
= 5
= 5
2.
On a game show, a contestant must select seven balls
from three different boxes. Box 1 contains three balls
(A, B, and C), box 2 contains three balls (D, E, and
F), and box 3 contains three balls (G, H, and I). The
contestant must abide by the following rules:
= 7
= 7
3.The seven children in the Cathey family—J, K, L, M,
N, O, and P—are all in school. Each child is either in
high school or college, but not both. The following is
known about the family:
M is in high school.
There is an odd number of children in college.
hs
c
= 7
= 7
= 7
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4.
At a local sea park, a dolphin show is given every
afternoon from Sunday through Saturday. During one
week, there are four dolphins available to perform—
Red, Sippy, Tigger, and Ugo. Exactly one dolphin
performs each day, according to the following:
No dolphin performs more than three times.
Sippy performs exactly twice.
5.
A psychologist has five consecutive appointments
scheduled for Tuesday. The psychologist will see seven
patients—M, N, O, P, Q, R, and S—over the course
of the appointments. Her schedule is governed by the
following conditions:
Each appointment is scheduled for either one
patient or two patients together.
6.
Tim is heading out for a backpacking trip across Europe
and space in his pack is tight. He can only pack five
items. His options include three kitchen items (A, B,
and C), three clothing items (D, E, and F), and three
personal items (J, K, and L). In choosing the items,
Tim must follow these guidelines:
Exactly one kitchen item must be packed.
K and L cannot both be packed.
7.Eight new students—M, N, O, P, Q, R, S, and T—will
be added to four different classrooms at the local
elementary school: 1, 2, 3, and 4. Each student will be
assigned to one classroom, according to the following:
At least one student is added to each of the four
classrooms.
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8.
Eight politicians—Bush, Cheney, Gore, Jefferson,
Lincoln, Madison, Obama, and Pelosi—are assigned to
three different committees: agriculture, education, and
traffic. Each politician is assigned to one committee.
The following must obtain:
Exactly twice as many politicians are assigned to
the education committee as the traffic committee.
Madison and Obama cannot be assigned to the
same committee.
9.
A magazine is selling ad space to ten different
advertisers: A, B, C, D, E, F, G, H, I, and J. Each of
the advertisers buy some ad space spread over four
consecutive pages of an upcoming issue. The pages
are numbered 31, 32, 33, and 34. The following rules
govern the sale of the ad space:
Each page features either one, two, or four
advertisements.
Each advertiser buys only one advertisement.
10.
There are five roles available in the upcoming school
play. Nine students are trying out from three different
classes. Of the nine students, three are freshmen (B, C,
and D), three are sophomores (J, K, and L), and three
are juniors (W, X, and Y). The selection of roles must
accord with the following conditions:
At least one student is chosen from each class.
If more than one freshman is chosen, then no more
than one sophomore can be chosen.
If X is selected, then Y cannot be selected.
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169
answer key
Here’s an overview of how to play the numbers on the preceding games. Make sure to look over
any examples that you missed.
1.
2.
3.
4.
170
3
1
1
= 5
2
2
1
= 5
3
3
1
= 7
3
2
2
= 7
hs
c
6
1
= 7
4
3
= 7
2
5
= 7
Chuck must spend hours trying to pick out his pants every
morning. Since he must wear each type of pants at least
once, he could go heavy on one type of pants (likely khakis),
wearing them three times and the other two types only
once. Or Chuck could be more egalitarian and wear two
types of pants twice and the third type of pants only once.
This one can be confusing because there are no rules. But
this is a grouping game with different categories, and it is
helpful to play the numbers. Since there are only three balls
in each box, there are only two ways to come up with seven
balls: either pull three balls from two boxes and one from the
third, or pull three balls from one of the boxes and two balls
from each of the other two.
This is a busy family. Since there must be an odd number of
children in college, it’s best to start there. The first odd number is
one, so there could be one child in college and six in high school.
The next odd number is three, so there could be three in college
and four in high school. Then there could be five in college and
two in high school. It might seem like all seven could be in college
(seven is, after all, another odd number), but that doesn’t fly
because we need M to be in high school.
s
2
3
2
0
= 7
2
3
1
1
= 7
2
2
2
1
= 7
/ Chapter 21
The goal here is to calculate in how many shows each
dolphin performs. Sippy is set at two, but the rest of
the dolphins are up in the air. Since no dolphin can
perform more than three times, let’s start there. One
dolphin performs on three days, another on two days,
and the final dolphin has the week off (it never said
that each dolphin has to perform). Or it could be the
case that one dolphin performs on three days and the
other two on just one day each. Finally, it could be
true that Sippy and two other dolphins perform on
two days, and the final dolphin only performs once.
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5.
6.
7.
8.
2
2
1
k
c
p
1
3
1
= 5
1
2
2
= 5
5
1
1
1
= 8
4
2
1
1
= 8
3
3
1
1
= 8
3
2
2
1
= 8
2
2
2
2
= 8
a
e
t
5
2
1
= 8
2
4
2
= 8
Bro Tip:
1
1
= 7
Wait a second - there’s only one distribution
here! That will happen once in a while.
Since each patient must be seen and each
appointment is scheduled for either one or
two patients, there must be two joint sessions
and three solo sessions.
The kitchen items are the easy part - only one is selected.
The other rule tells you that K and L, which are both personal
items, cannot be packed together, so at most two personal
items can be selected. Thus, there are only two distributions
for the remaining four items - either three clothing items and
one personal item, or two of each.
This one has a large number of distributions, more
than you are likely to see in a real game. But it’s
great practice. To split the eight students into
four classrooms, there could be a maximum of five
students in one of the classrooms. To find the other
distributions, simply borrow from the larger groups.
Once you get to the completely even distribution
(two students in each classroom), you can feel
comfortable that you found all five possibilities. And
take a deep breath.
Whoa, now it’s time for multiplication. In a situation like
this, the easiest way to proceed is to plug one politician into
the traffic committee. (It’s always easiest to start with one
when multiplication is involved.) One times two is two, so
that means two for the education committee, and five left
over for agriculture. Next, plug two politicians (hopefully
Jefferson and Lincoln) into the traffic committee. Then you
would have four on the education committee (hopefully not
Bush) and two on the agriculture committee.
Or you could just have zero on the traffic committee.
Actually, no. It might seem like that would work, but zero multiplied by two would still
give you zero on the education committee. That leaves all seven politicians for the
agriculture committee, and you know they aren’t all going to get along. Since Madison
and Obama can’t be on the same committee, this one doesn’t work.
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9.
10.
4
4
1
1
= 10
4
2
2
2
= 10
f
s
j
3
1
1
= 5
1
3
1
= 5
2
1
2
= 5
1
2
2
= 5
This is a severely overbooked ordering game. There
are ten players (advertisers) for the four slots
(pages). The principle of distribution is rather
complicated - each page features one, two, or four
advertisers. When you crunch the numbers, there are
two possibilities. Either two pages have four ads and
the other two only have one, or one page has four
ads and the other three each have two.
One of the big obstacles in this example is where to begin.
The last rule tells us that X and Y can’t both be selected,
limiting the number of juniors to either one or two. That’s
the best place to start. If one junior is selected, you aren’t
allowed to select two freshmen and two sophomores (due
to the second rule). You either have to go with all three
freshmen and one sophomore, or all three sophomores
and one freshman. If two juniors are selected, then there
must be either two freshmen and one sophomore, or one
freshman and two sophomores.
Hope that drill went well. Playing the numbers can be challenging for students, but it’s very
helpful. When you are doing a game and the time is ticking away, you have to fight the urge to
jump straight into the questions. They will look tempting - after all, that’s where the points are.
But skipping right to them is a mistake you have to avoid.
During the deduction phase, it’s crucial to play the numbers in certain games. Here’s a reminder
of the types of games that might require this extra step:
1. Underbooked or Overbooked Games
2. Games with Players from Different Categories
3. Unstable Grouping Games.
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Before we do the real deal, go back through this chapter and make sure you are comfortable
with all of the steps involved in playing the numbers. Then it’s time to practice. Find some
games that fall into one of these categories and there’s a good chance you will be playing the
numbers before you know it. Mix it up and try some ordering games and some grouping games.
Play those numbers!
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22/SCENARIOS
the big time
You know that big movie scene when the master finally entrusts the student with the key to
victory and then sends him off into battle?1 It’s a big moment. Well, we have arrived at that
crossroads. It took 23 chapters, lots of games, and a smattering of bad jokes to get here, but
now you are ready.
We saved the best for last. Don’t fade on us now—this is the most important chapter in the
whole book.
The basic routine for attacking games should be second nature by now. That’s a good thing repetition and a good game plan are crucial to your success. But now we are going to introduce
a powerful new technique. Right in the middle of some games, we are going to ask you to ditch
the normal strategy, make a sharp left turn, and head in a totally different direction. We call this
process making “scenarios” in a game.
Scenarios will enable you to work through a game faster and more accurately than you ever
thought possible. Why wait until now? It’s vital that you get lots of practice with the normal
steps before we introduce this advanced technique. You have to learn to walk before you can
run. But now, as Mufasa once famously told Simba, “It is time.”
The true difference between a novice and
a goddess is found in this chapter - it’s all about scenarios.
Godly Guidance:
What are they?
Logic Games are all about constraint. When a game is first introduced, there are thousands of
possibilities. Each player can be placed in any slot or on any team. Shauna could be selected
along with Peter, or Robert, or Taylor, or all of them. The freedom is exhilarating, but it’s
frightening at the same time. And then the constraint starts to creep in.
1
174
We always picture Karate Kid at this point. But that might just be our obsession with Mr. Miyagi. Feel free to
substitute your own bad action flick.
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The rules limit these possibilities. All of a sudden, Mr. Bantam can’t be scheduled for Tuesday.
And he can’t be scheduled for Thursday. Then the deductions phase begins and the constraint
really starts to pile up. Since Shauna can’t be with Taylor and she never hangs out with Robert,
she must choose between Umlad and Veronica. This dialogue should sound familiar - it is the
basis for our approach.
You have come to appreciate and look for this type of constraint. Important deductions are
found when certain players are constrained to only a few slots. When you discover that the
alligator must be in cage 4 or cage 6, you’ve just deduced some very valuable information.
Since the beginning of this journey, you’ve been
trained to spot the areas of constraint in a game. Scenarios
allow you to use those skills in a new and powerful way.
BP Minotaur:
Some games are more constrained than others. Some of the games you attempt are heavy on
constraints and deductions. Other games are flexible and require a lot of work to answer the
questions (generally in the form of hypotheticals).
Certain constraints limit a game so much that there are only a few ways for it to work. That’s
when scenarios come into play.
When a game is limited to only a small number of possibilities, scenarios
should be created for each possibility before attacking the questions.
You should have a lot of questions swirling around your head right now. When do you make
scenarios? How do you make scenarios? What am I going to have for dinner? Try to forget
about dinner, because you need to focus on the task at hand.
On the next few pages, we will cover all of the important points relating to scenarios. Let’s jump
right in!
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Our goal here is to convince you that making scenarios is an amazing process that can
drastically improve your performance in Logic Games, so it’s time to talk details. The next step is
to learn why, when, and how to make scenarios on your own. Here’s an outline of what’s next:
1. Why are scenarios so important?
2. How often is it possible to create scenarios?
3. What types of games have scenarios?
4. When should you make scenarios?
5. How do you make scenarios?
why?
Hopefully, some of the benefits of making scenarios are already apparent. It saves you precious
time. The basic benefits are twofold.
First, the time you spend on a game will be drastically reduced. A tough game can easily
take you 12 minutes or more. But with scenarios, that same game might only take six or
seven minutes. Second, your accuracy will be greatly improved. When you have to work
through lots of hypotheticals, it’s easy to make mistakes. But when you do all of the work
beforehand with scenarios, you will get those same questions correct.
What you might not have realized is that the benefits go much farther. Making effective
scenarios for a game doesn’t just change your performance on that game - it can change your
performance on the entire section. By saving time and energy on one game, you will have more
of both to devote to the other games in the section.
Let’s use a quick example. Meet Joan. Joan is a very nice young lady who has been studying
her tail off for the LSAT. At first, she hated games, but she has improved dramatically. Joan can
now finish most games with decent accuracy. She is always rushed at the end of the section,
and she normally has to skip a few questions or a whole game. Here are two possible results:
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Games Section #1: Joan completes the first game in a respectable eight minutes.
She then tackles the second game. It’s a tough tiered ordering game, and she gets stuck
for a few minutes. Eventually, Joan works her way through it in 12 minutes. Joan starts
to freak out because she is running a bit behind. The third game takes her another 11
minutes. She drops a few questions because she is rushing. Joan only has four minutes
left for the final game, so she randomly guesses on most of the questions.1
Game 1
Game 2
Game 3
Game 4
8 minutes
12 minutes
11 minutes
4 min
Games Section #2: Joan still completes the first game in eight minutes. Good work,
Joan. When she attacks the second game, she notices a deduction that leads to three
scenarios. She works through the scenarios and they uncover more helpful deductions.
She flies through the questions and finishes in six minutes. Joan is thrilled. The third
game is tough and still takes her 11 minutes. But she is cool, calm, and collected - she still
has 10 minutes to leisurely finish the final game.2
Game 1
Game 2
Game 3
Game 4
8 minutes
6 minutes
11 minutes
10 minutes
Obviously, situation #2 is going to be preferable for Joan. You get the point - scenarios are
incredibly important. Creating scenarios on just one game can dramatically improve your
performance in the games section, which will improve your LSAT score (and your life).
how often?
Scenarios occur a lot - more often than you would think.
Bro Tip:
Hah, that’s basically cheating. I’m in.
1
Joan goes home after the test, eats a pint of ice cream, watches a lot of TV, and then signs up to retake the
LSAT.
2
Joan goes home after the test, watches a lot of TV, and then sets to work on her law school applications.
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That’s what many students assume when they first see the power of scenarios. But they are
mistaken—it’s not cheating; it’s working smart. Let’s cover a few points about the frequency of
scenarios.
1.
It’s almost guaranteed
Here are some stats on the prevalence of scenarios. You might be surprised at how often you
can break one of these challenging little logical puzzles into just a few scenarios.
Note: Statistics are based on all games from released LSATs in the modern era:
PT 1 (June 1991) through PT 68 (December 2012).
42% of all games can be broken into helpful scenarios.
Wow! More than 2 out of 5 games in the history of the LSAT can be broken into scenarios.
Every time you approach a new game, there’s nearly a 50% chance that you should break the
game into scenarios. That’s wonderful - you have many chances to use this powerful technique.
Of course, this also puts a lot of pressure on you to identify when and how to create scenarios.
Here’s the stats on how often scenarios have appeared on each Logic Games section since 1991:
Games with Scenarios
Tests
Percentage
0
10
14.7%
1
20
29.4%
2
24
35.3%
3
9
13.2%
4
5
7.4%
If you were in Vegas, you
would never see odds this
amazing.
Those are impressive stats. 85% of games sections include at least one game that should
be broken into scenarios. 56% of sections have given students two or more opportunities
to make scenarios. That’s a lot of games and even more scenarios.
When you take the LSAT, ask not whether you
will get a game with scenarios. Ask how many.
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2.
It’s getting more common
Many other LSAT prep courses and materials don’t make a big deal out of scenarios. That’s
probably because they’re old. Scenarios were much less prevalent back when Clinton was in the
Oval Office. These days, however, scenarios are all over the place.
Here are the stats:
Years
Total Games
Scenarios
Percentage
1991 - 1997
96
28
29%
1998 - 2002
60
21
35%
2003 - 2021
216
123
57%
That’s crazy. The prevalence of scenarios has nearly doubled over the years. Since 2003, over
half of the games on the LSAT have broken down nicely into scenarios. Here are some additional
stats about recent exams:
•
•
•
The September 2006 LSAT, the June 2009, and the June 2012 LSAT each featured four
games that could all be broken into scenarios.
Since 2007, the average number of games with scenarios per section is 2.41.
The last LSAT that didn’t have any games with helpful scenarios was October 2001.3
It’s not clear why scenarios are becoming more common, but the numbers don’t lie.
2.
It’s not really new
You might be wondering, “If scenarios are so helpful and so common, how have we made it
through this whole book without a mention?” The answer is that we haven’t.
When you were practicing different game types, you inevitably did a number of games that
involved scenarios. However, you likely dealt with them informally or didn’t complete the process.
This book is designed to turn you into a games ninja. That doesn’t happen overnight. It’s
important to learn and practice the basics before introducing the advanced strategies. So we
tiptoed our way around the issue. Our sincerest apologies, but it’s good for you.
After you complete this chapter, a great exercise is going back to some of the earlier games you
3
To give some context, 2001 was the year that American Idol and The Bachelor first premiered in the US. Both
shows are now in season 91 or so.
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practiced and completing them again using scenarios.
You have probably gotten the point of this section by now. To put it bluntly, you are very likely
to have at least one game with scenarios, and your performance on the whole section depends
on your execution. But no stress. We are here to help.
what types?
All of them. Scenarios are not limited to just one or two different types of games. They are
found across the board, from ordering to grouping to combo and even neither games. So you
always have to be on the lookout for opportunities to make scenarios.
As we move forward, you will see that the theme of scenarios is the same. Some form of
constraint is placed on a game that limits the possibilities and allows you to make scenarios.
This constraint can be present in any type of game.
The more detailed answer to this question is a little different. While you should always watch
for scenarios, certain types of games lend themselves to scenarios more frequently than others.
Take a look at the numbers on the next page.
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Game Type
Scenarios
Basic Ordering
0%
1:1 Ordering
53%
Underbooked Ordering
47%
Overbooked Ordering
48%
Tiered Ordering
57%
In and Out Grouping
39%
Stable Grouping
52%
Unstable Grouping
54%
Profiling
0%
Combo
40%
Characteristic Grid
24%
Weird Neither Games
21%
As you can
see, the big games types
(1:1 ordering, underbooked
and overbooked ordering,
tiered ordering, In and Out
grouping, stable grouping,
and unstable grouping) all
float around 50%. The
less common types of games
(basic ordering, profiling,
combo, and neither games)
are much less likely to have
scenarios. The latter games
try to challenge you with the
rules or a gimmick.
BP Minotaur:
Scenarios pop up in almost all game types, but they are more prevalent in some categories.
For example, if you are doing a tiered ordering game, you should really be on the watch for
scenarios. But if you are attacking a basic ordering game or a characteristic grid game, the odds
are much lower.
when?
That is a very important question. Scenarios are very common and super helpful when formed
correctly. The crucial step is determining when to invest the time and effort into making
scenarios.
Constraint is the name of the game. Certain rules constrain a game to such an extent that a
limited number of scenarios exist.
First, we are going to discuss the general requirements for scenarios. After that, we will dig a
little deeper and look at the types of rules and deductions that commonly lead to scenarios.
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Before you start to make scenarios in a game, you want to make sure that the game satisfies
both of the following requirements. If it does, scenarios will be very helpful. If not, you are
wasting your time chasing a pot of gold that doesn’t exist.
1.
There are four or fewer scenarios.
Scenarios are not designed to test some of the ways a game can work. The goal of the process
is to outline the only ways a game can work.
Here is the correct mindset when building scenarios:
“Boy, that block is pretty restricted in this game. It can only be placed in spots 1 and 2,
4 and 5, or 5 and 6. That’s all. No other way this game can work.”
When you have a realization like that, it’s time to jump in and build scenarios. Compare that with
the following internal dialogue:
“Hmm... looks like that big block has to take up three spots. It can go in the front, or it
could slide back in the middle. And it could probably go in some other spots as well.”
That’s no good. In this situation, the student is trying out some of the ways a game can work.
This won’t be very helpful because there could be other possibilities. The questions will be a
struggle. Here’s one more glimpse into the mind of a student:
“Oooh... if Charlie is assigned to the blue team, then both Daisy and Eddie have to go on
the red team. And then Farrah would have to be on the yellow team.”
While these might be helpful deductions, these are not scenarios. If Charlie is on the blue team,
other team members can be determined. But what if Charlie isn’t on the blue team? If you
aren’t covering all of the possibilities, you aren’t making effective scenarios.
When you start to test the different constraints on a game, a good general rule is that you only
want to create four or fewer scenarios. Anything more than that is going to take too much time
and effort.
Only make scenarios when you know you are covering the only ways that a game
can work and there are four or fewer scenarios.
Godly Guidance:
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It’s very common to make two or three scenarios.
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2.
It’s going to lead to more.
Scenarios aren’t designed to give you an opportunity to master just one rule or deduction. The
purpose is to uncover additional deductions that you wouldn’t spot otherwise. When you make
scenarios, you want to have a reasonable belief that there will be helpful deductions in most, if
not all, of the scenarios.
Once again, let’s play the mindset game. Here is one:
“Sharon and Mark have to go to either Dallas or Houston. If they go to Dallas, there’s
only one spot left and it would have to be Nina. If they go to Houston, it looks like I
could apply the third and fourth rule to figure out who goes to Austin.”
That’s the dream. Here, creating two scenarios leads to other deductions. Such deductions
would be difficult to spot without scenarios, giving you a huge advantage. Contrast that with
the following situation:
“Well, it looks like Bella has to sit in seat 3, 4, or 5. But I don’t have any other rules
about Bella or those seats.”
This is not an effective way to make scenarios. If you can’t activate other rules to find more
deductions, it’s unlikely that the scenarios will be helpful.
Only make scenarios when you have a strong suspicion that they will activate
other rules and lead to more deductions.
While you are practicing, it’s helpful to try to form
scenarios on every game. It won’t always work. But going through the
exercise will help train you to think about scenarios more and also
help you identify scenarios more accurately. You will find it works
much more often than you think.
BP Minotaur:
Now that you know the general requirements, it’s time to look at the rules and deductions
that normally generate scenarios. There are three situations that will generally be the trigger.
1.
Constrained Player(s)
The first, and most common, way you will find scenarios is with a constrained player or players.
This can result directly from a rule or more indirectly from a combination of rules.
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In some games, one player will be confined to only a few possible slots. In other games,
combinations of players will be similarly constrained. This is a very common way to make
scenarios. Here’s an overview:
Ordering Games
There are a few rules to watch in ordering games. Anytime you see one of the following rules or
deductions, scenarios should be on your mind.
1.
Blocks: One of the most common ways to form scenarios
is with blocks. They are big. They are ugly. And they tend
to not have many places they can land. Blocks occur in all
ordering games (1:1, underbooked, overbooked, and tiered)
as well as some combo games. Every single time you are
presented with a block, you need to examine where it can be
placed.
x
1
2
3
4
j
k
2. Arches: Another common culprit is arches. This
type of rule puts a strong constraint on a player he, she, or it must be assigned to one of only two
spots. Arches are also a common form of deduction.
Through a combination of ordering rules, many
games allow you to reduce the possibilities for a
player down to just two.
Grouping Games
In grouping games, the rules aren’t about spatial relationships. But there are still some common
grouping relationships that limit the possibilities for a player or players.
1.
Must Be Together: A very common grouping relationship
asserts that two players must be together. This can be very
helpful. If this is an In and Out game, you either select both
players or neither one. If there are multiple groups, there
might not be many groups that can accommodate these
lovebirds.
mx or ny
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p \ q
2. At Least One: The baby relationship is very important
because it establishes that one of two conditions
must always be met. This rule has a tendency to
set up two scenarios (one for each option) or three
scenarios (the third is formed by satisfying both
conditions) depending on the game.
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3. Two of Three: In grouping games, you will frequently
have to select two of three variables. This is more
commonly a deduction than a rule, but it occurs both
ways. Whenever this happens, it sets up three great
scenarios. You could select the first and second
variable, the first and third variable, or the second
and third variable.
a
b
c
This is not an exhaustive list of the ways that a player or players can be constrained and lead to
scenarios. Remember, one of these rules in isolation is not sufficient to justify scenarios. But this
is a good guide for common ways that constrained players lead to successful scenarios.
Spotting a constrained player is by far
the most common way to create scenarios.
BP Minotaur:
2.
Constrained Slot(s)
The next road to scenarios focuses on the slots rather than the players. Some slots, through a
rule or a combination of rules, become very restricted. Only two or three players can occupy the
slot. Earlier in the book, we used options to represent this important deduction. Since only a
few possibilities exist, this gives you a great chance to make scenarios.
Ordering Games
1.
Options: Some rules will simply provide you with an option
- one of two players must occupy a certain slot. But options
can also be deduced by eliminating all but two players from
one lucky slot.
v/z
1
2
3
Grouping Games
1.
Designated Spots: Some grouping games will
designate one member of the group as special in
some way. A committee might have a leader, a team
could have a captain, or the mob might have a head
honcho. When this happens, watch for rules that
restrict the possibilities for this slot. If there are only
a few, this could lead to scenarios.
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1:
l/m
c
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1:
2:
s
t
u/v
2. One Spot Left: Many times you will fill some, but
not all, of the spaces available in one of your groups.
When this happens, make sure to run through the
possibilities for the remaining slots. If you only have
one spot left and there are only two or three options,
it’s time for scenarios.
Since slots are a constant throughout games, you always have to be on the watch for
constrained slots. This type of constraint is easy to miss because it arises through a combination
of rules.
3.
Constrained Distributions
In the last chapter, you learned how to play the numbers. It’s an effective technique used to
identify all of the possible distributions in a game. Sometimes there will be a large number of
distributions. That’s a bummer. But many other games present you with only a limited number
of distributions. This is a great way to create scenarios.
To review, here are the types of games that commonly require you to play the numbers:
1.
Underbooked or Overbooked Games: In an underbooked game, you are presented with
fewer players than slots, so some of the players must occupy more than one slot. In an
overbooked game, there are more players than slots. So some slots must make room for
more than one player. Either of these situations could give rise to scenarios if there are
only a few possible distributions.
2. Players from Different Categories: When the players in a game come from different
categories (boy and girls, heroes and villains), you will commonly play the numbers to
decipher how many players can be selected from each category. This happens most
frequently with In and Out grouping games, and it commonly leads to scenarios.
3. Unstable Grouping Games: In unstable grouping games, you don’t know the sizes of the
groups. That sucks. But playing the numbers helps determine the possibilities. If there
are only a few, it’s time for scenarios.
When you play the numbers to determine the
distributions that are present, always stop yourself
when there are four or fewer. Applying the rules
to each scenario can yield a big payoff.
3
2
2
1
= 8
2
2
2
2
= 8
If you are able to play the numbers and use that to
build scenarios, you are quickly approaching pantheon member status.
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That’s an overview of when you should make scenarios. It will take some practice to train
yourself to spot scenarios, but make sure to follow the general guidelines. Constraint is the
name of the game.
how?
The general idea is to work through each scenario and plug in additional deductions as you go.
Here are some additional tips to help you sharpen your skills:
1. Don’t expect to fill every slot. The goal is to identify all of the deductions that you
can make in each scenario. Sometimes you will determine nearly everything, but other
times you will only fill a few slots. Think back to the chess tournament. One scenario was
nearly completed, but the second one had lots of open spaces. Even if your scenarios are
incomplete, they will give you a jump start on the questions and aid your understanding of
the game.
2. Scenarios can lead to more scenarios. When you start building scenarios, you might note
that you arrive at another fork in the road. If placing a block in one place means that another
slot now has only two options, don’t hesitate to break that one scenario into two scenarios.
As long as you are uncovering deductions along the way, the time investment will be worth it.
3. Utilize the scenarios for as many questions as possible. When you hit the questions,
it’s time for the big payoff. You want to reap the rewards of all your hard work. For each
question, examine the scenarios before doing any additional work. For absolute questions,
glance through all of the scenarios. For conditional questions, quickly look through the
scenarios and determine which ones are relevant for that question.
Scenarios will help you get through all questions
very quickly, except for elimination questions. Stick with the
original strategy for those little buggers.
BP Minotaur:
That concludes our overview of scenarios. You are probably excited to get started, but cool your
jets. Before you attempt real games, there’s a drill on the next page to help you develop your
new skills.
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scenarios drill
This drill is designed to develop your scenario-building skills. For each of the following:
1. Build the appropriate setup.
2. Diagram the rules.
3. Identify the biggest constraint on the game and build scenarios.
1.
2.
188
Five children’s toys—an abacus, a ball, a chess set, a doll,
and an elephant—are arranged side-by-side on a shelf. The
toys are arranged from left (first) to right (fifth), according
to the following conditions:
The doll is the second toy from the left.
The chess set is immediately to the right of the ball.
The abacus is somewhere to the left of the ball.
Six employees of the Hergot Corporation are assigned to
complete team-building exercises. The six employees—
Heather, Ivan, Jackie, Karl, Lin, and Matt—will be split into
three two-person teams: team 1, team 2, and team 3. Each
employee is assigned to one team. The following must
obtain:
Ivan and Lin must be assigned to the same team.
Karl must be assigned to team 2.
Heather and Karl cannot be assigned to the same team.
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3.
4.
5.
At a fancy dinner event, guests are served seven consecutive
courses. The seven courses are the following: jicama, kale,
lentils, macaroni, nutella, omelettes, and pizza. The courses
are served one at a time, according to the following:
Jicama is served before pizza.
Macaroni is served before nutella.
Kale is served first or last.
Lentils are served fifth.
Nutella and omelettes are served consecutively.
Six contestants—U, V, W, X, Y, and Z—perform six
consecutive songs in a singing competition. Two of the
contestants sing hip-hop, two sing reggae, and two sing
show tunes. The following conditions apply:
The two reggae songs must be separated by at least two
other songs.
X sings fifth.
The first song performed is a hip-hop song.
A show tune is the only song performed between the
performances by V and W.
V performs after U but before Z.
U sings either a reggae song or a show tune.
A table at the holiday party offers four different snacks:
nachos, poppers, quesadillas, and wings. Ted eats six snacks,
consecutively and one at a time. He eats each type of snack
at least once. The following conditions govern his snacking:
Ted enjoys poppers at least twice in a row, but he
doesn’t eat poppers fourth.
Ted cannot eat wings later than third.
If Ted eats nachos fourth, then he also eats nachos
second.
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6.
7.
8.
190
Exactly four of seven products—beer, chicken, dentistry,
eggs, fire alarms, gelatin, and ham—are featured in
commercials during halftime of the big game. The selection
of commercials is consistent with the following:
If beer is featured, then ham is not.
If chicken is featured, then dentistry is not.
If fire alarms are not featured, then eggs are featured.
Of the three commercials, beer, chicken, and gelatin,
exactly two are selected.
Eight inmates—F, G, H, I, J, K, L, and M—are assigned
to three different work crews on Tuesday. Two inmates
are assigned to Rose Street, three are assigned to Sawyer
Avenue, and three are assigned to Tunnel Road. The
following conditions govern the assignment:
J is assigned to Rose Street.
Neither L nor M is assigned to Sawyer Avenue.
If G is assigned to Tunnel Road, then H is assigned to
Rose Street.
F and I are assigned to the same crew.
Six puppets—Fergie, Gregg, Howie, Ivanna, Jules, and
Kid—are scheduled to perform at a local show that is
running from Monday through Wednesday. Each day, one
puppet will perform in the morning and one will perform in
the afternoon. Each puppet will perform exactly once. The
following conditions must hold:
Fergie performs in the afternoon on the same day that
either Gregg or Howie performs in the morning.
Jules and Kid perform on an earlier day than Gregg.
If Ivanna performs in the afternoon, then Howie also
performs in the afternoon.
/ Chapter 22
blueprintprep.com/lsat
9.
10.
Five travel destinations are being chosen for a “best of the
best” list in a travel magazine. The five will be chosen from
among three tropical destinations (Anguilla, Bermuda, and
Curacao), three adventure destinations (Peru, Roatan, and
South Africa), and three romantic destinations (Maldives,
Napa, and Ojai). The selection is in accord with the
following:
At least one destination from each category is selected.
At least as many tropical destinations are selected as
adventure destinations.
If Anguilla is selected, then Ojai is not.
If Curacao is selected, then Bermuda is not.
If Napa is selected, then Peru is also selected.
Seven clowns—Ricky, Suzy, Tuffy, Verby, Willy, Yoogy,
and Zimmy—are assigned to three different birthday parties
on Saturday. The three parties are for Bobby, Cindy, and
Eddie. Each clown is assigned to one party, and each party
is assigned at least one clown, according to the following:
Eddie’s party is assigned exactly one more clown than
Cindy’s.
Zimmy is assigned to Bobby’s party.
Verby cannot be assigned to Eddie’s party.
Tuffy and Verby must be assigned to the same party.
Willy and Yoogy cannot be assigned to the same party.
If Ricky is assigned to Bobby’s party, then Yoogy must
be assigned to Cindy’s party.
blueprintprep.com/lsat
Scenarios /
191
answer key
Here are the solutions to the previous drill. Make sure you formed scenarios correctly and found
the resulting deductions.
1
a
d
b
c
e
1
2
3
4
5
•
•
This is a 1:1 ordering game.
The block leads to two constrained players
(B and C). The block has only two possible
placements.
In scenario 1, the block goes in slots 3 and 4.
A must be in slot 1, and E goes in slot 5.
In scenario 2, the block slides over to slots 4
and 5. There should be linked options for A
and E in slots 1 and 3.
•
a/e
d
e/a
b
c
1
2
3
4
5
•
•
2
1:
i
l
1:
h
m/j
2:
k
m/j
2:
k
j/m
3:
h
j/m
3:
i
l
•
3
m
n/o o/n
1
2
3
j
l
p
k
4
5
6
7
m
1
2
k
m/j
1
2
/ Chapter 22
•
•
•
p
n/o o/n
192
•
This is a stable grouping game with
three groups.
The I and L combo are highly
constrained - they must be on team
1 or team 3.
In both scenarios, H must stay away
from K, and linked options can be
formed for M and J.
3
3
l
4
5
m/p
l
4
5
•
6
7
n/o o/n
6
7
•
This is a 1:1 ordering game.
The block with N and O leads to
three scenarios.
In scenario 1, N and O are in
slots 2 and 3. M must go in slot
1, and K is pushed to slot 7. J is
served before P, so J is in 4 and
P is in 6.
In scenario 2, N and O are in
slots 3 and 4. M must go in slot
1 or 2, and P must be in slot 6 or
7 (served later than J).
In scenario 3, N and O are in
slots 6 and 7. K must go in slot
1. J is earlier than P, so either M
or J is in slot 2, and either M or
P is in slot 4.
blueprintprep.com/lsat
4
5
r
•
•
x
z/y
•
5
6
v
x
z
3
4
5
6
n
w/q
n
p
p
2
3
4
5
6
h
s
r
h/s s/h
w
u
v
y/z
1
2
3
4
h
r
s
h/s
y
w
u
1
2
q/w
1
2
3
4
•
•
•
q
1
•
5
6
•
6
in:
b
c
e
out:
g
d
h
f
•
•
•
in:
b
g
out:
c
h
in:
c
g
out:
b
d
blueprintprep.com/lsat
f/e
•
f/e
•
Now it’s time for tiered ordering.
The V and W block has only two
possibilities.
In scenario 1, V and W are in slots 1 and
3. But U must precede V, so V must
be in slot 3. U is a show tune in slot 2.
The two reggae songs are separated
in slots 3 and 6. Two pairs of linked
options finish off the deductions.
In scenario 2, V and W are in slots 2
and 4. U can’t sing hip-hop, so U can’t
go in 1. This pushes U into slot 3 and V
into 4. Z is in slot 6 (after V). To keep
the reggaes separated, one of them
must go in slot 2.
This is a delicious underbooked
ordering game.
Since P and W can’t go in slot
4, it must be either N or Q. This
constrained slot leads to two scenarios.
In scenario 1, N is in slot 4, so N must
also go in slot 2. The PP block is in
slots 5 and 6 and there are linked
options for slots 1 and 3.
In scenario 2, Q goes in slot 4.
There’s no further deductions since
the PP block still has three possible
placements.
Here is an In and Out grouping game.
The final rule sets up three scenarios - the
selection could include B and C, B and G, or C
and G.
In scenario 1, B and C are selected, but G is
not. D and H feel the hate and are left out.
The out group is full, so E and F must be
selected.
In scenario 2, B and G are selected, but C is
not. H can’t be selected with B. Either E or F
(or both) must be selected.
In scenario 3, C and G are selected, but B is
not. D can’t be selected with C. Again, either
E or F (or both) must be selected.
Scenarios /
193
7
r:
j
s:
f
t:
l/m
•
•
i
•
•
8
r:
j
l/m
s:
g
h
k
t:
f
i
m/l
m:
h
j/k
i
a:
f
k/j
g
m
t
w
•
•
•
m:
j/k
g
i
a:
k/j
f
h
m
t
w
•
m:
j/k
h
i
•
a:
k/j
f
g
m
t
w
m:
g/h
a:
f
m
t
w
•
•
This is a stable grouping game with three groups.
The final rule places a strong constraint on two
players. F and I must be assigned to Sawyer Avenue
or Tunnel Road. That sets up two scenarios.
In scenario 1, F and I go to Sawyer Avenue. Neither L
nor M can be assigned to Sawyer Avenue, so at least
one of them must go to Tunnel Road.
In scenario 2, F and I go to Tunnel Road. L and M
can’t be assigned to Sawyer Avenue, so they form
linked options on Rose Street and Tunnel Road. The
only remaining spots are on Sawyer Avenue, so the
remaining inmates (G, H, and K) are also determined.
This is a combo scheduling game.
The first rule provides a block with F in the afternoon
and either G or H in the morning. This block could
go on any of the three days, and that leads to three
scenarios.
In scenario 1, F is on Monday afternoon. G can’t
be scheduled for Monday, so H takes the Monday
morning slot. J and K must be on an earlier day than
G, so they form linked options on Tuesday. Since H
is in the morning, I must be on Wednesday morning,
and G fills in Wednesday afternoon.
If F is on Tuesday afternoon, either G or H could be
on Tuesday morning. Split this scenario into two
scenarios; now there will be a total of four.
In scenario 2, G is on Tuesday with F. J and K
form linked options on Monday to stay in front of
G. The conditional rule dictates that I must go on
Wednesday morning and H on Wednesday afternoon.
In scenario 3, H is on Tuesday with F. J and K are still
linked options on Monday. Since H is in the morning,
I must be in the morning on Wednesday. G takes the
last spot on Wednesday afternoon.
In scenario 4, F is on Wednesday afternoon with
either G or H in the morning. Since there appears to
be a number of options for the remaining variables,
this is a good time to stop.
Note: It is possible to split the final scenario into two
more scenarios (G or H on Wednesday morning), but
try to limit yourself to four or less scenarios.
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9
b/c
p
m
n
o
t
a
r
r
r
•
•
•
a
b/c
p
m
n
t
t
a
r
r
•
a
b/c
t
t
m/n
a
a
r
•
10
b:
z
t
v
•
•
c:
•
e:
b:
z
w/y
c:
t
v
e:
y/w
r
blueprintprep.com/lsat
•
s
Next up is an In and Out grouping game with
players from different categories.
It’s important to play the numbers. There are
three distributions that lead to three scenarios.
In scenario 1, the selection includes one
tropical, one adventure, and all three romantic
destinations: M, N, and O. If N is selected, P is
selected. A can’t be selected with O, so B or
C takes the last slot.
In scenario 2, two tropical, one adventure,
and two romantic destinations are chosen. B
and C can’t both be selected, so A is selected
with one of them. O is out, so M and N are
selected. P fills the final slot.
In scenario 3, there are two tropical, two
adventure, and one romantic destination. A is
selected with either B or C. A forces O out, so
M or N is the romantic spot chosen.
The final example is an unstable grouping
game.
After playing the numbers, two distributions
emerge. That spells two scenarios.
In scenario 1, Bobby gets four clowns (lucky
guy), Cindy gets one, and Eddie gets two. V
can’t entertain Eddie, and there’s not enough
room for both T and V at Cindy’s party, so T
and V head to Bobby’s party. The other slots
are still up in the air.
In scenario 2, Bobby gets two clowns, Cindy
gets two clowns, and Eddie gets three. T and
V can only fit at Cindy’s party. W and Y form
linked options for Bobby and Eddie. Finally, R
and S take the last two slots with Eddie.
Scenarios /
195
That’s it for our introduction to scenarios. In case this didn’t come through clearly, this is really,
really important. Don’t leave it up to chance. This is a skill that builds upon all you have done
earlier in this book. And like any skill, you need practice to develop and hone it. So while you
are practicing any games in the future, be on the lookout for scenarios. You can’t practice this
stuff too much.
Congratulations! At this point, you are done with all of the new game types and strategies. It’s
been quite a ride and we hope you are feeling like a goddess of wisdom yourself. But before we
let you go, we have a few more items to discuss.
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23/TIMING
faster, faster...
Now we’re going to discuss some testing strategies. To complete the Logic Games section, you
have a whopping 35 minutes. That’s not a lot of time. That’s one rerun of Seinfeld with a snack
break. In Los Angeles, that’s the time it takes to complete a 1.7-mile commute. Shoot, you can
waste that much time choosing a filter for an Instagram post.
There are two important parts of doing well on Logic Games: (1) You have to be good, and
(2) you have to be fast. We have spent the last 23 chapters discussing how to be good, but
the second issue deserves some discussion as well. Obviously, these two issues are related.
As you improve your skills, you will naturally get faster. But there are some other tips we
would like to share.
The best way to improve your speed is to focus on
deductions. Rather than trying to rush through the questions,
deductions allow you to spend less time on the questions.
BP Minotaur:
games are not created equal
Your job is to complete four games in 35 minutes. With the aid of a fancy calculating machine,
we have discovered this leaves you with an average of 8:45 per game. For this reason, many
students think success in a games section looks like this:
Game 1
Game 2
Game 3
Game 4
8:45
8:45
8:45
8:45
This is actually a terrible plan. Not all games are created equal, and it’s dangerous to think that
they all should take the same amount of time.
The amount of time that should be allotted to a game is influenced by two factors:
(1) the difficulty of the game, and (2) the number of questions it contains.
Turn the page for some interesting facts about the games section.
blueprintprep.com/lsat
1.
The games at the end of the section are more difficult.
There’s a clear pattern that emerges when you look at the difficulty of games across the section.
Put simply, they get progressively more difficult. Since you are mentally fatigued and feeling the
time crunch at the end of the section, this is a troubling fact.
Blueprint rated the difficulty of the every game since 1991. The scale ranged from 1 (your dog
would have a decent shot at solving the game) to 5 (Einstein would have needed some help).
Here are some of the findings:
•
•
•
The average for the first game
is pretty low - only 2.03.
The second game jumps up
significantly to 2.98. The third
and fourth games are rated 3.38
and 3.55, respectively. So they
are more difficult than the first
two, but pretty similar to each
other.
The medians show the same
pattern. The median for the
first game is 2, the second
game is 3, the third game is also
3, and the fourth game is 4.
There are some outliers. All
four games, including the
fourth, had at least one game
rated as a 1. Also, all four
games had at least one game
rated as a 5 (even the first one).
This graph should teach you two important lessons: (1) games get progressively more difficult
as you work through a section, and (2) the games in the beginning of the section should take
significantly less time than those at the end.
2.
Some types of games are harder than others.
During this adventure, you might have had more trouble with certain game types. That wasn’t
a coincidence. Some types of games tend to be on the easier side. Other types of games are
generally more difficult.
On the next page, you can see a chart that breaks down the relative difficulty for the game types
we have discussed. This is another factor that affects the amount of time a game should take.
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Game Type
Avg. Difficulty
Basic Ordering
1.50
1:1 Ordering
1.81
Underbooked Ordering
3.21
Overbooked Ordering
3.47
Tiered Ordering
3.00
In and Out Grouping
3.64
Stable Grouping
3.35
Unstable Grouping
3.43
Profiling
3.45
Combo
3.63
Characteristic Grid
2.33
Weird Neither Games
3.29
Here are the real outliers.
You gotta like your chances.
It’s interesting to see how close many of
the difficulty ratings are to each other.
Most of the common categories range
between 3.00 and 3.64. But there are the
two exceptions:
•
Basic ordering games (1.50) and
1:1 ordering games (1.81) tend to
be much easier than other game
types.
You are likely to find simpler ordering
games early in the section. When you
attack one of these games, it should be
possible to complete it in as little as five or
six minutes.
There are twists in all game types, so you can’t perfectly diagnose the difficulty of a game until
you are in the thick of it. But these general guidelines can help you shape your strategy. Now,
let’s discuss some tips for how to improve your timing.
questions
The Blueprint strategy is largely designed around what happens before you hit the questions.
We urge you to search for deductions and slowly work through the setup and rules. But once
you complete those steps, you can definitely save time when working through the questions.
Here are some strategies:
•
Don’t read all of the answers. This is a tough one. Everyone likes to feel comfortable.
You don’t just want to know that the right answer is right, you also want to make
sure that the wrong answers are wrong. Unfortunately, that wastes valuable minutes.
Suppose you are doing a must be true question. If you read (A) and can see that it must
be true, don’t waste time checking that the other answers could be false.
blueprintprep.com/lsat
•
Use elimination questions to your advantage. There are two things you know about
elimination questions. First, they are super easy. Don’t ever leave an elimination question
blank, even if you skip the rest of the game. It’s a free point. Second, they give you a
good chance to visualize a game. If you want to gauge the difficulty of a game before
fully committing to it, just do the elimination question. You can answer the question by
simply reading the introduction and the rules. You don’t even need to build a setup.
develop a game plan
To maximize your performance on games, you need to have a plan. Here’s the dangerous
mindset of most students walking into the LSAT:
“Boy, I sure hate those games. But I’ll give it my best. I’ll work hard and try
to finish as many as I can. And, above all, I’m hoping for easy games.”
That’s not a plan. That’s just hoping for the best. Would you walk into an important job
interview without a plan? Would you go on a date without thinking through a plan for the
evening? Of course not. Logic Games should be no different.
Before we discuss various plans for the section, we need to discuss something. It’s a brutal truth
that students don’t want to hear. For many students, it’s a good idea to plan on skipping at
least one of the games. Frantically rushing through four games with low accuracy can be very
detrimental to your overall score.
Completing fewer games with better accuracy can improve your
overall score. Rushing to do more can be stressful and counterproductive.
BP Minotaur:
You don’t need to decide on a strategy right now. It’s too early for that. You will continue to
improve as you practice more games. But as the test approaches, it’s vital to develop a game
plan you are going to use to attack the section. Here are three strategies that work well for
students:
Plan 1: Push for four
If you are capable of completing all four games, that’s great. We are very proud. But you still
need to have a plan for managing your time appropriately. If you spend too much time on the
early games, you won’t have enough time to complete the later, more difficult games.
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Here is a rough idea of how the section should look:
Game 1
Game 2
Game 3
Game 4
7:00
8:00
10:00
10:00
The goal is to complete the first half of the section in roughly 15 minutes. Push yourself to move
quickly in order to reduce the stress and mistakes on later games.
You don’t have to complete the four games in order. Odds are that the first two games will be
easier, and you have to play the odds. So always complete the first two games. There could
be a brutal game waiting for you as either the third or fourth game. It’s great to preview both
games and attack the easier one first. Do the elimination questions for both the third and
fourth games. You don’t have to build a setup - just read through the introduction and the rules.
Choose the game that seems easier and attack that one first.
Plan 2: Aim for three
For many students, the best plan is to attempt to complete three games. It’s important to do
this in the right way. You always want to do the first game, but you don’t always want to do the
first three games. After you finish the first game, do the elimination question for the second
game. Unless it looks like cruel and unusual punishment, work through the second game. Then,
do the elimination questions for both the third and fourth games and pick the one that seems
easier. Skip the other game altogether and know that you made the right decision.
But there’s no way I can get a good score if I
skip a whole game. We all gotta rise and grind.
Bro Tip:
Admirable attitude, Broseidon, but the numbers don’t back you up. Let’s use an example.
Assume that a games section has 23 questions (five on the first game and six on the others).
Betty is an LSAT student. She can solve most games, but her accuracy suffers when she is
pressed for time. Here are two ways it could play out for Betty:
Option 1: Betty tries to rush through all four games, but her accuracy suffers. She gets 100% on
the first game but only averages 50% on the final three games. Correct answers: 14
Option 2: Betty focuses on accuracy and slows down a bit. She still hits 100% on the first game.
Betty only misses one question on the second game and one on the third game. She
skips the fourth game, but she gets the elimination question and guesses correctly on
one other question. Correct answers: 17
Option 2 is clearly better for Betty, and it might be better for you.
blueprintprep.com/lsat
Plan 3: Ace two
Some students simply can’t get through games quickly, no matter how much they try. They
can build the proper setup, represent the rules, spot deductions, and find most of the correct
answers. It just takes a while. When they try to rush, everything falls apart.
If this happens to be you, you should aim to complete two games perfectly. Complete the first
game and then choose between the other three games. Remember to answer the elimination
questions for the remaining games. Let’s see how Betty would fare using this strategy.
Option 3: Betty spends about 15 minutes and gets 100% on the first game. She chooses
to attempt the third game and only misses one question. Betty completes the
elimination questions on the second and fourth games and gets two lucky guesses.
Correct answers: 14
(Note that Betty’s score using this strategy is the exact same as her score when she
rushed through the section with lower accuracy.)
A true ancient Grecian deity learns through
trial and error. As the test approaches, try these different
strategies and determine which one works best for you.
Godly Guidance:
Even though this chapter is devoted to timing, don’t incorporate timing into your studies
prematurely. While you are learning the techniques, it’s important to work slowly and focus on
the details. You need to develop the correct approach; then you can work on speeding up.
As you progress, slowly introduce timing pressure into your practice. Finally, as test day
approaches, settle on a personal strategy for the section and practice using that strategy
repeatedly.
With proper techniques and a good plan, you can accomplish great things in 35 minutes.
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24/NEXT...
perfect practice makes perfect
The training wheels are now coming off. You have blossomed into a beautiful butterfly and it’s
time to set you out into the world. Okay - enough cheesy metaphors.
What should you do now? You need more practice. But practice doesn’t make perfect. Perfect
practice makes perfect. In this book, we only recommend the real deal - games from past tests.
You can find replica games, but they aren’t as helpful. Make sure to only use 100% grade-A,
genuine LSAT games when you study.
You can (and probably should) buy Prep Plus directly from LSAC. This includes access to
existing relased exams, in an online interface that represents what you’ll interact with on the real
LSAT. No need for the olden days of print booklets of exams - it’s the 21st century!
When you continue to practice, don’t just start taking full practice tests. There are a few stages
you should work through to maximize your score.
Here are a couple pointers for each stage:
Stage 1: Individual Game Types
In this book, we focus on individual types of ordering, grouping, and combo games. You should
continue to do the same on your own. By repeatedly doing the same type of game, you will
become more comfortable with the important features and common deductions.
Of course, it would be annoying to search through endless tests to find another In and Out
grouping game to practice. So we recommend finding resources that help you identify games
by type. Blueprint has a full filtering system for our students that we think is pretty amazing
(totally unbiased opinion).
Don’t spend the same amount of practice time on all game types. Mapping games do not
require as much attention as tiered ordering games. You have to play the odds. Spend your
time mastering the types of games you are most likely to see. Here’s a chart that shows the
prevalence of each game type dating to 1991 (and since 2004 for more recent numbers).
blueprintprep.com/lsat
Up Next /
203
Game Type
# Since 1991
Percentage
# Since 2004
Percentage
Basic Ordering
10
4%
6
6%
1:1 Ordering
45
17%
21
23%
Circular Ordering
2
1%
0
0%
Underbooked Ordering
19
7%
9
9%
Overbooked Ordering
21
8%
8
10%
Tiered Ordering
37
14%
13
14%
In and Out Grouping
28
10%
11
11%
Stable Grouping
23
8%
10
10%
Unstable Grouping
24
9%
3
4%
Profiling
12
4%
4
5%
Combo
20
7%
6
7%
Characteristic Grid
17
6%
1
3%
Mapping
8
3%
0
0%
Operation
5
2%
0
0%
Cyclical
1
0%
0
0%
As you can see, certain game types are much more common than others. It’s no coincidence
that a large portion of this book focused on the most common ones.
Here are more details:
•
•
•
204
1:1 ordering games are the most common game type. You are nearly assured that one will
pop up on your LSAT.
Underbooked ordering, overbooked ordering, tiered ordering, In and Out grouping, and
stable grouping games are also very common.
The games section has been less varied recently. Since 2004, common game types have
popped up more, and rare game types have nearly disappeared.
/ Chapter 24
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Stage 2: Full Sections
When you feel comfortable with individual game types, it’s time to attack entire sections. The
new challenge will be jumping between game types. Some sections will include four different
types. Warning: Do not time yourself yet. You can’t immediately go from 0 to 60. Give yourself
plenty of time to complete the section and search for deductions.
Stage 3: Timed Sections
When you feel comfortable working through sections, then it’s time to apply the timing pressure.
However, don’t think that you have to immediately crank it to 35 minutes. It can be helpful to
begin by giving yourself some extra time (45 or 50 minutes is a good starting point) and then
cutting the time down as you get more comfortable.
Well, that’s all from us at Blueprint. After over 200 pages, there’s literally nothing left to say
about Logic Games. Except that we hope you kick some LSAT butt on test day.
We hope you enjoyed the journey. At Blueprint, we strive to provide the absolute best LSAT
preparation that has ever been created. Hopefully, you think we fulfilled that mission.
For more information about the LSAT, and for more wonderful resources, just stop by our
website. Best of luck from the Blueprint team. Sayonara.
www.blueprintprep.com
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Up Next /
205