Techniques for
Solving Logic Puzzles
Logic Puzzles
 Logic puzzles operate using deductive logic.
A well-designed logic puzzle has only one correct answer, and
one can use the available information to discover that answer.
There are an unlimited number of types of logic puzzles, and no
set of guidelines can cover all of them. You must use your own
ingenuity to modify these guidelines to fit new situations.
Click to proceed
Logic Puzzles
Basic steps to solving logic puzzles
1. Read the prompt carefully. What will a solution include?
2. Devise a method for capturing and displaying all of the
possible solutions.
3. Use the information given and deductive logic to rule out
solutions. (Use reductio if needed)
4. Only one solution should remain, and it must be the correct
solution. You’re done!
Click to proceed
Logic Puzzles
Let’s apply these steps to an actual logic puzzle.
You are trying to find out which of your three friends are going to the prom. Use the information below to determine
which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
This is a fairly standard logic puzzle. With a little ingenuity, we should be able to figure it
out.
Click to proceed
Step One: Logic
Read Carefully.
Determine
Puzzles
the solution requirements
Let’s apply these steps to an actual logic puzzle.
You are trying to find out which of your three friends are going to the prom. Use the information below to determine
which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
There seems to be only one dimension called for in the solution. For
each of your friends, either she is going or she isn’t. You are done
This is a fairly standard logic puzzle. With a little ingenuity, we should be able to figure it
once
you determine which friends are going and which ones are not.
out.
Click to proceed
Step two: devise a method to display
all possible solutions
You are trying to find out which of your three friends are going to the prom. Use
the information below to determine which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
Susan
Tammy
Ursula
First, we should consider just listing each
person with a box for yes or no. Let’s see
whatconvention
that would will
lookbe
like.
Our
to put an “X” in a box
when it is proven false, and a check when
proven true. An open box means we have
not
Click to proceed
Step two: devise a method to display
all possible solutions
You are trying to find out which of your three friends are going to the prom. Use
the information below to determine which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
Susan
Tammy
Ursula



For example, given the chart above, it would
indicate that Susan and Ursula are going, and
Tammy
not. each statement and see if it
Let’s
goisthrough
would allow us to rule in or out any of our
boxes.
Click to proceed
Step two: devise a method to display
all possible solutions
You are trying to find out which of your three friends are going to the prom. Use
the information below to determine which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
Susan
Tammy
Ursula
Statement one simply indicates that there will
be at least one box which has a check.
Unfortunately, it doesn’t tell us how many, or
which ones. In fact, it doesn’t allow us to put
an “X” or a check anywhere. Let’s move
on.
Click to proceed
Step two: devise a method to display
all possible solutions
You are trying to find out which of your three friends are going to the prom. Use
the information below to determine which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
Susan
Tammy
Ursula
Statement two tells us that if there is a check
next to Susan, then there is an “X” next to
Tammy.
Since
we don’t know if there is a check next
to Susan, it really doesn’t allow me to do
anything. Remember, these are conditional
Click to proceed
Step two: devise a method to display
all possible solutions
You are trying to find out which of your three friends are going to the prom. Use
the information below to determine which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
Susan
Tammy
Ursula
Statement three guarantees that either there
is a check next to Susan, or an “X” next to
Ursula.
Unfortunately,
either possibility is still open,
and the statement doesn’t allow us to fill in
anything.
Click to proceed
Step two: devise a method to display
all possible solutions
You are trying to find out which of your three friends are going to the prom. Use
the information below to determine which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
Susan
Tammy
Ursula
Statement four let’s us know that if only one
person went, it had to be Tammy or Ursula.
But we don’t even know if it was only one
person, so that really doesn’t help us.
Click to proceed
Step two: devise a method to display
all possible solutions
You are trying to find out which of your three friends are going to the prom. Use
the information below to determine which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
Susan
Tammy
Ursula
Statement five indicates that if there is an “X”
next to Tammy, then there is an “X” next to
Ursula.
By
itself, this statement does not allow us to
mark our grid. We don’t know if there is an
If you have already begun thinking hard, you can use hypothetical reasoning (reductio ad
“X”
next to Tammy.
absurdum) to solve this puzzle as it stands using this grid. If so, you are very
smart!
Click
to What
proceed
do you need me for?
Step two: devise a method to display
all possible solutions
You are trying to find out which of your three friends are going to the prom. Use
the information below to determine which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
Susan
Tammy
Ursula
Perhaps we should try to rethink our possible
solutions, and display them in a new way.
If we think about it, we can make a list of all
the possible combinations we might find in
our solution. Think hard on your own to
see
if
Click to proceed
Step two: devise a method to display
all possible solutions
You are trying to find out which of your three friends are going to the prom. Use
the information below to determine which friends are going and which are not.
1.
2.
3.
4.
5.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not Susan.
If Tammy did not go, then neither did Ursula.
Susan
Tammy
Ursula
There are eight possibilities, so we need
some more room. Let’s move things around.
Step two: devise a method to display
all possible solutions
Using the statements below, determine
which of your friends is going to prom.
1.
2.
3.
4.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not
Susan.
5. If Tammy did not go, then neither did
Ursula.
1. Susan, Tammy, and Ursula
2. Susan and Tammy
3. Susan and Ursula
4. Susan
5. Tammy and Ursula
6. Tammy
7. Ursula
8. None
Did you get all eight possibilities?
Using our new grid, let’s see if we can use the
available information to rule out any possible
solutions.
Click to proceed
Step three: using deductive logic to
eliminate solutions
Using the statements below, determine
which of your friends is going to prom.
1.
2.
3.
4.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not
Susan.
5. If Tammy did not go, then neither did
Ursula.
1. Susan, Tammy, and Ursula
2. Susan and Tammy
3. Susan and Ursula
4. Susan
5. Tammy and Ursula
6. Tammy
7. Ursula

Statement one allows us to rule out the eighth
solution, so let’s mark it with an “X”.
The circled 1 let’s us know what statement we
used to rule out this solution. It allows us to
check our answers or backtrack when Click
we toget
proceed
8. None

Step three: using deductive logic to
eliminate solutions
Using the statements below, determine
which of your friends is going to prom.
1.
2.
3.
4.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not
Susan.
5. If Tammy did not go, then neither did
Ursula.
1. Susan, Tammy, and Ursula
2. Susan and Tammy




3. Susan and Ursula
4. Susan
5. Tammy and Ursula
6. Tammy
7. Ursula
8. None


Think about statement two. It says that if
Susan is one of the members of our solution,
then
is to
not.
That Tammy
allows us
rule out any solution which
includes Susan and Tammy, solutions one
and two. Let’s mark those.
Click to proceed
Step three: using deductive logic to
eliminate solutions
Using the statements below, determine
which of your friends is going to prom.
1.
2.
3.
4.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not
Susan.
5. If Tammy did not go, then neither did
Ursula.
1. Susan, Tammy, and Ursula
2. Susan and Tammy




3. Susan and Ursula
4. Susan
5. Tammy and Ursula
6. Tammy
7. Ursula

Statement three is a little tougher. It allows us
to rule out any solution which does not
include
Susan,
but In solution 5 and 7,
does include
Ursula.
Susan is not going, but Ursula is, which would
make statement 3 false.
Click to proceed
8. None

Step three: using deductive logic to
eliminate solutions
Using the statements below, determine
which of your friends is going to prom.
1.
2.
3.
4.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not
Susan.
5. If Tammy did not go, then neither did
Ursula.
1. Susan, Tammy, and Ursula
2. Susan and Tammy




3. Susan and Ursula
4. Susan
5. Tammy and Ursula


6. Tammy


7. Ursula
8. None


That means we can rule out solutions 5 and
7, and we can cross them off our list.
Click to proceed
Step three: using deductive logic to
eliminate solutions
Using the statements below, determine
which of your friends is going to prom.
1.
2.
3.
4.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not
Susan.
5. If Tammy did not go, then neither did
Ursula.
1. Susan, Tammy, and Ursula
2. Susan and Tammy
3. Susan and Ursula
4. Susan
5. Tammy and Ursula








6. Tammy


7. Ursula
8. None


Statement four allows us to rule out solution
4.
Now, there are only two possible solutions
left, and one more statement we can use.
Hopefully, it allows us to rule out one solution.
Click to proceed
Step three: using deductive logic to
eliminate solutions
Using the statements below, determine
which of your friends is going to prom.
1.
2.
3.
4.
At least one of your friends is going.
If Susan is going, then Tammy isn’t.
Either Susan is going, or Ursula isn’t.
If only one person went, it was not
Susan.
5. If Tammy did not go, then neither did
Ursula.
1. Susan, Tammy, and Ursula
2. Susan and Tammy
3. Susan and Ursula
4. Susan
5. Tammy and Ursula










6. Tammy

8. None

Statement five indicates that if Tammy is not a
part of our solution, then neither is Ursula. In
solution 3, Tammy is not present, but Ursula
is. So statement five allows us to rule it out.
7. Ursula


Click to proceed
Step four: the only remaining
solution must be correct

2. Susan and Tammy

3. Susan and Ursula

1. At least one of your friends is going.
4. Susan

2. If Susan is going, then Tammy isn’t.
5. Tammy and Ursula
3. Either Susan is going, or Ursula isn’t.

4. If only one person went, it was not
6. Tammy

Susan.
7. Ursula

5. If Tammy did not go, then neither did
8. None

Ursula.
Since the sixth solution is the only one which
remains after applying all of our information, it
must be the correct solution.
So, Tammy is going to prom, and Susan and
Ursula are not. We’re done!
Click to proceed
Using the statements below, determine
which of your friends is going to prom.
1. Susan, Tammy, and Ursula







Logic Puzzles
Remember, not every logic puzzle will be solved in the same way as
this one. You need to use your creativity in devising solution
grids and other techniques
Wasn’t that fun!
Keep in mind that one kind of grid can make a solution more or
less difficult than another.
Check back for presentations on hypothetical reasoning and multidimensional solutions.