Puzzled
By Steve Poris
“Logic is the beginning of wisdom, not the end.”
---Lt. Commander Spock, in Star Trek VI: The Undiscovered Country
Logic puzzles require the solver to use deductive reasoning to determine the
solution. These puzzles can take many forms, including the simple syllogisms that many
of us learned back in college, such as:
If all Encore residents are 55 or over, and
if all people over 55 are brilliant and rich,
then is it true that all Encore residents are brilliant and rich?
No need for me to give the answer, but the point is that in this and all other logic
problems, the solver is given certain premises (which you must assume are true) from
which the eventual solution can be deduced. The most important thing to remember is
that a statement can’t be true and false at the same time; it is either one or the other.
Although that may seem obvious, consider whether each of the following is true or false:
1. “I am lying right now.”
2. Theere are four misstakes in this senntence.
In sentence 1, if the sentence is true, it must be a lie, and if it’s a lie, it must be
true. Hmm. And think about sentence 2; you can see three blatant mistakes (theere,
misstakes, and senntence), but there is also a fourth mistake—the statement that there are
four mistakes (there seem to be only three). But if it turns out that there really are four
mistakes (the fourth being the word “four”), then the word “four” is not a mistake, and so
there are only three mistakes, but then “four” is a mistake...and on and on. (So even these
sentences are not true and false at the same time; they seem to switch back and forth.)
Many logic puzzles rely on this true/false dichotomy to challenge the solver to
come up with a logical solution. A famous puzzle sets up the premise that a missionary is
going to be killed by a native tribe, with the only question being the form of execution.
The tribal law states that the victim will be given the opportunity to make a final
statement, and if it is determined that the final statement is true, the victim will be burned
at the stake, and if the final statement is false, the victim will be beheaded. The puzzle’s
object is to determine what statement the missionary made that saved his life. (Answer:
The missionary states “I will die by beheading.” If the tribal judge determines that this is
true, the victim will be burned, which makes the statement false, which means the victim
will be beheaded, which makes the statement true….so the tribal judge decides to let the
victim go free.)
Probably the most popular type logic puzzle is a format in which a scenario is
described (“Seven dogs competed at a dog show”), clues are given (“Neither Misty nor
Rex was a German Shepherd”; “John brought a poodle”), and the objective is posed
(“who owns each dog, what breed is each dog, and what is each dog’s name?”). The
solver must fill out a matrix designed to sort out the clues and enable him to deduce the
solution. These are often referred to as "logic grid" puzzles. The most famous (and
possibly the hardest) example may be the so-called Zebra Puzzle, which asks the question
“Who Owned the Zebra?” If you would like to try this puzzle, you can find it online at
Wikipedia (http://en.wikipedia.org/wiki/Zebra_Puzzle) where not only the puzzle but the
solution and all steps need to solve it are given.
Finally, I want to mention a category of logic puzzles known as “Knights and
Knaves”. In these puzzles, all inhabitants of a fictional island are either knights, who
always tell the truth, or knaves, who always lie. The puzzles usually involve a visitor to
the island who meets small groups of inhabitants. The aim is for the visitor to deduce
whether the inhabitants are knights (truth-tellers) or knaves (liars) from what they say.
An example of this type of puzzle involves three inhabitants referred to as A, B
and C. The visitor asks A whether he is a knight or a knave, but does not hear A's answer.
B then tells the visitor "A said that he is a knave" and C tells the visitor "Don't believe B:
he is lying!" To solve the puzzle, the solver must note that no inhabitant can say that he is
a knave (it would be a lie if a knight said it, and it would be the truth—a no-no—if a
knave said it). Therefore B's statement must be untrue, so he is a knave, and C's statement
must be true, so he is a knight. Since B is a knave, he will always lie. Therefore B was
lying when he said that A said he was a knave. Therefore A must have said he was a
Knight.
I’ll leave you with a knights and knaves puzzle to ponder: John and Bill are
residents of the island of knights and knaves. John says “We are both knaves.” Who is a
knight and who is a knave?