Puzzle

Logic Puzzle

Last Updated Oct 6, 2008 09:19 PM

A logic puzzle is a puzzle deriving from the mathematics field of deduction.

This branch was pioneered by Charles Lutwidge Dodgson, who is better known under his pseudonym Lewis Carroll, the author of Alice's Adventures in Wonderland. In his book The Game of Symbolic Logic he introduced a game to solve problems such as

some games are fun
every puzzle is a game
Are all puzzles fun? Not Necessarily.

Puzzles like this, where we are given a list of premises and asked what can be deduced from them, are known as "syllogisms". Of course, this example is trivial. Dodgson goes on to construct much more complex puzzles consisting of up to 8 premises.

In the second half of the 20th century mathematician Raymond M. Smullyan has continued and expanded the branch of logic puzzles with books such as The Lady and the Tiger, To Mock a Mockingbird and Alice in Puzzle-Land.

Here is perhaps the most famous of this type of puzzle:

Two men stand at a fork in the road. One fork leads to Someplaceorother; the other fork leads to Nowheresville. One of these people always answers the truth to any yes/no question which is asked of him. The other always lies when asked any yes/no question. By asking one yes/no question, can you determine the road to Someplaceorother?
The fact that there are two men is a red herring - you only need one of them. Ask either of them the question:
"If I ask you if the left fork leads to Someplaceorother, will you answer 'yes'?"
If the person asked is a truthteller, he will answer "yes" if the left fork leads to Someplaceorother, and "no" otherwise. But so will the liar (because if he had just been asked whether the left fork led to Someplaceorother, he would have lied about it, but when asked the hypothetical question above, he will lie about his lie and pretend that he would have answered truthfully).
So, either way, go left if the answer is "yes", and right otherwise.
An alternative approach is to ask "What would the other man say if I asked him whether the left fork led to Someplaceorother?" then go right if the answer is "yes" and left otherwise.
Another form of logic puzzle, popular among puzzle enthusiasts and available in large magazines dedicated to the subject, is a format in which the set-up to a scenario is given, as well as the object (for example, determine who brought what dog to a dog show, and what breed each dog was), certain clues are given ("neither Misty nor Rex is the German shepherd"), and then the reader fills out a matrix with the clues and attempts to deduce the solution.

See also Puzzle 539 1 - 3