Math CentralQuandaries & Queries


Question from Ghader:

The puzzle below I know the answer to; because someone told me! My question is: how could I answer it using logic, maths, etc. what field of inquiry does this kind of problem fall into?
Puzzle: You are in a room with two men: one is a compulsive liar and the other is a compulsive honest. There are two doors: one leading to heaven, the other to hell. The two men know which door leads to where. You want to go to heaven but are allowed only ONE question from one or the other of the two men. What would that question be?
[The question to ask, from either man, is: "if I asked the OTHER man which door leads to heaven, which door would he point?". You would then choose the other door.]

Has this answer got any basis in logic or maths at all?

Yes; you can model asking a man a question with correct answer A by the operation A^x where ^ is "exclusive nor" and x is the man's identity (1 if he tells the truth, 0 otherwise.) Asking the other man is modeled by A^(not x). The goal is to find an expression in this "algebra" that does depend on A and does not depend on x.

So your solution reduces to A^(not x)^x = A^False = not A.

A simpler solution: "If I asked you which door leads to heaven, which door would you point to?" A^x^x = A^True = A; take that door!

Even reduced like this to Boolean algebra there is an element of trial and error in coming up with solutions.

If you are interested in this kind of thing, I recommend the books of Raymond Smullyan.

Good Hunting!

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