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you walk up to two people, one of them always tells lies and the other always tells the truth. they know that the other tells lies or the truth.

asking one question to one person figure out who the liar is.

the question must be yes/no and cannot be something anyone can know or work out like "is 2+2=4?"

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can you please clarify on the kind of questions that are (dis)allowed? currently the puzzle can be solved in a trillion different trivial ways and it is unclear what you mean by "cannot be something anyone can know or work out". –  Ittay Weiss Jan 15 '13 at 1:59
    
Can you please clarify how this is a mathematics question? –  Jonas Meyer Jan 15 '13 at 2:03
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Do you mean "if I ask the other person to point at the truth-teller, will he point at himself?". Whoever says yes is the truth-teller. + @JonasMeyer I think such questions, while bordering on off-topic, are legit. –  Ittay Weiss Jan 15 '13 at 2:06
    
See the clever answer of Kaspar Hauser in the film The Enigma of Kaspar Hauser. Hopefully you will accept his answer, unlike the arrogant mathematician-philosopher who poses the question in the film. –  Matemáticos Chibchas Jan 15 '13 at 3:28
    
@MatemáticosChibchas: Given that this is a Herzog movie, it wouldn't have been dropping a naked midget on one guy, then asking him: "Did I just drop a midget on you?" –  gnometorule Jan 15 '13 at 4:12
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closed as off topic by Jonas Meyer, Alexander Gruber, Thomas, Martin Argerami, Stefan Hansen Jan 15 '13 at 6:44

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2 Answers

You need to ask the person you meet the following question. "If I ask the other person, if you are a liar, will he say no?"

Let $T$ denote the person who tells the truth and $L$ denote the person who lies.

If you ask $T$, if the other person lies he will say "Yes" and if you ask $L$, if the other person lies he will say "Yes".

Hence, if you ask $T$, "If I ask the other person, if your are a liar, will he say no?" The answer will be "No".

Whereas, if you ask $L$, "If I ask the other person, if your are a liar, will he say no?" The answer will be "Yes".

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You can also ask: "If I asked you ten minutes ago, who would you have said the liar is?" This will result in the liar being pointed out, since the liar, ten minutes ago, would have said the other guy, thus he must say himself (since he always lies). The guy that tells the truth, well, he'll say the correct guy both times.

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