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You are standing in front of ten people, one of which is a truth-teller while the other nine are togglers . (A toggler is a person who toggles between the-truth and the-lie for every question asked.) You have no clue who the truth-teller is and who the togglers are.

You are given the chance to ask one and only one question to any, but only one of the ten people. From the provided answer you must be able to deduce with certainty the identity of the truth teller.

Question: So what is that question you will be asking?

Gamow
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2 Answers2

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"Which people here are truth-tellers"?

If the person you asked is a truth teller, he will indicate himself.

If he is a toggler in "truth" mode, he will indicate the truth teller.

If he is a toggler in "lie" mode, he will indicate the 9 togglers (this is my interpretation of telling "the-lie", and note they only toggle after each question and this is a single question). But as you know there is only one truth teller you know it must be the unindicated person.

IanF1
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    Very nice. I guess in any case, you can be sure that the truth teller is the person that is classified like no other, similar to your last sentence. – blakeoft May 01 '15 at 12:07
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    Strictly speaking, they could lie by pointing out five people out of the 10. – Glen O May 01 '15 at 15:01
  • @GlenO I would interpret 5 out of 10 as telling "partial truth", rather than "the-lie" as specified in OP. But you're right it's a matter of interpretation! – IanF1 May 01 '15 at 16:30
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    lie is often defined as something that is not true. so both partial or impartial truth is a lie and your method fails, becuase there is no surity that he may point a correct person or a wrong person. – RE60K May 01 '15 at 16:50
  • @ADG Yes, I agree that is one possible interpretation. My answer relies on a stricter definition of lie. – IanF1 May 01 '15 at 16:51
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    @IanF1 What if he says no-one? Seems like a fully blown lie to me. – George Reith Oct 06 '15 at 16:06
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    A sentence that is false is a lie. That "partial truth" does not make sense. – miracle173 Oct 06 '15 at 17:30
  • Fair enough. Like i said, it was my interpretation of the scenario, YMMD. – IanF1 Oct 06 '15 at 18:08
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"If I asked you another question immediately after this, and then I pointed to another person in your group and asked 'Are they the truth-teller?', who could I point to in order for you to say 'yes'?"

Makes use of the fact that the togglers always alternate between truth and lie.

Glen O
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  • If he starts in lying mode then his answer to the third question would be any one person that is not the truth teller, he is going to lie about that statement and name any other person which could still leave you with a false answer. – Poelie May 01 '15 at 09:54
  • @Poelie - I suppose that is a possibility. It's easily fixed, though. I'll update. – Glen O May 01 '15 at 09:59
  • I highly doubt he would understand your qustion :D.(the person) Please explain in detail (I can't get it sorry) – RE60K May 01 '15 at 17:00