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I am a newbie to Stack-Exchange and if there is any problem in my question -- I apologize beforehand .

I was working my way through some Propositional Logic Questions in Discrete Maths by Rosen , when I came across the following question :

An explorer is captured by a group of cannibals. There are two types of cannibals—those who always tell the truth and those who always lie. The cannibals will barbecue the explorer unless he can determine whether a particular cannibal always lies or always tells the truth. He is allowed to ask the cannibal exactly one question.

Find a question that the explorer can use to determine whether the cannibal always lies or always tells the truth.

My Solution :

If I were to ask you whether you are a liar, would you answer yes?

  • The honest person would say NO.
  • The liar would say YES (due to double negation).

Doubt :

Am I correct in saying my answer will work? It almost seems too simple.

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  • $\begingroup$ Thanks @Thumbnail - how do we do the greying area thing ? $\endgroup$
    – pranav
    Commented Dec 23, 2014 at 16:46
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    $\begingroup$ It's hinted block quote. $\endgroup$
    – Thumbnail
    Commented Dec 23, 2014 at 17:27
  • $\begingroup$ If you're patient enough you can watch this video, otherwise you can read this dialog... $\endgroup$
    – Pierre-Yves Gaillard
    Commented Jun 20, 2017 at 19:36
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    $\begingroup$ I would ask "is 1 plus 1 equal to 2?" Liar "no", honest person "yes" $\endgroup$
    – miracle173
    Commented Jun 20, 2017 at 19:41

3 Answers 3

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You have exactly the right idea. You force the liars to make two negations. This question works just fine, as will others, as long as they are "honest" liars.

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  • $\begingroup$ Thanks @RossMillikan . Also can you explain the bit about honest liars -- I am not sure that I get it ... $\endgroup$
    – pranav
    Commented Dec 23, 2014 at 16:14
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    $\begingroup$ Basically you have to believe that they will follow the logic and lie every time, including hypothetical cases. In popular parlance a liar could be anybody who tries to deceive you. At that point you can't necessarily trust the answer. $\endgroup$
    – Ross Millikan
    Commented Dec 23, 2014 at 16:37
  • $\begingroup$ Got it @RossMilkman :) $\endgroup$
    – pranav
    Commented Dec 23, 2014 at 16:47
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    $\begingroup$ Suppose that the liar says that he is a liar. Then he has told the truth about himself and thus not lied. But then he is not a liar, and thus his statement about himself is false, and consequently he is a liar. $\endgroup$
    – Doug Spoonwood
    Commented Dec 23, 2014 at 17:49
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Well I think this will also work-"if I can find whether you are a liar or truther will you stop barbecue me?"
Liar will say No.
Truther will say yes.

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The gist of the answer is to actually ask a question within a question.

Let's break down the following revealing question:

"If I were to ask you whether you are a liar, would you answer yes?"

Here, indeed, we have two questions that are:

  1. Are you a liar
  2. Would you answer yes to question 1?

By asking the second question, the liar is revealed. The honest would not respond differently. Let's take a look by asking these two questions to the two cannibals.

ASKING THE LIAR:

  1. Are you a liar?
  • Honest answer (he wouldn't say this): YES
  • Actual answer (negation of honest answer): NO
  1. Would you answer yes to question 1?
  • Honest answer (he wouldn't say this): NO
  • Actual answer (negation of honest answer): YES

ASKING THE THRUTFUL:

  1. Are you a liar?
  • Honest answer: NO
  • Actual answer: NO
  1. Would you answer yes to question 1?
  • Honest answer: NO
  • Actual answer: NO

So the honest cannibal will say NO consistently, whereas the liar will lie about a lie, which will reveal him.

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