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In a group of three people (A, B and C), everyone has a different hair color (blond, black or brown, not necessarily in this order) and everyone may be either a knight (always telling the truth) or a knave (always lying). This is what they say.

  • Blond-haired person: "C has brown hair".
  • Black-haired person: "C is a knave".
  • Brown-haired person: "A and B are knights".

Determine the hair color of C.

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  • $\begingroup$ A tiny little doubt - According to your question, is it that they all are knights or all are knaves. or one knight and the others knaves and so on. $\endgroup$
    – 19aksh
    May 19, 2019 at 11:55
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    $\begingroup$ @Ak19 Each of them can be either a knight or a knave - they don't have to be all of the same kind. $\endgroup$
    – Maiaux
    May 19, 2019 at 11:56
  • $\begingroup$ @Ak19 - In fact, they cannot all be the same kind by the second question. If they're all knaves or all knights, the black-haired person could not say that "C is a knave". $\endgroup$
    – David Hammen
    May 19, 2019 at 16:10

3 Answers 3

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One possibility is that

The brown-haired person and black-haired person are A and B in some order. Then since they are both knights, the black-haired person speaks the truth when he says that C is a knave.

This means that

C is the blond-haired man, who is clearly lying when he says that C has brown hair (because he's describing himself!) Therefore C has blond hair.

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    $\begingroup$ oops sniped... bye $\endgroup$
    – Omega Krypton
    May 19, 2019 at 12:22
  • $\begingroup$ coming back with explanations for other cases :) +1! $\endgroup$
    – Omega Krypton
    May 19, 2019 at 12:28
  • $\begingroup$ I'll accept your answer because you were the first to answer correctly, but how did you rule out all the other cases? $\endgroup$
    – Maiaux
    May 19, 2019 at 13:01
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Blond

Explanation

See the following images... they also explain the other cases
enter image desc here
enter image description here

Conclusion

C is a knave with blond hair, A and B are knights with black/ brown hair

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El- Guest and OK have got the answer before me..

C is

Blond haired

Explanation

First let's start from the black haired person. If he were a knight, C would be a knave and can't have black hair. If he were a knave it would directly imply that C can't have black hair. (as he would be telling about himself in both cases) $$$$ Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction. So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction. $$$$ So, the blond haired person must be a knave and it must be C .

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