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The question is as follows,

In the Land of Liars there are exactly three Clans. Black clansmen always tell lies. White clansmen always speak the truth. Red clansmen are sometimes truthful. A,B and C are three people from the Clans Black,White and Red not necessarily in the given order.D is a clansman from the land of Liars.They were asked what their clans were and then what clan D is from. Their responses were,

A. I am not a white ;D is a black

B. I am not a black ;D is a Red

C. I am not read; D is a white

D. I am not a black; I am a white

Which of the following can be concluded?

1) D is a red

2) D is a white and C is red

3) A is red , B is a black , C is a white and D is a white

4) C is a white and D is a red

5) B is red

I think the answer is 3. A cannot be white. Also A has to be telling the truth in his first question always. So A is either Black or Red.

But the rest seem impossible to analyze. Is my answer correct and how do I solve this sort of a question quickly?

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  • $\begingroup$ This is an old puzzle, but I was wondering if there is a way to solve this by probability? $\endgroup$ – NoChance May 10 at 22:30
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Only a red can say "I'm not a white," because a white would be lying and a black would be telling the truth. So, A is a red. A black cannot say "I'm not a red." Therefore C is a white, because A is already taking up the red slot. By exclusion, B is a black. If C says that D is a white, then D is a white.

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Here's one way to deduce conclusion 3. Neither A nor C can be black, for then they would have told the truth bout themselves, which black folks never do. Since A, B, and C represent all three of the clans, B must be black, and therefore what he says about D is false; D is either white or black.

Consider first the possibility that D is black. Then C lied about D. Since we already know that C isn't black, C must be red. Since A, B, and C represent all three of the clans, A must be white. But then A lied about himself, which white folks never do. So this possibility, D being black, has led to a contradiction.

So now we know that D is white. And that means A lied about D. Since we already know that A can't be black, he must be red. Since A, B, and C represent all three of the clans, C must be white.

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