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Three suspects are arrested for a bank robbery. Suspect $A$ says he did not rob the bank. Suspect $B$ says he did not rob the bank. Suspect $C$ says suspect $B$ did not rob the bank.

If $A$ is telling the truth, then that means $B$ and $C$ are lying, which means that $B$ robbed the bank.

Is this correct?

EDIT: Sorry for not including this, the restriction is only one is telling the truth.

Asaf Karagila
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Jason
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3 Answers3

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Given the assumption that only one suspect is telling the truth, the solution can be established in one fell swoop: If B is telling the truth, then C is also telling the truth; this would violate the assumption, so B must be lying, and hence he is the robber.

You can, of course, consider all the other possibilities as well and rule them all out, but you don't need to.

Barry Cipra
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  • Technically, one should also verify that when when B is lying, exactly one of A and C is telling the truth. (Puzzles don't have to be logically consistent: it could very well be the case that the puzzle is posed to have no solutions...) – Willie Wong Sep 03 '14 at 09:17
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Assume A is telling the truth, then B and C must be lying then, B must rob the bank, but as B is lying, he must have robbed the bank, C is lying so B has robbed the bank, So A is not lying, he's telling the truth.

Assume B is telling the truth then A and C are lying, then B must rob the bank according to C, contradiction.

Assume C is telling the truth so B hasn't robbed the bank, B is lying this means he has robbed, contradiction.

RE60K
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Yes that is the only logical choice.

James
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