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Three prisoners wear hats of unknown color and must guess their own color using logic alone. How does the first prisoner know his hat color?

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Three prisoners each wear either a black or white hat and can see only the hats of the others, not their own. If the first prisoner can deduce his own hat color purely from the silence of the others who could not guess theirs, how does he do it?
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Three prisoners each wear either a black or white hat and can see only the hats of the others, not their own. If the first prisoner can deduce his own hat color purely from the silence of the others who could not guess theirs, how does he do it?

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Answer

His silence after seeing two hats of a certain combination, paired with the others' inability to answer, lets him logically deduce his own hat color through elimination.

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