The Prisoners and Hats

3 prisoners wear hats: 2 white, 1 black (they know the distribution). They stand in a line - each sees only the hats in front. The back person says 'I do not know.' The middle says 'I do not know.' The front says 'I know mine is white.' How?

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Quick Answer & Explanation

If back saw 2

The answer to this riddle is If back saw 2. Difficulty: Hard · Solved by 7,976 puzzle lovers.

If back saw 2 blacks, he would know his is white. He did not, so middle and front are not both black. Middle sees front is white, and if front were black, middle would know he is white. Since middle does not know, front deduces he is white.

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