Four prisoners, four hats and a wall

Question

Four prisoners are given hats: two black and two white. They know this. They are arranged as follows and cannot move or turn: - Prisoner A stands at the back and can see prisoners B and C in front of him. - Prisoner B stands in the middle and can see only prisoner C. - Prisoner C stands at the front, facing a wall, and sees nobody. - Prisoner D stands on the other side of the wall and sees nobody, and nobody sees him. The hats, from back to front, are: A black, B black, C white, D white. Nobody may speak except to call out their own hat colour, and the first correct call frees all four; a wro…

Accepted Answer

B calls out "black", after a short pause. What A sees. A sees B's hat (black) and C's hat (white). If he had seen two hats of the same colour, he would know his own must be the other colour, since there are only two of each. He sees one of each, so his own could be either. A cannot call, and he stays silent. What B hears. B sees only C's hat, which is white, and knows that A can see both B and C. B reasons: "If my hat were the same colour as C's, A would have seen two whites and would have called out 'black' at once. A has said nothing. So my hat is not the same as C's. C is white, so I am bl…

Four prisoners, four hats and a wall

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