Prisoners in Hats

Logic Level 2

There are three prisoners called A, B, and C. The guards say they can all go free if they win this game, and if they don't win, they die. There are three black hats and two white hats. Three of the five hats get put on the prisoners, and none of them can see their own hat color. If one of them guesses their color hat correctly, they all win. They are positioned in a room where

C can see B and A, B can see A, and A sees no one.

< A < B < C

A few minutes of silence go by. Then someone speaks, and they all go free! Who speaks up, and what does he say?

B says he is wearing a white hat. A says he is wearing a black hat. C says he is wearing a white hat. B says he is wearing a black hat. C says he is wearing a black hat. A says he is wearing a white hat.

Valor Gjertsen by Valor Gjertsen , 14, USA

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1 solution

Valor Gjertsen
Jun 28, 2019
  • Because there were a few minutes of silence, we know that C couldn't have seen that there were two white hats and spoken up because he would have known that instantly.
  • So there were three other options that C could have seen, Black Black, White Black, or Black White.
  • B would have known it wasn't White White because C didn't say anything.
  • If B saw a white hat on A, he would have known (since it could not be White White), then he must have been black. But he is silent, so he must not see White on A.
  • A then realizes "none of them talked, so it was either Black Black or White Black and both of them end in black, so"

A says he is wearing a black hat.

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