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## Tuesday, July 29, 2008

### 3 Heads & 5 Hats

In a small village in the middle of nowhere, three innocent prisoners are sitting in a jail. One day, the cruel jailer takes them out and places them in a line on three chairs, in such a way that man C can see both man A and man B, man B can see only man A, and man A can see none of the other men. The jailer shows them 5 hats, 2 of which are black and 3 of which are white. After this, he blindfolds the men, places one hat on each of their heads, and removes the blindfolds again. The jailer tells his three prisoners that if one of them is able to determine the color of his hat within one minute, all of them are released. Otherwise, they will all be executed. None of the prisoners can see his own hat, and all are intelligent. After 59 seconds, man A shouts out the (correct) color of his hat!

The Question: What is the color of man A's hat, and how does he know?

Answer: The Answer: Man A is wearing a white hat.

An explanation:
From the fact that neither B nor C gives an answer, we conclude that both these men have insufficient information to determine the color of their hats. Let us start with man C. He must be seeing at least one white hat on the heads of A and B (if he would see two black hats, he would know that he is wearing a white hat). Man B therefore knows that he and/or A is wearing a white hat. Since he cannot give an answer, he must be seeing a white hat on A's head (if B would see A wearing a black hat, he would know that he himself wears a white one). From the fact that neither C nor B can give an answer to the jailer's question, A finally concludes that he is wearing a white hat!