The puzzle

Imagine that four prisoners have been buried up to their necks in desert sand.

Each man can see only what is in front of him, and the wall completely blocks his view of the other side. Their captors place hats on their heads. They are told that there are two hats with black bands and two with white, but none of them is allowed to see the colour of his own, and the brim hides it from view.

The buried men are given two minutes, in which time one of them must correctly call out the colour of his own hat-band. If the first one to speak gets it right, inside the time limit, they will all be freed. If not, they will be left there to die.

No communication is allowed, and an incorrect call means they all lose. In short, one of them has to make a life-and-death decision for all of them.

After about one minute, one of the prisoners calls out the colour of his hat-band correctly. He doesn’t guess, and there is no trick to the question. He works it out purely by reasoning.

Which one of the prisoners answers, and how does he know he is right?

Butterworth J. and G. Thwaites (2011) Thinking Skills. Cambridge: Cambridge

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