Classic Five-Hat Problem

The problem posed on the BBC Radio 4 Today programme in April 2015 was actually a dressed-up version of this one. It goes like this:


 * Three men stand one behind another so that no.3 can see both no.1 and no.2 and no.2 can see only no.1. Hats are placed on their heads from behind, and so each man cannot see the hat on his own head. They are told that there are two hats of one colour (say, red) and three hats of another colour (say, white).


 * No.3 is asked if he can say what colour hat he is wearing, but he cannot.


 * No.2 is now asked if he can say what colour hat he is wearing, but he too cannot.


 * No.1 is now asked if he can say what colour hat he is wearing, and he answers with confidence.


 * What colour hat is he wearing and how does he know?''

Now go to the answer.

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