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Wednesday, December 7, 2011

The Coloured Hats


Three men, Alan, Brian and Colin are blindfolded and are told that either a red hat or a green hat will be placed on each of their heads.  After this is done, the blindfolds are removed and the men are asked to do the following:

·      To raise a hand if they see a red hat.
·      To leave the room as soon as they are sure of the colour of their own hat.

            All the hats happen to be red, so all the men raise a hand.  Several minutes elapse until Colin, who is more astute than the others, leaves the room.  How did he deduce the colour of his hat?

Answers:

C asks himself, “Can my hat be green?”  If so then A will know immediately that he has a red hat, for only a red hat on his head would cause B to lift his hand.  A would have therefore left the room. B would reason in the same way and also leave.  Since neither has left the room, C deduces that his own hat must be red. 

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