A logician invites 6 of his logician friends to help him celebrate his birthday. Each of the 6 guests is wearing a hat which is either red, yellow, or blue, and the logician host informs them all that there is at least 1 of each color. After they eat the cake, the host stands up and exclaims there is a special party prize for the first person who can deduce what color hat is on their head. The party guests all looked around the room at each other but no one claimed the prize immediately. Suddenly all 6 guests stood up and correctly identify what color hat was on their head.

What were the colors of their hats and how did they know?

The answer must be 2 of each colour.
As no one gives the answer immediately each guest must see at least 1 red, 1 blue & 1 yellow hat,
but if he sees, for example 2 red, 2 blue and 1 yellow he canot assume that his is yellow an so it is imposible to know his hat colour.
But after the pause each guest relises that they all stumped for the same reason.
Therfore we know that any guest sees at least 1R,1Y &1B, and that he knows that the
others also see this, this means that the colour he only sees one of must be the colour
of his hat , because he knows that the other person wearing that colour can see a hat
of that colour !

Posted by stig on 2004-12-01 20:39:35