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?

first guy looks around and sees at least 1red 1blue 1yellow (at least).
he sees that everyone else is puzzled.
He thinks...
The guy next to him has a red hat.
This guy doesn’t know either. Soo….
This means that guy number 1 knows that there must be another red hat. We now know that there are two red hats.
Guy 1 looks around again and sees the guy wearing the blue hat is puzzled. He must be able to see another blue hat….so there are at two blue hats.
We have 1y, 2b, 2r.
This guy looks at the guy wearing the yellow hat and realizes that there must be another y hat
We have 2y, 2b, 2r
Logically there must be 2 of each.
Guy one thinks, well I can see two reds, I can see see two blues (or whichever he can see) and I can see 1 yellow, so I must have the one remaining yellow!!!

Posted by Emma on 2004-12-07 08:22:55