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?

there must be 2 yellow, 2 red, and 2 blues or else one of the people would instantly know what color hat they have...because of the line "The party guests looked around the room at each other but no one claimed the prize immediately." shows that no one definitely knew right away what color hat he/she was wearing so there could not be a combination of 1, 2, 3 because the person wearing the color on only one hat would know instantaneously what color he/she was wearing

my math students helped me out with this one...

 

; )

 

 

 

 

 

Posted by mathteach on 2004-11-23 16:53:43