OpenChess

Three men sit in chairs (#1, #2, and #3), in a straight line, all facing north, one behind another. Each man will have a hat placed on his head. No one can see his own hat at any time. The man in Chair #1 is in the front, he cannot see anyone else. The man in Chair #2 is behind Chair #1 and he can only see the man in Chair #1. The man in Chair #3 is behind Chair #2 and he can see both men in Chairs #1 and #2.

On the table, there are three blue hats and two white hats. Each of the three men will be randomly given one of those five hats and two will be discarded. No one will know the color of the discarded hats or the color of his own hat. The first person to use logic to determine what color hat is on his own head wins.

After five minutes, the man in Chair #1 stands up and says, "I win. I know the color of my hat."

The riddle is: What color was it, and how did he figure it out?

- Jeff Rosenspan

Blue.
the third man cannot see two white hats, because he would know his hat is blue.
then it is possible for the first two men only:
-white for the first, blue for the second,
-blue-white,
-blue blue

but, in the first case, the second man should know that his hat must be blue, otherwise the third man should have seen two white hats, and had answered that his hat is blue.
therefore the first man has a blue hat.