Chess-like Riddles, Jeff Rosenspan

[JeffRosenspan]

Three men sit in chairs (#1, #2, and #3), in a straight line, all facin
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 th
front, he cannot see anyone else. The man in Chair #2 is behind Chai
#1 and he can only see the man in Chair #1. The man in Chair #3 i
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 th
three men will be randomly given one of those five hats and two will b
discarded. No one will know the color of the discarded hats or th
color of his own hat. The first person to use logic to determine wha
color hat is on his own head wins.

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

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

- Jeffrey Rosenspa


--
JeffRosenspan

[Nils Gösche]

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?

Man #1 is thinking:

Suppose #1 and #2 are wearing a white hat.
-> Then #3 will immediately deduce that he is wearing a blue hat since
there are only two white hats in total.
He remains silent, however, so the assumption must be wrong.

So, at least one of #1 or #2 must be wearing a blue hat.

Suppose #1 is wearing a white hat
-> Then #2 will know, using the reasoning above, that he must be the one
with the blue hat.
He remains silent, however, so the assumption must be wrong.

For this reason, #1 must be wearing a blue hat. So, #1 can as well jump
up and scream »MY HAT IS BLUE!!«

Regards,