Three men were sitting on a bench, strattling it. So, each man had one leg one each side of the bench.
They were sitting there for a while, when a woman came by with five very valuable hats; three blue and two red. She put a hat on each man without telling them what color their hat was.
Remember, they were strattling the bench, so each man could see what color hat the men or man in front of them had, but not the color of their own hat. So, the guy in back could see they middle and front guys' hat; the guy in the middle could see the front guy's hat, and the front guy could not see anyone's hat.
The woman told the men that whoever could stand up and say the color of their own hat first would keep all the hats. The rules were simple:
1) You could not move your head.
2) You could not talk to anyone else.
3) You had to have proof of why you knew the color of your hat (to prove that you weren't just guessing).
The men could not see the woman or the hats she was holding (and therefore had not given out).
After about an hour of thinking, the man in front stood up and stated (correctly) that his hat was blue.
How did he know this?
(scroll down for a hint.)
Hint: you do not have to find the color of everyone's hat; just the color of the front guy's hat.
Answer: The front guy knew that he had a blue hat because if his hat was red, one of the other guys would have already knew the color of their hats.
You see, if the middle guy's hat was blue, and the front guy's hat was red, the middle guy would have known that his hat was blue because if it were red, the back guy would would have seen that the only two red hats were taken, so he'd know his hat was blue.
And if the middle guy's hat was red, as I previously stated, the back guy would would have seen that the only two red hats were taken, so he'd know his hat was blue.
You probably don't understand it completely, so read through it again untill you do.