There was a sheriff in a town that caught three outlaws. He said
he was going to give them all a chance to go free. All they had to
do is figure out what color hat they were wearing. The sheriff had
5 hats, 3 black and 2 white. Each outlaw can see the color of the
other outlaw’s hats, but cannot see his own. The first outlaw
guessed and was wrong so he was put in jail. The second outlaw
also guessed and was also put in jail. Finally the third blind
outlaw guessed and he guessed correctly. How did he know?
Let us look at it this way. Here are our possibilities:
Now we can eliminate # 6
because in this case the first outlaw would be sure to know that he
had on a black hat. # 7 can be eliminated for the same reason for
the second outlaw’s guess.
In # 2, the first outlaw has
to see at least 1 black hat (if he saw two while hats he wouldn't
have guessed wrong). From this we know that outlaw 2 or outlaw 3 has
a black hat (possibly both). Now outlaw 2 has the same dilemma, but
he knows that one or both of outlaw 2 and 3 has a black hat. He can
see that outlaw 3 has a white hat so in that case he would guess
black and be correct, but he didn't (since we know he guessed
wrong). Given this, we can remove option 2 from consideration.
Options 1,3,4,5 all have outlaw 3 wearing a black hat. Thus,
assuming that convicts 1 and 2 are as logical as possible, the only
options left all have outlaw 3 wearing a black hat.