This was posted by kirk_florida13 in another thread. This is the only way I have to move it here.
Guys, can you help me in the puzzle white hats? I will show you the Puzzle
The Puzzle: Cannibals ambush a safari in the jungle and capture three men. The cannibals give the men a single chance to escape uneaten.
The captives are lined up in order of height, and are tied to stakes. The man in the rear can see the backs of his two friends, the man in the middle can see the back the man in front, and the man in front cannot see anyone. The cannibals show the men five hats. Three of the hats are black and two of the hats are white.
Blindfolds are then placed over each man's eyes and a hat is placed on each man's head. The two hats left over are hidden. The blindfolds are then removed and it is said to the men that if one of them can guess what color hat he is wearing they can all leave unharmed.
The man in the rear who can see both of his friends' hats but not his own says, "I don't know". The middle man who can see the hat of the man in front, but not his own says, "I don't know". The front man who cannot see ANYBODY'S hat says "I know!"
How did he know the color of his hat and what color was it?
The man in front knew he was wearing a black hat because he knew the first man did not see two white hats and he knew that the second man did not see one white hat because if he saw a white hat, the second man would have known that his hat was black from hearing the first man's statement.
(I am really confused with the second man. Please help.)
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.
Welcome to the forum.
You are not the first to ask about this puzzle. I seem to remember a thread about it some time in the last two years.
I think the point you are missing is that the puzzle statement implies that the men respond in that order. So the middle guy not only has his own eyes to give him a clue. He also knows that the back guy has said he cannot tell.
Let's suppose I'm the middle guy. The back guy has said he cannot tell. What does that tell me? Answer: back guy cannot see two white hats; because if he could see two whites, he would know for certain his own was black.(there are only a maximum of two whites) So back guy is saying "At least one hat in front of me is black"
So if I (in the middle) can see a white in front of me I know that my own hat must be black.
But the middle guy says he doesn't know his own hat so he must be seeing a black hat on the front guy.
The front guy can make the same deductions and come to the conclusion his hat is black.
Hope that helps,
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Of course this is all assuming that the guys aren't freaked out and can figure out what's going on.
The back guy and middle guy might be unable to think under the pressure and so just say "I don't
know". But then at least one of them must guess, so they have at least a 50/50 chance! I'm
not sure I could think under those circumstances!
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.