Three men are captured by cannibals in the jungle. The men are given one chance to escape with their lives. The men are lined up and bound to stakes such that one man can see the backs of the other two, the middle man can see the back of the front man, and the front man can't see anybody. The men are shown five hats, three of which are black and two of which are white. Then the men are blindfolded, and one of the five hats is placed on each man's head. The remaining two hats are hidden away. The blindfolds are removed. The men are told that if just one of the men can guess what hat he's wearing, they may all go free. Time passes. Finally, the front man, who can't see anyone, correctly guesses the color of his hat. What color was it, and how did he guess correctly?
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Answer: The back man can see the hats worn by the two men in front of him. So, if both of those hats were white, he would know that the hat he wore was black. But, since he doesn't answer, he must see at least one black hat ahead of him.
After it becomes apparent to the middle man that the back man can't figure out what he's wearing, he knows that there is at least one black hat worn by himself and the front man. Knowing this, if the middle man saw a white hat in front of him, he'd know that his own hat was black, and could answer the question correctly. But, since he doesn't answer, he must see a black hat on the front man.
After it becomes apparent to the front man that neither of the men behind him can answer the question, he realizes the middle man saw a black hat in front of him. So he says, correctly, "My hat is black."