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This puzzle belongs to the classic family of hat problems, a tradition of logical puzzles where the decisive information is not always in what is seen, but in what each participant can deduce from the answers of the others. The variant of the third blind wise man makes the mechanism especially elegant: whoever ends up solving the problem seems to have less information than anyone else, but knows how to better interpret the two previous negative answers.
Each “I don't know” reduces the set of possibilities, until certainty comes not from looking at a hat, but from understanding what others should have known.
Three perfectly logical wise men are sitting in a circle. The king informs them that he has five hats: three white and two black.
Next, place a hat on each wise man and hide the other two. The hats are visible to others, although no one can see theirs.
Then the king asks them in turn, always in the same order, if they can deduce with certainty the color of their own hat. The first one answers no.
The second also answers no. Then the third, who is blind, answers yes.
What color is your hat?
Answer: The third wise man's hat is white. Explanation: Let's call the three wise men A, B and C, according to the order in which they respond. C is the third wise man, the one who is blind. A answers first. If A had seen that B and C were both wearing black hats, he would have known immediately that his own hat was white, because there are only two black hats available. But A replies that he doesn't know. Therefore, B and C cannot both wear black hats. Then B answers. B has heard A's answer. Suppose C were wearing a black hat. In that case, B could reason like this: "If I also wore black, then A would have seen two black hats and would have known that his was white. But A didn't know. Therefore I can't wear black; I would have to wear white." So, if C were wearing a black hat, B would have been able to deduce his own color. But B also replies that he doesn't know. So C concludes that his hat cannot be black. If it were, B would have known that his was white. Since B couldn't figure it out, C's hat has to be white. The key is that each negative answer eliminates one possibility. The third wise man does not solve the riddle by looking at hats, but by understanding what the other two could have deduced.
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