Three wise men, five hats, and the blind one knows

Question

A king has five hats: three white and two black. He places one hat on each of three wise men, hides the other two, and tells them what the five hats were. The first two men can see each other and the third man, but not themselves. The third man is blind. The king asks the first man: "What colour is your hat?" He replies, "I cannot tell." The second man is asked and, after thinking, also says, "I cannot tell." The blind man then says, "I know what colour my hat is." What colour is the blind man's hat, and how did he work it out?

Accepted Answer

The blind man's hat is white. The first man's silence. There are only two black hats. If the first man had seen two black hats on the others, he would know his own must be white. He said he could not tell, so he did not see two black hats: at least one of the second and third men wears white. The second man's silence. The second man knows the fact above. He looks at the blind man. If the blind man's hat were black, then, since at least one of "second, third" is white, the second man would deduce that he himself is white, and he would say so. He said he could not tell, so the blind man's hat i…

Three wise men, five hats, and the blind one knows

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