A king places a hat on the heads of three wise men chosen from a set of 3 white hats and 2 black hats. None can see their own hat, but each sees the other two. The king announces at least one white hat is present. He asks who knows their hat color. After a long period of silence, one wise man correctly states his hat color. What color is it and how did he know?
White. He deduced it because nobody answered immediately.
If a wise man saw two black hats, he would immediately state his hat is white (since only 2 black hats exist). Silence meant no one saw two black hats. If someone saw one black and one white hat, he would reason: "If mine were black, the other person would see two black hats and speak. Silence means mine is white." Since everyone remained silent even through that step, all three realized they must be seeing two white hats, making their own hat white.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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