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This puzzle is pure reasoning. However, explaining the reasoning is more difficult than the reasoning process itself. I do my best; any problems, or should you know a better way to explain it, let me know ... email ... I would appreciate it; thank you.
- Tom, who sees both Dick and Harry, says he does not know the color of the hat he (Tom) is wearing. If Dick and Harry were both wearing white hats, Tom would know that he (Tom) is wearing black.
- Since Tom does NOT know his color, it means Dick and Harry are either both wearing black or one is wearing black and one is wearing white. They cannot both be wearing white. Again, if they WERE both wearing white, then Tom would have known that he (Tom) is wearing black.
- Dick, who only sees Harry, says he does not know the color of the hat that he (Dick) is wearing. If Dick saw white on Harry's head, Dick would reason that he (Dick) cannot be wearing white, otherwise Tom would have concluded that seeing two whites, he (Tom) would be wearing black.
- However, reasons Harry, Tom does not know what color he (Tom) is wearing because he does not see two white hats. Therefore, Dick, not seeing a white hat on Harry's head, cannot conclude that he (Dick) is wearing black. Dick realizes that he (Dick) could be wearing black or white. Therefore, reasons Harry, Dick is looking at a black hat on his (Harry's) head.
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