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The Mad Hatter

The Puzzler


RAY: Here's the answer:

The clue is that for a moment or two, nobody moved. Nobody knew for certain what color his hat was, and that's what told the wisest guy that all of the hats were red. Here's how he figured it out. Each of them had acknowledged seeing at least one red hat. Now, Wiseguy #1 knows he can see two red hats, right? Now, *if* Wiseguy #1 had a white hat on, Wiseguys #2 and #3 would have known what color their hats were.

Step 1:
Wiseguy #1 knows he can see two red hats.
Step 2:
Wiseguy #1 thinks, "Hey, if I were wearing a white hat, Wiseguy #2 would see one red hat and one white."
Step 3:
Wiseguy #1 then thinks, "If I were wearing a white hat, and Wiseguy #2 saw one red hat and one white (and if he were wearing a white hat himself), then Wiseguy #3 would have seen two white hats. So, Wiseguy #3 wouldn't have raised his hand to the first question.

So it all comes down to this:
Finally, it hits him. Wiseguy #1 thinks, "If that were true, Wiseguy #2 would be sure that he had a red hat. But since Wiseguy #2 was actually unsure about his hat color, it can only mean one thing, my hat is red."

[ Car Talk Puzzler ]

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