THE RED HAT

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The Red Hat

Once upon a time there lived a king who wished to find the wisest man in the realm to be his assistant. He summons the 3 known wisest men to his court and he administers the following test.

He sits them in a circle, facing each other and he says Im going to put either a red hat or a white hat on each of your heads. He proceeds to place a red hat on each of their heads. Obviously they can see each other but there are no mirrors in the room so they cant see whats on their heads. He says If you can see a red hat, raise your hand. They all raise their hands. Then he says If you can tell what color hat you have on, stand up.

Time goes on, one guy looks at another guy, he looks at the other guy. The other guy looks at him. Finally one guy stands up. The question is how did he know he was wearing a red hat?
Hint: For a moment or two, nobody moved. Nobody knew for certain what color his hat was, and thats what told the wisest guy that all of the hats were red.
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 wouldnt have raised his hand to the first question.

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."
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