The Mad Hatter

Nov 28, 1998

RAY: By the way, we are no longer accepting e-mail puzzler suggestions.

TOM: Whoa.

RAY: If you have an e-mail puzzler suggestion, we don't want it.

TOM: Wow.

RAY: Because they all stink.

TOM: Really?

RAY: Yeah.

TOM: What did we used to call it?

RAY: A sweeping.

TOM: A sweeping generalization.

RAY: Well, every week Catherine hands me 200 e-mails. First of all, half of them are "A complaint was received by the Pontiac division of General Motors Corporation about some bozo's ice cream melting," and I don't want that one anymore. Then there's 500 liars and truth tellers - I used that one three weeks ago. Stop sending it! So I'm using this one typewritten on a piece of paper from 1973.

TOM: I've said over and over again that snail mail is the only way to go.

RAY: Well, this was sent here about five years ago by a guy names Richard Roobok. I like it and I used it about 25 years ago.

TOM: He's the inventor of the Roobok Cube, isn't he?

RAY: Roobok's Cube. Once upon a time there lived a king who wished to find the wisest man in the realm to be his assistant. So he summoned --

TOM: That's it. You're going to find the wisest guy in the whole world.

RAY: It is well.

TOM: And you are going to give him the title of assistant.

RAY: First assistant. He summons the three wisest, the three known wisest men to his court, and he is about to administer the following test. He says to them sit down you morons. I'm going to put either a red hat or a white hat on each of your heads and facing them in a circle and standing behind them, he proceeds to place three red hats on their heads. One red hat on each of their heads. He says to them if you see -- obviously they can see, not themselves, but there are no mirrors in the room. They can see just the other two contestants. If you can see a red hat --

TOM: I wish I hadn't said that about the mirrors because I was going to use that for the answer.

RAY: If you can see another red hat...

TOM: Raise your hand.

RAY: Raise your hand. They all what -- raised their hands because they're each wearing a red hat. Then he says if you can tell what color hat you have on, stand up. Time goes by, nothing happens. One guy looks at another guy who looks at the other guy. The other guy looks at him. Finally one guy stands up and he says I'm wearing a red hat.

TOM: Wow.

RAY: Now it didn't hurt that he noticed the king holding three white hats in his hand.

TOM: Or he was looking in the other guy's glasses.

RAY: Could you put your head down a little bit. The question is how did he know that he was wearing a red hat?


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."

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