Prisoners and Hats and a Jungle, Oh My!

The Puzzler

RAY: Here's what the prisoners do. They decide if Prisoner Number 30, the guy at the end of the line, looks ahead and sees an odd number of black hats, he says, "I have a black hat." If he sees an odd number of white hats, he'll say, "I have a white hat."

Now, here's how this works. Prisoner looks up and sees one white hat. So he says, "I have a white hat." Well, two bad for him, because he happens to wearing a black hat. So they take him outside, and he gets what, two in the back.

But Prisoner Number 29, the guy right in front of him, he looks ahead, and he sees that one white hat, and he says, oh, if Prisoner Number 30 said that he had a white hat, that must mean he saw an odd number of white hats. I see an odd number of white hats, too. Therefore I have a black hat.

And so Prisoner Number 28 says the same thing. Prisoner Number 27 says the same thing, and so on until we get to Prisoner Number 10.

Prisoner Number 10 says, hm, all these guys behind me have said that they have black hats, because they're seeing an odd number of white hats. I don't see any white hats. Therefore, I must have the white hat.

TOM: Good, good.

RAY: Prisoner Number 9 looks ahead. He doesn't see any white hats. He knows the guy behind him declared that he had a white hat. And he knows there's an odd number of white hats, and he cannot have a white hat.

TOM: Ah.

RAY: And each of the remaining prisoners, all of whom have black hats use the same rationale to declare that they also have black hats. So who's our winner?

TOM: Our winner this week is Leslie Warren from Lawrence, Kansas. Congratulations, Leslie!

[ Car Talk Puzzler ]

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