RAY: Hi! We're back. You're listening to Car Talk with us, Click and Clack, the Tappet Brothers, and we're here to talk about cars, car repair, and, duh, the answer to last week's Puzzler.

TOM:: Which was?

RAY: This was one of my series of coin-toss Puzzlers.

TOM:: This is the first in the series.

RAY: With Bill Gates thrown in to kind of obfuscate matters, but Bill Gates has a place here.

TOM:: Of course.

RAY: Right?

TOM:: Yeah.

RAY: Because he recognizes the power of the power...

TOM:: Of two.

RAY: Of two.

TOM:: Exactly.

RAY: Anyway, here's the Puzzler. A fellow finds himself at a party at Bill Gates' house, standing next to the great man himself, and Gates says to him, "Hey, how many people do you think are here?" The fellow looks around and says, "Jeez, I don't know. Eleven hundred?" Gates says, "That's right! You know, you're very good with numbers. Are you into games of chance, by any chance?" "Oh, no," the fellow says. "The chanciest thing I get involved in is tossing a coin." Gates says, "Well, do you think you could toss a coin 10 times in a row and call it correctly every time?" The guy says, "I don't think so."

TOM:: I don't think so either.

RAY: Gates says, "Well, do you want to make a bet? Because I can do it. After all, I'm Bill Gates and you're not." The fellow declines. "No, I don't want to make a bet. I don't think I can call it 10 times in a row. I don't think you can either. But I need the cab fare to get home, so I don't want to bet."

TOM:: Mmm-hmm.

RAY: Gates says, "Do you think there's anyone in this room who could call it correctly 10 times?" The fellow says, "I suppose there's a chance, but it's a pretty small chance." Gates says, "I'll tell you what. I'll bet there is someone who can call it correctly. And here's what calling it correctly consists of: If I toss the coin, I can call it, and if I'm right, that's a win for me. Or, if I toss the coin and you call it incorrectly, that's also a win for me. Got it?"

TOM:: Mmm-hmm.

RAY: "So," Gates says, "tell you what. I'll make you a bet. I'll bet you my $10 million to your $10,000 that it can happen in this room, that there's one person who can win 10 in a row." The guy says, "You're on." Was he right to take the bet?

TOM:: He's right, but he's gonna lose. Because it sounded very good. Maybe he just wanted Bill Gates to feel good. I mean, the guy's probably got an ego as big as Cleveland. Cleveland? As big as Australia, maybe.

RAY: Maybe.

TOM:: And if the guy didn't fall for his little trick here, then Bill Gates might have lost a little of his self-esteem.

RAY: Well, anyway, Gates is gonna win his money.

TOM:: Yeah.

RAY: Unfortunately. Because it is going to happen, and it must happen.

TOM:: Mmmm?

RAY: Let's say out of those 1,100 people we take, for the sake of convenience, 1,024 of them. It's just a number I picked out of the air.

TOM:: Just a number you picked out of the hat by doubling 512.

RAY: And let's take that 1,024 people and make 512 pairs of people.

TOM:: Yeah. OK.

RAY: OK? And each one of those pairs will do a coin toss. Well, obviously, one is going to . . . one of them is going to win.

TOM:: Mmm-hmm.

RAY: So, we're going to have 512 winners.

TOM:: Yeah.

RAY: OK? And conveniently, we take those 512 and we divide them into 256 pairs now.

TOM:: That's a nice number too.

RAY: Isn't it amazing?

TOM:: Yeah.

RAY: And, of course, we're going to have 256 people flipping coins. We're going have . . .

TOM:: One hundred twenty-eight winners.

RAY: Son of a gun!

TOM:: Isn't that something?

RAY: And you do that nine times.

TOM:: Yeah.

RAY: And you're down to two people.

TOM:: Mmm-hmm.

RAY: And inevitably, one of them's going to win.

TOM:: Mmm-hmm.

RAY: So, of those people that played, you had two people that wound up doing it correct nine times, and one person who had to do it correct 10 times in a row.

TOM:: Right.

RAY: And Gates wins his money.

TOM:: And that was his bet.

RAY: He wins all the time, man! I'm getting sick of it!

TOM:: He's getting sick of it too.

RAY: Who's our winner?

TOM:: The winner is Mark Kime from Valparaiso, Indiana. And for having his answer selected at random from among the thousands of correct answers that we got, Mark is going to get a $25 gift certificate to the store at the Car Talk section of cars.com, and with that $25 gift certificate, he can buy 1-9/16 copy of "A Haircut in Horsetown," the Car Talk Puzzler book.

RAY: That book is still in print?

TOM:: That book is in print. "A Haircut in Horsetown"? Oh, sure. That's a million-seller.

[ Car Talk Puzzler ]