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 the answer to last week's Puzzler. Here it is. I'm sure you'll remember it in a minute.

TOM: I remember it already.

RAY: You do?

TOM: Yeah.

RAY: Cool. Let's say you have two decks of playing cards, 52 cards each, regular cards.

TOM: Yeah.

RAY: And you put both decks together and shuffle them up.

TOM: Got it.

RAY: So, you've got 104 cards all shuffled together. Then you split them back into two equal piles. Well, you haven't looked at them now, in the traditional manner. You just counted them out so you have a pile of 52 on one side--we'll call that pile A--and a pile of 52 cards on the other side, and they're all mixed up.

TOM: Pile 2.

RAY: Pile 2. Here's the question: What are the chances that the number of red cards in pile A equals the number of black cards in pile 2? And question 2, or B: How many cards do you have to look at to be sure of your answer?

TOM: Yeah!

RAY: Well?

TOM: I happen to know the answer! It's·

RAY: Imagine! Go ahead.

TOM: The chances are: one!

RAY: Yeah, oh, 100 percent.

TOM: One hundred percent.

RAY: Imagine if you·let's say by some luck, you shuffled up all these cards and all the red cards wound up in one pile, we'll call that pile A. And for simplicity's sake, we'll call the other pile pile B, and all the black cards wound up in that. Then you would say, well, certainly the number of red cards in deck A, or pile A, equals the number of black cards in pile B. Now, I ask you to construct a scenario where it wouldn't be the case, always.

TOM: How about one and 51?

RAY: Exactly. Take a card out of pile A and donate it to pile B--but when you do that, you must reciprocate.

TOM: Right.

RAY: You must take a black card from pile B and donate it to pile A, and therefore you have 51 and one, and 51 and one, and no matter how you do this, if you wind up with 52 cards in each pile·this is like, do you remember the Puzzler years ago, where you had a thing of water and a thing of wine, you took a teaspoon of wine and put it in the·

TOM: Oh, that one!

RAY: Same thing.

TOM: [WHISTLES] And part B of the question: How many cards do you have to look at to verify your answer?

RAY: None.

TOM: None.

RAY: Not a one.

TOM: Isn't that a great·

RAY: You think it's great because you got the answer. If you hadn't gotten the answer, you'd be all over this thing.

TOM: For one thing, the answer was a given, because when you said, "What are the chances..."

RAY: I gave it away, you mean?

TOM: You gave it away. I mean, what are the chances. Are you expecting someone to say, "Twelve out of 49"?

RAY: Yeah.

TOM: Or, "Point 2375"?

RAY: Yeah.

TOM: Yeah. Everyone who would have thought that that was the answer would have given up, and the only ones who would not have given up would be the ones who said the answer has to be either zero or one.

RAY: OK, that's true. Anyway, who's our winner this week?

TOM: Our winner this week is Dominic Matranga. He's from Mobile, Alabama, and for having his correct answer chosen from among the thousands of correct answers we got, Dominic is going to win a $25 gift certificate to the Car Talk Shameless Commerce Division, with which he can...

[ Car Talk Puzzler ]