Stack the Deck

Mar 20, 1999

RAY: Ha! We're back. You're listening to Car Talk with us, Click and Clack, the Tappet Brothers, and we're here to discuss cars, car repair and the new Puzzler.

TOM: I can hardly wait!

RAY: You can?

TOM: I can.

RAY: No, you can't. Here it is. Let's say you have two ordinary decks of playing cards, minus the jokers. So, you have a deck of 52 cards and another deck of 52 cards.

TOM: Same color?

RAY: Well, yeah. They're both -·the backs of them are red.

TOM: Red.

RAY: OK? And the other sides, the business sides...

TOM: Are the same.

RAY: Are all the cards, aces, deuces, queens, etc. You take them and you shuffle them up--mix them all up as best you can.

TOM: Both decks together?

RAY: Both decks. You shuffle them all up.

TOM: One hundred four cards.

RAY: There you go. And then you divide them into two equal piles. OK? So, you've got a pile of 52 on one side of the table, and a pile of 52 on the other side of the table. Are you with me so far?

TOM: Yeah, I can tell already this is going to be so bogus! I can tell already. I can just tell. I have no idea what the question is, but...

RAY: Well, I don't even know what the question is yet! All right?

TOM: Well, I can tell that too!

RAY: I don't know what the question is!

TOM: All right. So, I've shuffled 104 cards together, and I've split them back into two piles of 52 each, and I've got one pile here on my left, and one pile to my right.

RAY: OK. So you have pile A and pile 2.

TOM: A and 2, got it.

RAY: OK? What are the chances that the number of red cards in pile A equals the number of black cards in pile 2? That's part one of the question. And then part two of the question: how many cards would you have to look at to be certain of your answer?

Answer: 

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, ".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.

Get the Car Talk Newsletter