Stack the Deck
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.
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?
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[ Car Talk Puzzler ]