Stacking Two Decks
RAY: Here’s how you solve it. 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. Take a black card from pile B and donate it to pile A, and therefore you have 51 and one, and 51 and one, no matter how you do this.
TOM: And part B of the question: How many cards do you have to look at to verify your answer?
RAY: None! Who's our winner this week?
TOM: Our winner this week is Dominic Matranga from Mobile, Alabama. Congratulations, Dominic!
[ Car Talk Puzzler ]