A magician invites me to do the following:
- Open a brand-new deck of playing cards and place it face down on the table.
- Count off the top 20 cards, turn them face up, and insert them at random into the remainder of the deck.
- Shuffle the deck thoroughly.
- Count off the top 20 cards and hand them to him under the table.
Now, after a period of mysterious activity under the table, he places his pack of 20 cards next to mine of 32. Using the dark arts, he says, he has arranged that both packs now contain the same number of face-up cards. We count, and they do. How has he accomplished this?