I hand you an ordinary deck of 52 cards. You inspect and shuffle it, then choose five cards from the deck and hand them to my assistant. She looks at them and passes four of them to me. I name the fifth card. At first this appears impossible. The hidden card is one of 48 possibilities, and by passing me four cards in some order my assistant can have sent me only 1 of 4! = 24 messages. How am I able to name the card? Part of the secret is that my assistant gets to choose which card to...