The magician’s assistant asks an audience member to randomly choose 5 cards from a deck without looking at them. The assistant returns one of the cards and hands the remaining four cards to the magician, who looks at them and tells what the fifth card is.

There is no sleight of hand. There is a way for the assistant to arrange the four cards so as to provide a code for determining the other card. Since this is a little tricky, I will give the following hint. The returned card is not chosen randomly. In some cases, there is only one card that can be selected. Think about the suits of the cards.