The Raven's Hat: Fallen Pictures, Rising Sequences, and Other Mathematical Games

A magician hands over a (sorted) deck of cards to a person in the audience. The magician turns away and then asks the contestant to riffle shuffle the deck three times (an example of a riffle shuffle is shown in the picture on page 35). She further asks the contestant to cut the deck at a place of his choice: that is, she asks him to split the deck into two parts and place the top part below the bottom part. The contestant then looks at and memorizes the new top card and places it somewhere in the middle of the deck. Finally, he is again allowed to cut the deck. The magician looks at the deck, studies it for a few seconds, and then picks out one card by elevating it, as shown in the figure on the following page. 1 There is no sign that the magician was secretly overlooking the scene, and nobody from the audience has given a hint.