Magic Card Tricks

Interesting article in the New York Times today about how people to this day still do not know how magician David Berglass did his "Any Card At Any Number" trick. In this trick, a magician asks a person or two to name a card (e.g. Queen of Hearts) and a number (e.g. 37) and then in a variety of ways produce a deck where that card appears at that order in the deck. The supposed standard way to do the trick is for the magician to manipulate the cards in some way but Berglass does his trick by never touching the cards. He can even do the trick impromptu when you visit him by leading you to a deck of cards somewhere in the room or from his pocket that has the card in the correct place. Now, I have no idea how he or anyone does this trick but one way to do the trick is to use "full enumeration", i.e. hide decks where every possibility is accounted for and then the trick is to remember which deck has that choice. So then the question is how many decks would you need? Well the minimal number of decks is 52 because a particular card could be in one of 52 positions. But how many more decks would you need? The answer is zero. 52 is all you need because for any particular arrangement of cards, each card is in one position. Then all you do is rotate all the cards by one, so the card in the first position is now in the second position for deck 2 and 52 moves to 1 and so on. What the magician can do is to then hide 52 decks and remember the order of each deck. In the article he picked the reporter's card to within 1 but claimed he may only be able to do it to within 2. That means he's hiding the decks in groups of 3 and 4 say and then points you to that location and lets you choose which deck.