A beautiful conceived trick, using three small objects, was marketed by Bob Hummer in 1951 under the title "Mathematical Three-Card Monte". Although Hummer's description involved three playing cards, the effect is applicable to any three objects.
The three objects are placed in a row on the table, their positions designated as 1,2,3. These numbers refer not to the objects, but to their positions. The magician turns his back. The spectator now switches the position of any two objects, calling out the numbers of the two positions. Thus if he switches the objects in positions 1 and 3 he calls out "1 and 3". He continues switching pairs of objects as long as he wishes, always calling out the numbers with each change. When he tires of doing this, he pauses and thinks of any one of the three objects. Then he switches the position of the other two without telling the magician the positions involved in the switch. After this is done, he goes back to switching pairs at random, each time calling out the positions being switched, and continues until he tires. The magician turns around and immediately points to the chosen object!
Method: While your back is turned, you can make use of your hand as a calculating device. Three of your fingers are designated 1,2,and 3. Before turning your back, note the position of any one object. Let us assume the three objects are a ring, pencil, and a coin, and that you observe that the ring is in position 1. Place your thumb against the finger you are calling position 1.
As the spectator calls out switches to you, your thumb moves from finger to finger following the position of the ring only. Thus if the first switch invloves the 1 and the 3, you move your thumb to finger 3. But if the switch involves the 2 and the 3, the ring is not involved, so you do nothing, keeping your thumb on finger 1.
After the spectator has thought of an object and made his secret switch of the other two, he begins calling switches again. You continue to follow the ring, even though his secret switch may have changed the position of the ring.
At the conclusion of the switching, your thumb wil be resting against a finger. Let us say it will be touching finger 2. Glance at position 2 on the table. If the ring is in this position, you know immediately that he thought of the ring, because its position has remained unchanged throughout the trick.
If the ring is not in the position indicated by your thumb, then glance at the other two objects. They will naturally be the ring and another object. The object that is NOT the ring will be the one thought of.
The method is delightfully simple. If you practice with the effect for a while you will soon discover why it works. Actually, the problem is one of elementary logic, with the fingers used a simple logic machine.
The trick is extremely effective when done with three face down cards. It is only necessary for you to have a secret mark on the back of one of the cards, such as a pencil dot or a slight crimp of one corner. This is the card that you will follow with your fingers as your back is turned. When it is time for the spectator to think of one of the cards, he must peek at its face and remember it. When you turn around you can immediately turn over the chosen card, even though the faces are down.
An excellent dinner table variation is to let the spectator, while your back is turned, conceal a match folder under one of three inverted coffee cups. Ask him first to switch the positions of the two coffee cups without telling you which cups they are. He then switches at random by sliding the cups along the table, each time calling out the two positions involved. You turn around and immediately lift the cup covering the folder, even though the spectator himself may have lost track where the folder is. To do this, it is necessary to find a small flaw or identifying mark on one of the cups so that you can follow this cup with your fingers as previously explained.
If spectators are in position to observe you while your back is turned, put your hands in your pockets. In this way the use of your hands as a calculating device will not be noticeable.
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