Math Delights

Trick courtesy of Shawn Gettler (tvtom at chelmsford.com)
adapted by Nancy Blachman, MathDelights.org

This simple card trick impresses audiences. The magic is in counting the cards accurately. You don't need to set up anything in advance. Just shuffle the deck and you are ready to start.

1. Ask a volunteer to pick up the top card and place it face up on the table. Each card represents a number — Ace is 1, Jack is 11, Queen is 12, King is 13, and the rest have their face value.
2. State its number and then count onto it enough cards to reach 13. For example, if the card is a Jack, say "Eleven..." and then deal 2 cards.
3. Repeat Steps 1-3 until 13 cannot be reached with the remaining cards. Set these aside (if the count works out evenly, don't worry).
4. Flip over all the stacks and rearrange them so you are unlikely to know which pile is which.
5. Have a volunteer choose 3 piles. Remove all of the other piles and add them to the cards (if any) remaining from step 3.
6. Pick up the pile of cards remaining from steps 3 & 5, count off 10 cards and set them aside.
7. Have a volunteer choose 2 of the remaining 3 piles and turn the top cards face up on these 2 piles.
8. Add together the values of the two face-up cards, count out their sum from the cards you're holding from step 6 and set them aside.
9. Have a volunteer count the number of cards left in your hand.
10. Ask a volunteer to flip over the top card on the remaining pile. The number of the card is equal to the number of cards left in your hand (determined in step 9), if you performed this trick as described.

How Does This Trick Work?

Improve Count 'Em Up?

Create a variation of this card trick that doesn't require that the magician count off 10 cards and set them aside (step 6). In other words, design the trick by having a volunteer select a different number of piles and/or place a different number of cards in each pile. For example, how can you redesign the trick so that you end up using 51 cards if the top card of the remaining pile in step 10 has an Ace on top?