Card Trick
by Charles Geer in the
Arithmetic Teacher May 1992
Walk around the classroom and have students pick one card each from the deck. Ask them to be
sure that no one sees their card. Have them perform the following mathematical operations:
1. Write the face value of the card that you selected on a piece of paper. The aces and face cards have the following values:
Ace = 1, J = 11, Q = 12 K = 13.
2. Double the face value.
3. Add 3.
4. Multiply by 5.
5. If the card you selected is a club, add 1; a heart, add 3;
a diamond, add 2; or a spade, add 4.
6. Now tell me your answer and I will show you the card that you selected.
For the most dramatic results, have an oversized deck of cards (7" x 4.5"), ordered by
suit and value, for yourself. After completing the mental calculations listed below, you
instantly determine the card any student selected and then pull it out of your deck.
By mentally subtracting 15 from the final answer your student gives you, your two or three digit
answer tells you the face value and the suit of the card.
The digit(s) in the tens and hundreds place(s) tells you the face value of the card; you will have a number in the
hundreds place only when the card's face value is a ten, or a face card.
The ones digit tells you the suit of the card. A one in the ones place means that the suit of the card is a club,
a two indicates a diamond, a three indicates a heart, and a four indicates a spade.
I order my demonstartion deck with the clubs on top, then diamonds, then hearts, then spades -- Then I don't have to
memorize how the suits were ordered.
Why does this work?
1. Write the face value of the card that you selected on a piece of paper.
Let c = value of the face card.
2. Double the face value.
Then you get 2c.
3. Add 3.
Then you get 2c + 3.
4. Multiply by 5.
Then you get 10c + 15.
5. If the card you selected is a club, add 1; a heart, add 3;
a diamond, add 2; or a spade, add 4.
Let s = suit, so you now have 10c + 15 + s.
6. Now tell me your answer and I will show you the card that you selected.
Subtract 15 to get 10c + s.
The face value is in the tens place and the suit is in the units place.