### Mathematical Card Tricks

Here is a mathematical card trick taken from "Mathematics Magic and Mystery" by Martin Gardner (Dover books, pp 7):

A spectator shuffles the deck and places it on the table. The magician writes down the name of a card on a piece of paper and places it face down without letting anyone see it.

12 cards are dealt on the table, face down. The spectator is asked to touch any four. The touched cards are turned face up. The remaining cards are gathered and returned to the bottom of the deck. Assume that the picked 4 cards are 3,6,10 and a King. The magician states that he will deal cards on top of each four in the following way.

If the card is 10 or any court card, do not deal anything on them.

If the card is not the above, deal a number of cards till they count to 10. For instance, if the card is 3, deal 7 cards by counting: 4,5,6,7,8,9,10. if the card is a 6, deal 4 cards counting: 7,8,9,10.

The values of the original 4 cards are added. In this case 3+6+10+10=29. The spectator is handed the pack and asked to count to the 29th card from the top. This card is turned over. The magician reads his prediction and discovers it the chosen card.

Using only sec 1 algebra, can you figure out how this is done?

## 3 Comments:

so... whats the answer to this card trick?

The magician saw the last card of the deck, which is the 52th card. When we remove 12 cards from the top of the deck, the 52th card becomes the 40th card. If I let A, B, C and D be the four face-value of the cards. Then when I remove the number of cards to deal on the 4 cards, then I am removing 10 - A + 10 - B + 10 - C + 10 - D cards from the top of the deck. When I total up of A, B, C and D, and remove the sum of A, B, C and D, I am essentially asking for the 40th card.

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