# An Arithmetic Magic Trick

Think of a 2-digit integer. Subtract from the number the sum of its digits and find the result in the table below. Note that each cell of the table contains a number and a geometric shape. Concentrate hard on the shape that shares a cell with the result of your calculations. When ready, press the "Check it!" button ...

What if applet does not run? |

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Copyright © 1996-2018 Alexander Bogomolny

## An Arithmetic Magic Trick

What if applet does not run? |

Let the number you thought about be 10a + b. Subtracting the digits gives

(10a + b) - (a + b) = 9a

which is always a multiple of nine. If you look carefully at the table, you will not fail to notice that all multiples of 9 are in cells with the same shape. This is the shape you are to notice and concentrate on.

(Without the computer, this property of the decimal system can be used as a similar one is employed in the Math Telepathy trick: after you calculate the result and tell me one of the digits, I magically produce the other digit of that number.

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Copyright © 1996-2018 Alexander Bogomolny

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