THE TRICK OF 7, 11, AND 13

Ask a friend to pick any three-digit number. Tell him or her to multiply the number by 7, then 11, and then 13 on a calculator. Before they have a result, you already will know the answer.

Let’s see how this works. Imagine your friend picks 123. You can instantly say the final result is 123,123. Or if your friend picks 479, you know the answer is 479,479.

The pattern is very simple so you can only do this trick once. The trick is that a number ABC multiplied by 7, then 11, then 13 will be ABC, ABC as a six-digit number.

Proof

Note that 7 x 11 x 13 = 1001. When you multiply ABC by 1001, that is the same as multiplying by (1000 + 1). Multiplying by 1000 shifts the number ABC by three spots to get ABC, 000. Then we multiply by 1 and add the result, which means adding ABC to the number again. The final result is ABCABC as a six-digit number.

EXERCISE

Attempt these simple questions