by Bill Graham

12,345,679 x 9 is 111,111,111. Multiply the original number by nine times the desired digit. If you want all fours, multiply 12,345,679 by 36 (4 x 9).

The puzzle from last time asked you to choose any random three-digit number. For example, use 347. Enter it twice on your calculator making the six-digit number 347,347. If you divide it by seven, do you get a remainder? The answer is 49,621 with no remainder. Then divide that answer by 11 and check for a remainder. Finally, divide that answer by 13 and check for a remainder. There are no remainders, and the answer is the three digit number you started with, that is, 347. If you try this same procedure starting with any other three digit number, the answers will always be whole numbers (no remainders), and the final quotient will always be the number you started with. How come?

If you can divide a number evenly by seven, 11 and 13, that means that they are factors of that number. It happens that seven times 11 times 13 equals 1,001 or 1,000 plus one. If you multiply a number by one, you get the same number for an answer. If you multiply a number by 1,000, the original digits move three places to the left. Therefore, if you create a six-digit number by repeating two three-digit numbers, it always will be evenly divisible by seven, 11 and 13.

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