Puzzle Archive 

4. Repetition... Choose any 3digit number and repeat it to get a 6digit number. For example, if you start with 123 then we have 123123. Divide by 13
Try this for several starting numbers. What do you notice and can you explain why it happens?
Scroll down the page for the answer.
The result is the number that you started with. Note that 7 x 11 x 13 = 1001. If you multiply your 3digit start number by 1001 you have your 6digit repetition. Dividing by 13, 11 and 7 is just the opposite of this, so you end up where you started.
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