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Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

### Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

# Producing Zeros

##### Age 11 to 14 ShortChallenge Level

You could write this problem out as $1\times3\times4\times6\times7\times8\times9\times(2\times5)\times10$. The product of the first seven numbers is not a multiple of ten, but the last part gives us $10\times10$ so the overall product must be a multiple of $100$, but not a multiple of $1000$. So the answer is two zeros.