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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!

### Have You Got It?

Can you explain the strategy for winning this game with any target?

### Counting Factors

Is there an efficient way to work out how many factors a large number has?

# Even So

##### Age 11 to 14 Challenge Level:

Find some triples of whole numbers $a$, $b$ and $c$ such that $a^2 + b^2 + c^2$ is a multiple of 4. Is it necessarily the case that $a$, $b$ and $c$ must all be even? If so, can you explain why?