### Adding All Nine

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?

# Find from Factors

##### Age 11 to 14 ShortChallenge Level

21  and  35 are factors
so 3, 7 and 5, 7 are prime factors

If 3, 5 and 7 are the only prime factors then the factors are:
1, 3, 5, 7,
15, 21, 35, and the number itself

The number itself = 3$\times$5$\times$7 = 105

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.