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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?

# Special Sums and Products

##### Age 11 to 14Challenge Level

The numbers 4 and 12 have a special property.

$$\begin{eqnarray} 4 + 12&= 16\\ 4 \times 12&= 48 \end{eqnarray}$$
and 16 is a factor of 48.

Find some other examples of pairs of numbers such that their sum is a factor of their product.

What condition must exist for pairs of numbers to be related in this way?