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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?

# Cogs

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

A and B are two interlocking cogwheels having p teeth and q teeth respectively where $$3\leq q\leq p \leq 12$$

One tooth on B is painted red. Find the values of p and q for which this red tooth on B contacts every gap on the cogwheel A as the wheels rotate.