### Why 24?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

### Factoring a Million

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

### Fac-finding

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

# A Biggy

##### Age 14 to 16 Challenge Level:

Find the smallest positive integer $N$ such that ${N\over 2}$ is a perfect cube, ${N\over 3}$ is a perfect fifth power and ${N\over 5}$ is a perfect seventh power.