We'll give you any number with just four squares

Pierre Fermat, who lived in Toulouse, wrote in 1638 that any number can be made by any one of these ways:


1. Add three triangle numbers.

These are the triangle numbers:

2. Add four square numbers.

These are the square numbers

49   36   25   16   9   4   1   0

3. Add five pentagonal numbers.

 These are the pentagonal numbers:

 4. Add six hexagonal numbers.

These are the hexagonal numbers:

We had a go at the easiest one: making lots of numbers with four square numbers. We all picked a number, and then thought hard about which combination of squares would make it (Zero is a square number too.)