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
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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.)