### Doodles

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

### Russian Cubes

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

### Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

# Mod 3

##### Age 14 to 16Challenge Level

Prove that if $a^2+b^2$ is a multiple of $3$ then both $a$ and $b$ are multiples of $3$.