### 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?

# Cosines Rule

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

Why is the $60$ degree angle opposite the side of median length?

For the second part all you need is the cosine formula and some algebraic manipulation to get the required result.