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?

L-triominoes

Age 14 to 16Challenge Level
Look at the picture below showing different odd sizes of triomino.

Can you see a way to build round the red triomino to make the orange one?
To build round the orange one to make the grey one?
Can you continue to make a size $7$ triomino? And then a size $9$?