### 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?

### N000ughty Thoughts

How many noughts are at the end of these giant numbers?

# Euler's Officers

##### Stage: 4 Challenge Level:

See Teddy Town

You can construct orthogonal Latin squares $S^{i,j}$ and $T^{i,j}$ of prime order $m$ where the $S^{i,j} = si + j \pmod m$ and $T^{i,j} = ti + j \pmod m$ and $s$ not equal to $t$.