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 $t$.