### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

### 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?

# Iffy Logic

##### Stage: 4 and 5 Challenge Level:

Thanks to Rushaan and Spencer from Cape Academy, Western Cape, South Africa who sent us the most complete solution. The full solution is:

Interestingly, if $n, m$ are positive whole numbers (as stated in the question), then $n> 0$ is always true (a tautology). So, we can in fact correctly write $n> 0$ IF [Any of the statements]