What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
Start with the problem What Numbers Can We Make?
Think of a simpler problem:
If you choose $2$ from $3$ numbers you can always select $2$ numbers that add up to an even number. Why?