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?
Four circles of diameter 1 unit fit easily enough in a square of side 2 , but what is the smallest square into which we can fit 3 circles of diameter 1 unit?