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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?

Areas and Ratios

Do you have enough information to work out the area of the shaded quadrilateral?

Network Trees

Age 14 to 18
Challenge Level

When drawing trees with 7 vertices, you might find it helpful to start by working out what the sum of the degrees of the 7 vertices must be.