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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?

Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Cross-country Race

Age 14 to 16 Challenge Level:

Eight children enter the autumn cross-country race at school.
How many possible ways could they come in at first, second and third places?

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