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Rotating Triangle

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

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Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

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Russian Cubes

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

Why 24?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

This problem is in two parts. The first part provides some building blocks which will help you to solve the final challenge. These can be attempted in any order. Of course, you are welcome to go straight to the Final Challenge without looking at the building blocks!

Click on any of the questions below to get started.

Question A

Question B

Question C

Question D