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

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

When Charlie retires, he's looking forward to the quiet life, whereas Alison wants a busy and exciting retirement. Can you advise them on where they should go?

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.

Explore the lattice and vector structure of this crystal.

A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

Can you describe this route to infinity? Where will the arrows take you next?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...