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Efficient Cutting

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

Partially Painted Cube

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

How many different ways could you paint two faces of a cube? Or three? Or four?
Can you work out a way of counting how many cubes are left unpainted in each case?