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Nine Colours

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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Muggles Magic

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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Cogs

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the cogwheel A as the wheels rotate.

Conway's Chequerboard Army

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

To reach target C you will need a counter on target B and a counter on target A to jump over it.

To reach target D you will need a counter on target C and a counter on target B to jump over it.