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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

Here is a solitaire type environment for students to experiment with. It requires forward planning and logical thinking.

The narrator Christopher in the novel The Curious Incident of the Dog in the Night-time remarks that Conway's soldiers is "a good mathematics problem to do in your head when you don't want to think about something else because you can make it as complicated as you need to fill your brain by making the board as big as you want and the moves as complicated as you want" (Mark Haddon 2003).

If students have enjoyed this problem they may be interested in reading Mathematical mysteries: The Solitaire Advance and Conway's Angels and Devils Game