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Tic Tac Toe

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Nine Colours

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

If you have 27 small cubes, 3 each of nine colours, can you make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour?


In the picture, the top face and the left face have one of each colour.

Unfortunately the third face has two greens, two blacks, no reds and no browns, so this is not a valid solution.

You might like to explore this problem using cubes. If you don't have any cubes, you could record your work on squared paper by drawing and colouring each layer.




This problem features in Maths Trails - Working Systematically, one of the books in the Maths Trails series written by members of the NRICH Team and published by Cambridge University Press. For more details, please see our publications page .

Printable NRICH Roadshow resource.

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