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More Marbles

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

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Rolling Triangle

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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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.


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

I start with 3 marbles, one red, one green and one blue.
I can trade any one marble for two others, one each of the other two colours.

Is it possible to make a number of such trades and end up with five more blue marbles than red?
I don't care how many green marbles I have at the end.

After this problem you may like to take a look at More Marbles