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# Marbles

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

## You may also like

### More Marbles

### Rolling Triangle

### Nine Colours

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Age 11 to 14

Challenge Level

- Problem
- Student Solutions

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

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?

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.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?