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Marbles

Age 11 to 14
Challenge Level Yellow starYellow star
  • 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

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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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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.

Nine Colours

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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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