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Three Cubes

Can you work out the dimensions of the three cubes?

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?

Marbles in a Box

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Painted Cube

Age 14 to 16
Challenge Level

How many vertices, faces and edges are there in a cube?

Where are the cubes with no faces painted?
Where are the cubes with 1, 2, 3, 4, 5, 6 faces painted?
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.
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NRICH is part of the family of activities in the Millennium Mathematics Project.