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All in the Mind

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

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Painting Cubes

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

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Boxed In

A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

Tic Tac Toe

Age 11 to 14 Challenge Level:
The ideas in this problem have been expanded and made into another, more detailed investigation. See Marbles in a Box.
In the game of Tic Tac Toe (i.e. noughts and crosses) there are 8 distinct winning lines.

Investigate how many distinct winning lines there are in a game played on a 3 by 3 by 3 board, with 27 cells.

A winning line connects 3 cells.

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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