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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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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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Tic Tac Toe

In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?

Boxed In

Age 11 to 14 Challenge Level:

The diagram shows a rectangular box (a cuboid).
The areas of the faces are $3$, $12$ and $25$ square centimetres.
What is the volume of the box?


The areas of the faces of a cuboid are p, q and r. What is the volume of the cuboid in terms of p, q and r?