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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?

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?

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?