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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?

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

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

All in the Mind

Age 11 to 14 Challenge Level:

This is quite a difficult problem to imagine in your head. If you've tried very hard without success, then actually dangle a cube into some water.