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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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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?

Cuboids

Age 11 to 14 Challenge Level:

It may be simpler to focus on just three faces (the three different faces), rather than on all six.

This net of a cuboid may help.

Try to be systematic:
if the height is $1$, what are the possible combinations for the width and depth?
if the height is $2, 3, 4$... what are the possible combinations for the width and depth?