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All in the Mind

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. 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?

Noughts and Crosses

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the interactivity below to get a feel for the problem.

Clicking on a face gives a layer (e.g. clicking on one of the darkest faces selects a horizontal layer), then clicking on either a face or a corner star gives a winning line.
For long diagonal winning lines click directly on a corner star (hover on one of the vertices of the large cube to reveal a star).

Full screen version.

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