### 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?

### 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?

# Nine Colours

##### Stage: 3 Challenge Level:

Each colour must appear on all six faces of the larger cube.

Small cubes can be placed
• at the corners of the large cube,
• on the edges of the large cube,
• in the middle of the faces of the large cube,
• or at the very centre of the large cube.
How many faces of the small cube will be visible in each of these different positions?

A small cube will need to go in at the very centre of the larger cube.
Where will the other two small cubes of the same colour go?