You may also like

problem icon

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?

problem icon

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?

problem icon

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?

Painted Cube

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

Imagine a large cube made up from $27$ small red cubes.

Imagine dipping the large cube into a pot of yellow paint so the whole outer surface is covered, and then breaking the cube up into its small cubes.

How many of the small cubes will have yellow paint on their faces?
Will they all look the same?

If you can see this message Flash may not be working in your browser
Please see to enable it.

Now imagine doing the same with other cubes made up from small red cubes.
What can you say about the number of small cubes with yellow paint on?

Click here for a poster of this problem.