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?

Three Cubes

Can you work out the dimensions of the three cubes?

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?

Twelve Cubed

Stage: 3 and 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

A wooden cube with edge length $12$cm is cut into cubes with edge length $1$cm. What is the total length of all the edges of all these centimetre cubes?

If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.