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?
Can you work out the dimensions of the three 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?
This problem features in Maths Trails - Working Systematically, one of the books in the Maths Trails series written by members of the NRICH Team and published by Cambridge University Press. For more details, please see our publications page
Printable NRICH Roadshow resource.