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?
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?
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?
This problem will feature in
Maths Trails - Visualising, one of the books in the Maths Trails
series written by members of the NRICH Team and published by
Cambridge University Press. Maths Trails - Visualising is due to be
published later this year, but for more details about the other
books in the series, please see our publications page .