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?
Six points are arranged in space so that no three are collinear.
How many line segments can be formed by joining the points in
Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in
every possible order to give 5 digit numbers. Find the sum of the
The diagram shows a skeletal view of a 2 by 2 by 2 cube with one
route 'down' the cube.
How many routes are there on the surface of the cube from A to
(No `backtracking' allowed, i.e. each move must be away
from A towards B.)