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 pairs?
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 resulting numbers.
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 B? (No `backtracking' allowed, i.e. each move must be away from A towards B.)