Colouring The Cube
Probability
Level
4
Find the number of different ways of painting a cube by using a different colour for each face-from six available colours. (Any two colour schemes are called different if one cannot coincide with the other by rotation of the cube.)
The answer is 30.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
As rotations have to be avoided, it is best to start by fixing a colour on one of the faces so that all the other colours are placed in relation to this face. There are then 5! ways to place the other 5 colours in relation to this first colour. However, the first face has four sides so each combination of colours in relation to the first face will be repeated 4 times.
So the number of different ways is 5!/4 = 3 0 .