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
Chin Siang from Tao Nan School, Singapore
solved this problem using a Pascal's Triangle method.
You are only allowed to move on the surface of
the cube and only in the directions of the arrows shown in the
sketch. (You might like to mark out a cube and put arrows on all
the line segments and mark the numbers of routes for yourself
before reading on).
How many ways can you get to each `junction
point'? Look at the arrows that go towards that point and consider
where you might have come from to reach it. To get the number of
routes to that point you add up the numbers at the other ends of
the segments which have arrows going towards it.
The numbers on the sketch give the total
number of different routes to each point. So there are 54 routes
from A to B. Can you see the