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
Sarah Dunn, Madras College, St Andrew's, Scotland and Soh Yong
Sheng, Raffles Institution, Singapore both solved this in the same
way. You write the word EUROMATHS by starting at the top left hand
corner and taking the next letter by stepping one step down or one
step to the right in this array.
We draw a grid denoting the number of moves possible to reach
each place. The number of possible routes are calculated by adding
the number of the gridplace on the left and top, and if it is on
the extreme left or top then there is only 1 route to get there.
The number added will be correct as the square can only be accessed
through these squares. There are altogether 70 possible ways.
Can you generalise this result to a 6 by 6 square, or a 7 by 7
square ... or an n by n square? Have you seen this pattern before?
You may like to try a 6 by 6 array written in a slightly different