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
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube.
How many routes are there from A to B?
To add up all the permutations of all the 5 digit numbers
written using the digits 1, 2, 3, 4 and 5 just once each time. A
good way to tackle problems is to try simple cases and here you
might try 21 + 12 = 33 then try it with 3 digits and so on. Ong
Xing used the following method.
There are 5! numbers, and in each column of the sum each of the
digits 1, 2, 3, 4 and 5 appears 4! = 24 times. The sum of each
column is therefore 24(1 + 2 +3 + 4 +5) = 24 x 15 = 360.
The total sum is 360(1 + 10 + 102 + 103 + 104) = 360 x 11111 =
Joel used this even shorter argument. The number of permutations
is 5!, that is 120. The average is 3, so the total is 33333 x 120 =