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?
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
How many tricolour flags are possible with 5 available colours such
that two adjacent stripes must NOT be the same colour. What about
By these rules NRICH can
at first change to RNICH but not to RINCH. What are the other
orders of the letters of the word NRICH that can be obtained in
just one change of this sort?
The following example shows very simple 'bell music' starting
with a round and ending with a round of 4 bells, showing 8 of the
24 possible permutations, or orders.
Can you find the changes so that, starting and ending with a
round, all the 24 possible permutations are rung once each and only