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
Look at a die. Had you noticed before that 1, 2 and 3 are
opposite 6, 5 and 4 respectively so that opposite faces add to
I'll call a die which has this property a standard die.
I don't know when this standard convention was adopted, but I
know that if you make standard dice by writing 1, 2, 3, 4, 5, 6 on
blank cubes you will find there are 2 and only 2 different standard
Can you prove this
A mathematician friend from New Zealand, Prof Derek Holton,
tells us that one of the standard dice is used in the western world
and the other one is used in the east. Can any one confirm this
with an example?
Suppose we relax the condition that opposite faces sum to 7.
How many different dice can we