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## 'The Hair Colour Game' printed from http://nrich.maths.org/

Mrs Bunting's class was playing a game using interlocking cubes.
All the boys took a red cube and all the girls took a green
cube.

Then the children took a black cube if they had dark coloured hair
and a yellow cube if they had light coloured hair. They stuck their
two cubes together.

The pairs of cubes looked like this:

The children then got into four groups according to their pair
of cubes.

Can you explain what these pairs of cubes stand for?

Mrs Bunting showed them a way of recording the way they had
sorted themselves into different groups, called a tree
diagram.

At the bottom were all the pairs of cubes. Then they divided
into two branches. The red cubes went to the left and the green
cubes went to the right.

Then they divided into whether they had black cubes or yellow
cubes. Now there were four branches.

Here is the tree diagram:

The next day they did the same again except that this time, they
had three cubes each. As well as a having a green or red and a
yellow or black, they took a brown cube if they had brown eyes and
a blue cube if they had blue eyes.

How many different groups were there then? Can you draw the
new tree diagram?

What happens if no one had dark hair and blue eyes? How could
you show that?