Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# The Hair Colour Game

Ed from St Peter's College gave a good solution to the problem:

The first cube (or pair of cubes) means a boy with dark hair, the second cube is a boy with light coloured hair, the third is a girl with dark hair and the fourth is a girl with light coloured hair.

The next day there were eight groups because they added eye colour cubes.

If there was no one with dark coloured hair and blue eyes, you could still place it on the diagram, to show all the possibilities.

Daniel and Theo sent a clear and colourful tree diagram which you can see here.

Arjun from Vidyashilp Academy thought about the number of groups you would end up with for more cubes. He says:

For $1$ cube combination there are $2$ possibilities = $2^1$

For a $2$ cube combination there are $4$ possibilities =$2^2$

So, for a $3$ cube combination there are $8$ possibilities =$2^3$

Thus I can say that the total number of combination are $2^n$ where n is number of cubes.

Well done to everyone!

## You may also like

### Sponge Sections

### Plaiting and Braiding

### Celtic Knotwork Patterns

Or search by topic

Age 7 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Ed from St Peter's College gave a good solution to the problem:

The first cube (or pair of cubes) means a boy with dark hair, the second cube is a boy with light coloured hair, the third is a girl with dark hair and the fourth is a girl with light coloured hair.

The next day there were eight groups because they added eye colour cubes.

If there was no one with dark coloured hair and blue eyes, you could still place it on the diagram, to show all the possibilities.

Daniel and Theo sent a clear and colourful tree diagram which you can see here.

Arjun from Vidyashilp Academy thought about the number of groups you would end up with for more cubes. He says:

For $1$ cube combination there are $2$ possibilities = $2^1$

For a $2$ cube combination there are $4$ possibilities =$2^2$

So, for a $3$ cube combination there are $8$ possibilities =$2^3$

Thus I can say that the total number of combination are $2^n$ where n is number of cubes.

I wonder how we know this for certain? Could you convince us that this is always the case, Arjun?

Well done to everyone!

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

This article for students gives some instructions about how to make some different braids.

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.