Copyright © University of Cambridge. All rights reserved.

## 'Beads' printed from http://nrich.maths.org/

## Beads

Three beads are threaded on a circular wire and are coloured either red or blue.

Can you find all four different combinations?

You now repeat the following actions over and over again:

- between any two beads of the same colour put a red bead
- between any two beads of different colours put a blue bead
- then remove the original beads.

Describe what will happen to each of the combinations.

**If you can see this message Flash may not be working in your browser**
**Please see http://nrich.maths.org/techhelp/#flash to enable it.**
### Why do this problem?

This

activity presents a very non-threatening challenge that could be used to get pupils thinking. It is one of those activities in which pupils will probably not have an instant idea of the solution and so encourage creative thinking.

### Possible approach

It would be good to use a white board displaying the interactivity for pupils to come and try out. This could lead quickly to some good classroom discussions.

### Key questions

Why do you think that?

Tell me about you thoughts?

What do you mean by (such things as "goes on and on")?

### Possible extension

Pupils encouraged to explore changing some of the numbers of beads. They could also change a rule slightly.

### Possible support

Some practical apparatus to make a system of beads of their own.