### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# Beat the Drum Beat!

##### Age 7 to 11 Challenge Level:

This problem follows on from We'll Bang the Drum so you may like to try that one first if you haven't already.

Here are drums that can be placed on a wheel. As the wheel goes round, each drum beats.
Before you read any further, explore the interactivity by making some different rhythms.

In how many ways can you create a rhythm with a steady beat?
Explain how you have done this.
If there were 12 positions on the wheel, in how many ways would you be able to create a steady beat? How do you know?

Now place just three drums on the wheel to create a new rhythm.
What would happen if you played this rhythm backwards? Would it sound different?
Using three drums, make a rhythm which would sound the same forwards as it does backwards.
How many different ways can you do this using just three drums?

Now try creating rhythms which sound the same forwards and backwards with four drums.