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Beat the Drum Beat!

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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.
How about five drums?
How could you tell just by looking at the arrangement of drums whether it would sound the same when the wheel rolled forwards or backwards?

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