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You could have a go at
before trying this problem.
This is a very practical activity - you might like to use some
musical instruments, for example a drum or a triangle, rather than
using your hands and parts of your body.
Begin a rhythm: clap, clap, click (your fingers), clap, clap,
click, clap, clap, click, clap, clap, click ...
What will you be doing on the $15$th beat?
How do you know this without actually doing it?
What will you be doing on the $20$th beat?
Again, explain how you can predict this.
How about on the $99$th beat?
What would you be doing on the $100$th beat?
If there is someone else with you, ask them to come and join in. If
you're on your own, it doesn't matter, you'll just have to imagine
that someone else is there.
You and your friend are going to both start a different rhythm at
the same time.
You will do clap, clap, click, clap, clap, click ... as you did
Ask your friend to do click, clap, clap, click, clap, clap, click,
clap, clap ...
Have a go so that you get a steady rhythm going.
If you both start at the same time, when will you both click your
fingers at the same time?
Are there other ways that you could have clapped and clicked for
this to be the case?
How could you change your rhythms so that you do click at the same
How could you predict when this was?