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# All Tangled Up

Here is an interactive tool you can use to try out your ideas. Experiment with the sequences suggested in the problem (remember, $T$ is Twist and $R$ is Turn). What do you notice about the fractions that emerge?

To prove relationships generally, it may be helpful to use algebra.

For the final part of the task, it's useful to work backwards.

Consider the alternative function that maps $x \mapsto x-1$, an inverse twist.

Choose a fraction, and find a way to use the inverse twist and the turn functions to get back to zero.

How does that help you get from zero to your chosen fraction using the original twist and turn functions?

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Age 14 to 18

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- Problem
- Getting Started
- Student Solutions
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Here is an interactive tool you can use to try out your ideas. Experiment with the sequences suggested in the problem (remember, $T$ is Twist and $R$ is Turn). What do you notice about the fractions that emerge?

To prove relationships generally, it may be helpful to use algebra.

For the final part of the task, it's useful to work backwards.

Consider the alternative function that maps $x \mapsto x-1$, an inverse twist.

Choose a fraction, and find a way to use the inverse twist and the turn functions to get back to zero.

How does that help you get from zero to your chosen fraction using the original twist and turn functions?