Challenge Level

Twisting has the effect of adding 1: $$x\mapsto x + 1$$ Turning transforms any number into the negative of its reciprocal: $$x\mapsto -\frac{1}{x}$$ Starting at zero, these five moves: Twist, twist, twist, turn, twist

produce:$$0, 1, 2, 3, -\frac{1}{3}, \frac{2}{3}$$

Can you continue from there and then return to zero? You might find it helpful to record each step in a table.

The team use a strategy to help them get back to zero.

Can you figure out how they decide when to stop twisting and start turning?