Right, this is the starting position and this represents zero,
and we're going to have just two moves that are allowed, a twist and a turn.
So let's start by twisting.
This adds one so we're at one now; let's have another twist.
Another one takes us to two. Let's have a turn next.
This represents the negative of the reciprocal of the previous number.
So we were at two, we're now at negative 1/2.
Let's add one.
that means twisting so that takes us to 1/2.
Let's twist again a couple of times. That takes us to one and a half,
and now two and a half.
And let's change this into an improper fraction, to five halves,
before we turn.
Negative of the reciprocal of five halves
takes us to negative 2/5, so let's have a couple of twists.
That added one, that's 3/5
And let's have another add one, that's eight fifths.
Oh, let's have one more twist...
that's thirteen fifths, let's have a turn now.
We've now got them at negative 5/13.
I wonder whether they'll be able to disentangle themselves.
So the challenge is: Can they get back to zero?
"OK, we're at minus five thirteenths... shall we twist?"
So they've added one, that's taken them from -5/13 to 8/13
"...turn..."
Negative of the reciprocal takes them to -13/8.
"twist"
Add one takes them to -5/8
"twist"
Add one takes them to 3/8
"turn"
Negative of the reciprocal takes them to -8/3
"Twist"
Add one takes them to -5/3
"Twist" ... Add another one takes them to -2/3
"Twist"... Add one takes them to 1/3
"and turn"
Negative of the reciprocal takes them to -3
"Twist" ... -2 ... "Twist" ... -1... "And a twist!" ... and back to zero.
Well done! [applause]