Or search by topic
More Twisting and Turning printable sheet
This problem follows on from Twisting and Turning in which twisting has the effect of adding 1 and turning transforms any number into the negative of its reciprocal.
It would be nice to have a strategy for disentangling any tangled ropes...
I wonder if it is always possible to disentangle them...
Choose a fraction to start from.
From your chosen fraction, can you find a sequence of twists and turns that get you back to zero? Remember, twisting: x \mapsto x+1
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...