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More Twisting and Turning

Age 11 to 16
Challenge Level

Rachel thought through the problem like this:

For fractions $-\frac{n}{2}$

twist until reaching $\frac{1}{2}$, then turn to get $-2$, and twist twice.

For fractions $\frac{2}{n}$, start by turning once, then repeat as above.

Ved from WBGS in the UK sent in a more general solution:

If the entangled fraction is positive, then rotate,

If it is negative, then twist,

Repeat until the entangled fraction is 0

Ved also wrote a program which takes the numerator and denominator of the tangled ropes as inputs, follows this procedure, and writes a sequence of Ts and Rs to tell you how to untangle the ropes: