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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:
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: