Solution #14: Is the Rope Knotted?
We can assume without loss of completeness that at A the rope going from top
left to bottom right is on top. (If it is the other way a mirror solution is
produced which does not alter the probability.)
Then we have four equal possibilities. The segment BOC can be either on top
or underneath at each of the points B and C.
At B At C The rope is
On top On top Not knotted
On Top Under Not knotted
Under On top Knotted
Under Under Not knotted
Hence the chance that the rope is knotted is 1/4.
Source: Longley-Cook, L. H.
Categories: Reasoning, Probability, Topology