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.

  Segment BOC
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
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