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In the popular game "Human Knot", a group of people stands in a circle and each person grabs another person's hands at random (one with the left hand and one with the right hand). The goal is to untangle the resulting knot without breaking the chain of hands (of course this is not always possible).

Has anyone ever rigorously studied this game? There is a number of questions one can ask here, like what is the probability of obtaining a trivial knot, the probability of obtaining a link of more than one circle, how complex on average is the resulting knot, what change if we adopt a more realistic probabilistic model (people don't usually grab hands uniformly at random) etc.

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