## Untangling untanglables.

I conjecture (i.) a stochastic “mechanical algorithm” that untangles untanglable strings in finite iterations, (ii.) a class of heuristics that reliably reduce stochasticity and increase efficiency of this algorithm, and furthermore (iii.) a subclass of such heuristics that renders the algorithm superior in average- and worst-case time-complexity to any algorithm that must analyze a topological relationship between two points on the string.

Let there exist a function, *pull(a, b, F)*, where *a* and *b* represent points on a string (say, as scalar displacements from a common origin on the string) and *F* represents a force, that simultaneously pulls an untanglable string by force *F* at *a* and *-F* at *b*, until there is no movement. I conjecture that for any untanglable string there exists a scalar *f* such that invoking *pull* on a random *a*, random *b*, and *F** > f* untangles the string in a finite number of iterations.

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