Thurston asked for the maximal number of non-hyperbolic Dehn fillings on a one-cusped hyperbolic 3-manifold, and conjectured that the maximum is 10 which is only achieved by the figure eight knot complement. It's now been shown that the maximum is 10 by Lackenby-Meyerhoff, but I've also shown that there is an algorithm which will determine the finitely many manifolds with $>8$ exceptional Dehn fillings.
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