I've read that the proof of the superflip requiring a minimal solution of 20 moves relied heavily on the symmetry of the position and is purported to be quite clever. I just found it in the cube lovers archive, but haven't had a chance to read it in depth, yet.

Has anyone posited other positions that could be proved to require 20 moves similarly? Has it be postulated that the superflip could be the only position that requires 20 moves?


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Here you get more information

Here you get more information:

All known 20s

In addition to the 32,625 symmetrical distance-20 cubes that Herbert links to, there are an additional 4,336 unsymmetrical known distance-20 cubes. The 32,625 are exhaustive in symmetrical cubes; the 4,336 are not exhaustive (and I expect there are more unsymmetrical distance-20 cubes than symmetrical distance-20 cubes; they are just a bit harder to find.)

Together these positions account for 1,445,274 distinct cube positions (when not reduced by symmetry or antisymmetry).