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Using some new ideas, techniques, and computer programs, we
have successfully found optimal solutions to all symmetric positions
of Rubik's cube in the face turn metric (FTM). Furthermore we have
maneuvers for 1,091,994 20f* (positions whose optimal solutions
have 20 face turns) cubes and proven that there are no symmetric
21f* cubes. So if there are any cubes at depth 21 then these must
be unsymmetrical. To the best of our knowledge, at the start of this
investigation in January, only a few such positions were known (less
than a dozen). Expressions for all these cubes can be found on
Rokicki's home page http://tomas.rokicki.com/all20.txt.gz.