I have now running (for about 60 days already) a program that implements
Kociemba's algorithm to solve the cube. It tries to solve random
configurations and stops when a solution of 20 turns or less is found.
The random configurations are created by doing 100 random turns.
Until now, with 9000 configurations tried, all proved to be solvable
in 20 turns or less.
This strongly suggests that the diameter of the cube group is at most
21, or perhaps 22; but not more.
The figure of 9000 configurations in 60 days indicates that solution
of one configuration takes slightly less than 10 minutes. This is
contrary to what I thought was possible. Whenever I tried configurations
they were mostly solved within 2 or 3 minutes. This suggests that the
random configurations are more difficult to solve than what I and many
others brought up as possible difficult patterns.
But I still need to do some analysis on the ouput (now 3 Mb of data).
Continuing and waiting for a config that requires 21 turns, dik
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland
home: bovenover 215, 1025 jn amsterdam, nederland; e-mail: firstname.lastname@example.org