On 9 Aug 1994, Mark Longridge posted God's Algorithm results for
the squares group <H> consisting entirely of 180 degree turns.
Mark invited corroboration. The following will serve to verify
Mark's results, and will also provide the same information for
the M-conjugacy classes of <H>. Notice that the ratio of cube
positions to M-conjugacy classes never gets very close to 48.
Hence, there are a significant number of positions in <H>
at each level of the search tree that are at least somewhat
"symmetrical".

              M   Branching       Cube Branching  Ratio of
Level Conjugate      Factor  Positions   Factor   Cubes to
        Classes                                  M Classes

 0         1                      1                   1
 1         1           1          6        6          6
 2         2           2         27      4.5       13.5
 3         5         2.5        120   4.4444         24
 4        18         3.6        519   4.3250    28.8333
 5        56      3.1111       1932   3.7225    34.5000
 6       162      2.8929       6484   3.3561    40.0247
 7       482      2.9753      20310   3.1323    42.1369
 8      1258      2.6100      55034   2.7097    43.7472
 9      2627      2.0882     113892   2.0695    43.3544
10      4094      1.5584     178495   1.5672    43.5992
11      4137      1.0105     179196   1.0039    43.3154
12      2231      0.5393      89728   0.5007    40.2187
13       548      0.2456      16176   0.1803    29.5182
14       114      0.2080       1488   0.0920    13.0526
15        16      0.1404        144   0.0968          9

Total     15752                 663552             42.1249

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)                        (304) 293-5192
Associate Director, WVNET                            (304) 293-5540 fax
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