Analysis of the 3x3x3 <U, R> group
        ----------------------------------
ML's Conjecture: The < U, R > group is >=20 turns deep in qt metric
                 Now confirmed, Sept 1, 1994

                                          branching
Moves Deep       arrangements (q only)     factor

  0                    1                      --
  1                    4                       4
  2                   10                       2.5
  3                   24                       2.4
  4                   58                       2.416
  5                  140                       2.413
  6                  338                       2.414
  7                  816                       2.414
  8                1,970                       2.414
  9                4,756                       2.414
 10               11,448                       2.407
 11               27,448                       2.401
 12               65,260                       2.378
 13              154,192                       2.363
 14              360,692                       2.339
 15              827,540                       2.294
 16            1,851,345                       2.237
 17            3,968,840                       2.144
 18            7,891,990                       1.988
 19           13,659,821                       1.755
 20           18,471,682                       1.352
 21           16,586,822                       0.898
 22            8,039,455                       0.485
 23            1,511,110                       0.188
 24               47,351                       0.031
 25                   87                       0.002
              ----------
              73,483,200

Moves Deep       arrangements (q+h)     total
  0                      1                1
  1                      6                7
  2                     18               25
  3                     54               79
  4                    162              241
  5                    486              727
  6                  1,457            2,184
  7                  4,360            6,544
  8                 13,016           19,560
  9                 38,482           58,042
 10                113,094          171,136
 11                328,920          500,056
 12                942,351        1,442,407
 13              2,616,973        4,059,380
 14              6,774,848       10,834,228
 15             15,105,592       25,939,820
 16             24,231,019       50,170,839
 17             19,421,274       69,592,113
 18              3,843,568       73,435,681
 19                 47,465       73,483,146
 20                     54       73,483,200