From:

~~~ ~~~ Subject:

Distance Number Branching Number Branching Ratio of from of Factor of Factor Cubes to Start W-Conjugate Cubes W-Conjugate Classes Classes

0 1 1 1 1 2 2 6 6 3 2 5 2.5 18 3 3.6 3 14 2.8 54 3 3.857 4 41 2.929 162 3 3.951 5 122 2.976 486 3 3.984 6 365 2.992 1,457 2.998 3.992 7 1,091 2.989 4,360 2.992 3.996 8 3,256 2.984 13,016 2.985 3.998 9 9,627 2.957 38,482 2.957 3.997 10 28,282 2.938 113,094 2.939 3.9987 11 82,243 2.908 328,920 2.908 3.9994 12 235,611 2.865 942,351 2.865 3.9996 13 654,297 2.777 2,616,973 2.777 3.9997 14 1,693,858 2.589 6,774,848 2.589 3.9997 15 3,776,718 2.230 15,105,592 2.230 3.9997 16 6,058,483 1.604 24,231,019 1.604 3.9995 17 4,856,334 0.802 19,421,274 0.802 3.9992 18 961,504 0.198 3,843,568 0.198 3.997 19 11,954 0.012 47,465 0.012 3.971 20 16 0.001 54 0.002 3.375Total 18,373,824 73,483,200 3.9993

Notice that using Q+H turns instead of Q turns reduces the maximum

distance from Start from 25 down to 20.

When I first calculated God's Algorithm for <U,R> for Q turns, I calculated

it for cubes first, then for W-conjugate classes. In this case, I

really did it only for W-conjugate classes (problem is four times

smaller). The "Number of Cubes" column is then derived by calculating

the size of each W-conjugate class; no real search is needed to

obtain the number of cubes if the W-conjugate classes are already

in hand.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU

If you don't have time to do it right today, what makes you think you are

going to have time to do it over again tomorrow?