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I had intended to include the following table in my first

post concerning God's Algorithm for the 2x2x2 cube, but

I forgot. It addresses the question of how large are the

equivalence classes in the search tree, where the equivalence

classes are generated by the two rotational symmetry groups

and the one reflectional symmetry group. Most of the

equivalence classes have 24*24*2=1152 elements, but some have

fewer.

Size of Number Total Number Equivalence of of Class Nodes Permutations Represented 24 1 24 48 1 48 72 3 216 96 1 96 144 14 2,016 192 15 2,880 288 135 38,880 384 32 12,288 576 2,208 1,271,808 1,152 75,392 86,851,584 ---- ----- -------- Total 77,802 88,179,840

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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?