From @mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU Sun Dec 5 00:42:45 1993 Return-Path: <@mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU> Received: from MITVMA.MIT.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AB08439; Sun, 5 Dec 93 00:42:45 EST Message-Id: <9312050542.AB08439@life.ai.mit.edu> Received: from MITVMA.MIT.EDU by mitvma.mit.edu (IBM VM SMTP V2R2) with BSMTP id 3342; Sun, 05 Dec 93 00:28:55 EST Received: from WVNVM.WVNET.EDU (NJE origin MAILER@WVNVM) by MITVMA.MIT.EDU (LMail V1.1d/1.7f) with BSMTP id 3487; Sun, 5 Dec 1993 00:28:55 -0500 Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.1d/1.7f) with BSMTP id 5701; Sun, 5 Dec 1993 00:26:08 -0500 X-Acknowledge-To: Date: Sun, 5 Dec 1993 00:26:07 EST From: "Jerry Bryan" To: "Cube Lovers List" Subject: Addendum to God's Algorithm for the 2x2x2 Cube 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?