From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 6 15:05:42 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id PAA07299; Tue, 6 Oct 1998 15:05:41 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 27 Sep 1998 20:35:33 -0400 (EDT) From: Jerry Bryan Subject: Corners Only, Ignoring Twist To: Cube-Lovers Reply-To: Jerry Bryan Message-Id: I have been playing around with the idea of trying to calculate God's Algorithm all the way to the bitter end for the group which results from ignoring all twists of the corners and flips of the edges. It's a pretty big group. The order is |G|/(3^7)/(2^11), which is about 9.7*10^12, call it about 10^13 to make it a round number. (Another way to calculate it is 8!12!/2.) This is probably right at the bare edge, maybe even slightly past the bare edge, of the size of problem I can handle right now, which makes it a worthy endeavor. Also, it would provide a lower limit on the diameter of G (although the limit might not be any better than the ones we already have), which again makes it a worthy endeavor. Such a result might be suitable as the estimator function required by IDA* searches. The distance from Start in the no-twist, no-flip group would certainly be a lower bound for every position where twist and flip *are* considered. My only hesitation about suggesting this group as a suitable IDA* estimator function is that there are obvious pathological cases such as the superflip where this function would be a very poor estimator. In developing a no-twist, no-flip version of the program, I decided to try it out on the corners only case. Here are the results. Distance from Patterns Positions Start 0q 1 1 1q 1 12 2q 5 114 3q 24 876 4q 119 4931 5q 301 12972 6q 364 15066 7q 166 6300 8q 3 48 Distance from Patterns Positions Start 0f 1 1 1f 2 18 2f 9 243 3f 68 2646 4f 302 12516 5f 418 17624 6f 170 7080 7f 14 192 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990