From cube-lovers-errors@mc.lcs.mit.edu Sun Sep 13 16:29:34 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id QAA13820; Sun, 13 Sep 1998 16:29:34 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sat, 12 Sep 1998 13:01:52 -0400 (EDT) From: Jerry Bryan Subject: Weak Local Maxima, 6f from Start To: Cube-Lovers Reply-To: Jerry Bryan Message-Id: I finally have had enough time to add support to my God's Algorithm program to calculate weak local maxima. The shortest strong local maximum in the face turn metric is 9f, but the shortest weak local maximum has not previously been verified. It has long been known that Pons Asinorum is a weak local maximum at 6f from Start. I have been curious to know if Pons is the shortest, and if there are any other short weak local maxima. It turns out that 6f is indeed the shortest. There are two such positions unique to symmetry which are 6f from Start, the Pons and one other. The other one is quite pretty: L2 R2 D2 U2 B' F (6f*) The eighteen neighbors are as follows. L2 R2 D2 U2 F2 B' (6f*) L2 R2 D2 U2 F (5f*) B' F L2 R2 D2 U' (6f*) B' F L2 R2 D' U2 (6f*) B' F D2 U2 L2 R' (6f*) B' F D2 U2 L' R2 (6f*) L2 R2 D2 U2 B' (5f*) L2 R2 D2 U2 B2 F (6f*) B' F L2 R2 D2 U (6f*) B' F L2 R2 D U2 (6f*) B' F D2 U2 L2 R (6f*) B' F D2 U2 L R2 (6f*) L2 R2 D2 U2 B' F' (6f*) L2 R2 D2 U2 B F (6f*) B' F L2 R2 D2 (5f*) B' F L2 R2 U2 (5f*) B' F D2 U2 R2 (5f*) B' F D2 U2 L2 (5f*) = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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