From cube-lovers-errors@oolong.camellia.org Tue Jul 8 17:33:24 1997 Return-Path: cube-lovers-errors@oolong.camellia.org Received: from oolong.camellia.org (localhost [127.0.0.1]) by oolong.camellia.org (8.6.12/8.6.12) with SMTP id RAA09883; Tue, 8 Jul 1997 17:33:24 -0400 Precedence: bulk Errors-To: cube-lovers-errors@oolong.camellia.org Message-Id: <199707082039.QAA04704@life.ai.mit.edu> Date: Tue, 8 Jul 1997 16:43:50 -0400 From: michael reid To: cube-lovers@ai.mit.edu Subject: composition of superflip and pons asinorum the position which is the composition of superflip and pons asinorum is exactly 19 face turns from start. some time ago, jerry bryan found that this position is exactly 20 quarter turns from start, and he gave all minimal maneuvers, up to symmetry. one of these is 19 face turns long: B' D' L' F' D' F' B U F' B R2 L U D' F L U R D (19f, 20q) symmetry reductions for this position are much simpler (but not nearly as good) as for superflip and/or superfliptwist. if the first face turn is a 90 degree turn, then by symmetry, we may suppose it is U . if the first face turn is a 180 degree turn, then we may suppose it is U2 . i tested the two positions obtained by applying these possible initial turns. my program took about 6 and a half hours to exhaustively search these through 17 face turns. no solutions were found, and therefore the original position is more than 18 face turns from start. i realize that this is not nearly as satisfying as obtaining all minimal maneuvers. that will take about 13 times as long, but is feasible with my current program. mike