From cube-lovers-errors@mc.lcs.mit.edu Fri Oct 30 14:17:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA18032; Fri, 30 Oct 1998 14:16:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 26 Oct 1998 23:58:27 -0400 (EDT) From: Jerry Bryan Subject: 12q From Start To: Cube-Lovers Message-Id: |x| Patterns Lcl Positions Lcl Branching Max Max Factor 0q 1 0 1 0 1q 1 0 12 0 12 2q 5 0 114 0 9.5 3q 25 0 1068 0 9.368 4q 219 0 10011 0 9.374 5q 1978 0 93840 0 9.374 6q 18395 0 878880 0 9.366 7q 171529 0 8221632 0 9.355 8q 1601725 0 76843595 0 9.347 9q 14956266 0 717789576 0 9.341 10q 139629194 4 6701836858 42 9.337 11q 1303138445 0 62549615248 0 9.333 12q 12157779067 103 583570100997 2913 9.330 The last time a new level was calculated for the quarter turn metric was 4 February 1995. The cumulative number of positions now identified is 653625391832, or about 6.5*10^11. This is well past the "geometric halfway point" of sqrt(|G|), which is about 6.5*10^9. However, it is known that the diameter of G is at least 26q, strongly indicating that there is a bit of a tail to the distribution of positions by length. Of the 103 local maxima of length 12q, 70 of them also have their inverse as local maxima. For the other 33, the inverse is not a local maximum. For one of them, the inverse has 11 moves which go closer to Start. For seven of them, the inverse has 10 moves which go closer to Start. For eleven of them, the inverse has 8 moves which go closer to Start. For six of them, the inverse has 6 moves which go closer to Start. For two of them, the inverse has 4 moves which go closer to Start. And for six of them, the inverse has only 2 moves which go closer to Start. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us