From mreid@ptc.com Thu Jan 12 19:36:23 1995 Return-Path: Received: from ptc.com (poster.ptc.com) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA23412; Thu, 12 Jan 95 19:36:23 EST Received: from ducie.ptc.com by ptc.com (5.0/SMI-SVR4-NN) id AA08082; Thu, 12 Jan 95 19:34:56 EST Received: by ducie.ptc.com (1.38.193.4/sendmail.28-May-87) id AA25588; Thu, 12 Jan 1995 19:47:42 -0500 Date: Thu, 12 Jan 1995 19:47:42 -0500 From: mreid@ptc.com (michael reid) Message-Id: <9501130047.AA25588@ducie.ptc.com> To: cube-lovers@ai.mit.edu Subject: superflip Content-Length: 1768 i've also done some searching for short maneuvers for superflip, although not to the extent that dik has. i was never really satisfied with my efforts to exploit its symmetry and centrality. however, i've recently had some new thoughts about this which look promising. consider two cases: case 1: suppose that there is a minimal sequence for superflip which contains a half-turn. then, by applying R' U2 to superflip, we've moved 3q (or 2f ) closer to start. case 2: otherwise, every minimal sequence contains only 90 degree turns. then either R' U' gets us 2q (or 2f ) closer to start, or R' U gets us 2q (or 2f ) closer to start. (and probably both do.) it would be nice to reduce this latter case to only one of R' U' or R' U . can anyone do this? this was how i found the 24q sequence for superflip. i figured that case 1 was fairly likely, so i tested the position superflip R' U2 kociemba's algorithm found in succession 11 + 22 = 33q, 11 + 20 = 31q, 12 + 17 = 29q, 13 + 14 = 27q, 13 + 12 = 25q, which gives superflip in 28q. there was no improvement for quite some time until depth 17 in stage 1 when it found 17 + 6 = 23q. it searched for several days more and finished depth 17 and depth 18 in stage 1. i was about to give up when i saw that it found 19 + 2 = 21q, to give superflip in 24q. here's a nice (and quite surprising application) of the above use of symmetry and centrality: when searching for superflip in the face turn metric, it's sufficient to search through depth 17 in stage 1! suppose we have a 19f sequence for superflip. then, by considering parity, some turn must be a half-turn. now we may suppose (as above) that the last two face turns are U R2 , which is in stage 2! mike