From dik@cwi.nl Thu Jan 12 20:35:59 1995 Return-Path: Received: from charon.cwi.nl by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA26027; Thu, 12 Jan 95 20:35:59 EST Received: from boring.cwi.nl by charon.cwi.nl with SMTP id ; Fri, 13 Jan 1995 02:35:45 +0100 Received: by boring.cwi.nl id ; Fri, 13 Jan 1995 02:35:45 +0100 Date: Fri, 13 Jan 1995 02:35:45 +0100 From: Dik.Winter@cwi.nl Message-Id: <9501130135.AA14054=dik@boring.cwi.nl> To: cube-lovers@ai.mit.edu, mreid@ptc.com Subject: Re: superflip > 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. I have indeed considered this, but have not yet come to a conclusion. > 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. I do not know whether this is clear for all readers. My reasoning was similar but the conclusion different, but someway equivalent: If the minimal sequence contains a half-turn, we may just as well assume that that half turn is the last, and F2. I do not know whether the proof has been shown on this list, but it is simple. Suppose M is a minimal sequence, and Z is some random sequence, in that case Z M Z' is also superflip. Take Z the maximal sequence at the end consisting of quarter-turns only, we end with a sequence of equal length terminating with a half-turn. Because of symmetry we may just as well consider it to be F2. > 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 needs more than simple symmetry. There are 12*8 different endings, and we have 48 symmetries (24 by rotation * 2 by inversion). Leaving 2 cases. I considered this, but have not yet come to conclusions. On the other hand I do not yet know what to conclude from M M' = I for every superflip sequence. > 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! Yes, I had seen that. One of the major reasons I was not amused when the system crashed doing depth 17 in stage 1! I will restart the program doing depth 17, but I will first redo the counting so that counts larger than 2^32 are correct. dik