From cube-lovers-errors@mc.lcs.mit.edu Tue May 4 15:15:59 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA22863 for ; Tue, 4 May 1999 15:15:59 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <009301be95b5$fc951340$70c4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: Cc: "David Singmaster" Subject: Re: Reinventing (and some edge-flipping techniques) Date: Mon, 3 May 1999 23:40:28 +0100 David Singmaster wrote (1 May 1999) >Consequently I decided to get the edge orientations correct at the >beginning of work on the last face, so that I wouldn't have to worry >about what happened to the rest of the face. In case you haven't got >my notes at hand, I used BLUL'U'B' which is a simple conjugate of the >commutator [L,U]. When I read David Singmaster's algorithm in his Notes on Rubik's Magic Cube I thought his idea of curing the orientations of the edge-piece before positioning them was a great one, and adopted it in my own algorithm. One may be able to get away with only 6 turns to cope with the orientation, which is quite a gain on the number of turns needed if one takes the obvious route and orients once the pieces are in position. I then went on to apply the same principle to the corner pieces, by orienting them next, which can be done in 7 or 14 face turns by selecting the first of the following (for three twists) or the first followed by the second suitably applied (for two or four twists): F U2 F' U' F U' F' L' U2 L U L' U L These processes, which I mentioned in my last post, move the corner pieces as well as twist them, and also move the edge pieces but preserve their orientation. So, if applied after the edge pieces have been oriented but not positioned, they get the top face of the cube the right colour, and it can then be solved by orientation-preserving moves of the edge and corner pieces. I may be rather bad at perceiving patterns, but I find the simplification of having to look only at the faces of the top-layer pieces that lie in the side faces of the cube in order to work out what needs to go where enough of an advantage to make this order of the stages worthwhile even if it did not take fewer moves in total. Roger Broadie