From cube-lovers-errors@oolong.camellia.org Mon Jun 2 17:30:30 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 RAA04131; Mon, 2 Jun 1997 17:30:29 -0400 Precedence: bulk Errors-To: cube-lovers-errors@oolong.camellia.org X-Authentication-Warning: dot.mcis.washington.edu: davidb owned process doing -bs Date: Mon, 2 Jun 1997 13:13:44 -0700 (PDT) From: David Barr X-Sender: davidb@dot.mcis.washington.edu Reply-To: davidbarr@iname.com To: cube-lovers@ai.mit.edu Subject: Re: 5x5x5 practical Q's In-Reply-To: <3.0.32.19970601235733.0068d4f0@pop.radix.net> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII On Sun, 1 Jun 1997, Hersch Pilloff wrote: > Hello, > > I'm proud to say that after significant quantities of blood, sweat, and > tears, I have finally solved the 5x5x5 cube. I used some techniques from > the good old 3x3x3 cube as well as some general techniques I've found > useful over the past (often of the form A R A' R' where A is a set of > rotations preserving one face and R is a rotation of that face). One > problem I faced along the way and have not been able to solve to my > satisfaction is an issue of parity. I often put the big cube in a state > where exactly two "equivalent" off-center edge pieces on the upper face > were interchanged with one another. They had the correct orientation, I > simply needed to switch the two pieces. I would like to know if anyone has > an effective means of dealing with this situation. Take a look at some of the web pages about the 4x4x4 or 5x5x5 cubes; they have a sequence of about 20 moves for swapping two edge pieces. I used to have it memorized. Here's what I would do now (when I don't have the sequence memorized). Turn either the 4th or 2nd horizontal slice one quarter turn, then use your normal moves to put this slice's edge pieces back into place. You will end up with a solvable number of pieces out of place on the top. I don't understand what ARA'R' means. When I solve the 5x5x5 cube, I end up using mostly one type of sequence that moves three pieces. I'm not very familiar with 5x5x5 notation, so I'll describe a notation that can describe the sequence. I learned this notation from a book on the 4x4x4 that I bought in the early 80s. A number (1-5) refers to a slice move that causes a vertical column of pieces on the front face to move to the bottom face. 1'-5' are the inverses. L or R refers to a move that will move the bottom row of pieces on the front face to either the left or right side. Here's a sequence that moves three corner pieces: 1 L 5 R 1' L 5' R The shorthand for this move is 1L5, because the rest of the moves can be predicted from the first three moves. If you replace 1 and 5 with any two other columns (and possible swap the L and R moves), you can design a sequence that will move 3 pieces of any type. 1L5 and 5R1 will move three corner pieces. 1L3 and 5R3 will move three edge pieces. 1L2, 1L4, 5R2 and 5R4 will move three off-center edge pieces. 2L3 and 4R3 will move three center near-edge pieces. 2L4 and 4R2 will move three center near-corner pieces. A lot of the time, the three pieces you want to move aren't in locations that correspond to one of these sequences. In that case, make a move that puts the three pieces in the right place for one of the sequences, do the sequence, then undo your original move. For all I know, this is just another way of describing the moves that you are making. David