From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 4 16:11:19 1998 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 QAA06137 for ; Fri, 4 Dec 1998 16:11:18 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199812041806.NAA21024@pike.sover.net> Date: Fri, 04 Dec 1998 13:07:36 -0500 To: Jacob Davenport From: Nichael Lynn Cramer Subject: Re: (5x5x5) edge parity corrections Cc: Cube Lovers In-Reply-To: <00096300.C22092@scudder.com> Jacob Davenport wrote: >I don't like the edge parity correction move that I use in my solution, and >I'm hoping that someone can give me a better one. > >The parity problem is found in 5x5x5 cubes (and 4x4x4 cubes, I understand) >when two of the edges right next to the corners (which I call "wings") are >switched. Some fairly simple moves can get all three edges in line with >each other, but half the time two wings need to be switched. By the time I >figure this out when doing a 5x5x5 cube, I've solved most of it, and my >parity fixing move messes up many of the edges I've been working on. > >How do other people fix this problem? > >-Jacob Hi Jacob In both cases (4X and 5X) I solve this problem in the following way: 1] I solve the rest of the cube, leaving me with the two "switched wings" (in your terminology). 2] I then arrange things so both "wings" are on the same "off-center-slice". (Also it will always be the case that both of these winds are now on the same face.) This will be easy to do using the 3-wing swapping operators. 3] At this point I now rotate the "off-center-slice" containing the "switched wings" by a quarter turn. As a result of this move it will be the case that that the "off-center-slice" now has one of the previously "switched wings" in its "correct cubicle". The other three "wings" will be now be in a cyclic permutation. 4] Since --from your note above-- I assume you understand how to cycle three "wings", all you have to do now is put the "wings" in the right place and replace the damage to the off-center central faces that were messed up during that initial quarter-turn above. (And since they are in "paired" clusters, this should be pretty straightforward.) (In short, the quarter-turn of the non-central slice puts the cube back in the proper "orbit" for finishing up.) Now clearly this is far from maximal. And it's certainly not terribly fast. But I find it a very simple, and an easy (and easy-to-remember [and easy-to-explain]) way to clean up this potentially messy situation. Hope this helps Nichael -- Nichael Cramer nichael@sover.net deep autumn-- http://www.sover.net/~nichael/ my neighbor what does she do