From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 6 14:31:56 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 OAA21857 for ; Tue, 6 Apr 1999 14:31:55 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: wheeler@cipr.rpi.edu (Frederick W. Wheeler) Message-Id: <14088.45800.718995.311244@cipr.no_spam.rpi.edu> Date: Mon, 5 Apr 1999 08:56:08 -0400 (EDT) To: Cube-Lovers@ai.mit.edu Subject: Re: Inventing your own techniques In-Reply-To: <14080.1711.289304.134028@cipr.no_spam.rpi.edu> References: <14080.1711.289304.134028@cipr.no_spam.rpi.edu> Dear Cube-Lovers list: I received several very interesting replies to my e-mail last week regarding inventing techniques to solving cube puzzles. Here are some excerpts of note that were e-mailed to me but not the list. First, part of what I wrote ... Fred Wheeler writes: > For me, the most fun, and the ultimate challenge, in cubing comes > from figuring out how to solve the puzzle in the first place. I'd > really like to hear from people on this list on how you go about > inventing new moves and techniques or how you feel about learning to > solve a puzzle on your own. Wei-Hwa Huang sent me this teaser about conjugation. whuang@ugcs.caltech.edu (Wei-Hwa Huang) wrote: > After I understood conjugation well enough, I have never invented a > move that I can in all honesty call "new" -- although they may > appear "new" to others. The only new part is just applying it to > different types of moves and seeing what the result is. Later, at my request, Wei-Hwa Huang was kind enough to elaborate on conjugation. whuang@ugcs.caltech.edu (Wei-Hwa Huang) wrote: > I keep on meaning to write a more detailed explanation but can never > seem to find the time. > > Essentially, by conjugation I mean taking two routines (call 'em A > and B), consider their reverses (a and b), and juxtapose them (do > the move ABab). When A and B have a small intersection the results > of the conjugation is a simple permutation. And pretty much more > cube puzzles can be solved if you have the simplest permutations. > > Eg, to rotate two corner pieces, let > A = R'DRFDF' (rotate one corner in the top face without affecting > the rest of the top face) > B = U (rotate the top face) > > As A and B have a small intersection (one corner cubie), the move > ABA'B' is quite useful. > > Note that A is itself a move arrived at by conjugation. Tom Magliery also has a system for discovering solution techniques. Tom Magliery wrote: > rather than telling you my actual operation for fixing the "switched wings" > problem on the 4x and 5x cubes, i'll tell you how i discovered it: one of > the things i experiment with is repeated applications of short(ish) > sequences of moves. for example, i'll just take a particular 2 or 3-move > sequence, and apply it over and over again until the cube arrives back at a > state very similar to (but hopefully slightly different than) where it was > when i started. i was doing this (starting from a solved cube) one day > when i discovered with much jubilation that i had arrived at a state with > one switched wing pair. (there was also another slight jumble, but i > already knew an independent move to fix that by itself.) I also received a good suggestion that discovering new sequences may be easier on a computer simulator. This, way the cube can be reset to the solved state quickly before each new attempt to make it easier to see what the trial sequence actually changes. Unfortunately, I lost this particular e-mail and forget who sent it, so I cannot attribute it. My apologies to the author. Regards, Fred Wheeler -- Fred Wheeler wheeler@cipr.rpi.edu www.cipr.rpi.edu/wheeler