From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 12 20:07:12 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 UAA21764 for ; Tue, 12 Oct 1999 20:07:11 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 4 Oct 1999 18:47:12 -0400 (EDT) From: Daniel B Knights To: Cube-Lovers@ai.mit.edu Subject: 3-Cube in 1 One-Look Message-Id: Hi all, I'm new to this list, and new to the cube as well - only got my first one in March. Of course, now it doesn't leave my side. I have seen a few Cube-Lovers emails about solving the cube in a minimum number of looks. Here is a system that I use to solve the cube in 1 look, with 10-25 minutes of studying time. (Please excuse my lack of knowledge of terminology/group theory.) _________________________________________________ When most people solve the cube they do it by decomposing the whole problem into successively more specific subgroups. (e.g. first layer edges, first layer corners, second layer edges, etc.) I say "successively more specific" because the moves someone would use to position the first few pieces are very simple and intuitive, usually changing (but not solving) the unsolved pieces in the cube. As one approaches the solved state, one uses much more specialized algorithms that affect only the remaining unsolved pieces. For "multiple-look" purposes, this is a great approach. Often the smaller the subgroup of pieces affected by an algorithm, the larger the number of moves in that algorithm, and since there is usually no perceived order to the unsolved pieces, there is no benefit to preserving them with lengthy specialized moves. To a person visualizing an entire solution in his or her head, however, these types of moves are very expensive in terms of memory. Instead I begin from the start using specialized moves that affect as little of the cube as possible. I might start off with an algorithm to permute 3 corners (hopefully putting at least two of them in the correct place/orientation) while leaving the other 5 corners and all 12 edges untouched. In fact, by the time I have all of the corners solved, the edge pieces are in exactly the same random configuration as when I started! (with the possible exception of having interchanged exactly 2 of them.) The solution has then been decomposed into 2 nearly independent problems. The moves I use are mostly single-layer permutations with some commutators mixed in when necessary. One can get the corners solved after applying 5 or 6 move sequences, and then solve the edges with an additional 7 or 8 sequences. (This has nothing to do with the number of moves used to solve the cube. In fact, when I solve it with my eyes closed, I average 150-200 moves!) _____________________________________________________ The Rules: I would consider it cheating to use a pen and paper. Basically, you have to sit down with a random cube and look at it for a while without manipulating it. Then close your eyes and start solving. When you next open them, it should be solved. (You don't get to "practice" the moves before you go.) _____________________________________________________ So, has anyone else tried this? I'm curious to know what method someone else uses. I use my 15 minutes of studying time to plan out where I'm going to need to move the pieces. I wonder if anyone with better memory skills can just memorize the locations of all the pieces and then work out the entire solution with their eyes closed. Dan Knights Middlebury College http://www.middlebury.edu/~knights/