From cube-lovers-errors@mc.lcs.mit.edu Sat Jan 3 21:37:36 1998 Return-Path: Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id VAA15379; Sat, 3 Jan 1998 21:37:35 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Sat Jan 3 05:56:11 1998 From: roger.broadie@iclweb.com (Roger Broadie) To: , "Bryan Main" Subject: Re: 5x5x5 Date: Sat, 3 Jan 1998 10:55:50 -0000 Message-Id: <19980103105500.AAA11342@home> > From: Bryan Main > To: Cube-Lovers@ai.mit.edu > Subject: Re: 5x5x5 > Date: 29 December 1997 13:31 > I just got one of these for christmas and had a question or two. > First is there a cube program so I can play with it and not destroy > all the work I have done? And I have solved one side, and all of > the edges without much problems. However, can I solve the middle > pieces without destroying the edges? As of yet I haven't found a > way to keep the one side I have finished and move one of the center > pieces on another side. I don't want moves, I just want to know if > it is possible to solve this way or if I need to start looking at > another way to solve it. > bryan Yes, if the corners of the top layer are also in the right place. You can move them around by normal 3x3x3 moves, but in doing so you may find that the parity of the edge pieces is changed. If you can swap a pair of edge pieces on a 4x4x4, all will be well, and all the pieces in the ring of eight around the piece at the centre of each face can be dealt with by 3-cycles to move these pieces to a different face or around on the same face. There is a hidden complication. The new type of pieces introduced by the 5x5x5 are those at N, S, E and W in the central block of nine in each face. If the corner pieces of the cube are correctly placed, the parity of these new pieces is tied to that of the edge pieces introduced by the 4x4x4, i.e. those next to the corner pieces of the cube. So if a pair of these edge pieces is swapped, so will be a pair of the new 5x5x5 central pieces. But the swap of the edge pieces will cure them at the same time. Often the change to the centre pieces will not even show, because it will take place within the same face. Thus the sequence Georges Helm gave some time ago to swap the 4x4x4 edges also cures the 5x5x5 centre pieces. If it is applied to a cube in the start position, it swaps Bl and Br visibly, and interchanges FHl and FHr (where H is the central slice parallel to U) invisibly. It also makes an even-parity change to the 4x4x4 centre pieces on the front face - in fact it rotates by 180 degrees the (l, u+H+d) and (r, u+H+d) strips on this face. Roger Broadie