From ccw@eql12.caltech.edu Fri Dec 16 13:55:58 1994 Return-Path: Received: from EQL12.Caltech.Edu by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA22563; Fri, 16 Dec 94 13:55:58 EST Date: Fri, 16 Dec 94 10:54:10 PST From: ccw@eql12.caltech.edu Message-Id: <941216105410.25001944@EQL12.Caltech.Edu> Subject: A comment on Cyclic Decomposition To: cube-lovers@life.ai.mit.edu, mark.longridge@canrem.com X-St-Vmsmail-To: ST%"cube-lovers@life.ai.mit.edu" Mark Longridge proposes looking for processes that can be expressed in the form (S1 S2 S3... SX) ^N = Goal State He calls such a processes "Cyclicly Decomposable". I think that the results would be far richer if there was also allowed to be one cube rotation in the subprocess. I know of 2 examples. I will use a * after a move to represent a full cube move. I am a little rusty on this one, and I don't have a cube here to verify it, but (L' R F*) ^ 6 (12q) is (or should be, if I remember it correctly) the Pons Asinorum. We also know that this pattern takes at best 12q, so it is actually optimum. The existance of this process has always made me wonder how many different ways there are to do the Pons, especially with different face effects in the Supergroup. The other one is my favorite process. (L D L' R' F'*)^4 (16q) This twists 3 corners on one face. I suspect this one is also optimum as I have never heard of a process that twists 3 corners in less than 16q. It has one very interesting feature, L' R' F'* can be done as 1 combined two-hand motion. A casual observer may think you are only turning the cube and not see the face turns involved. This makes the process look magic, achieving a state in far fewer apparant moves then people think is possible. This process is so fast and easy to remember that it is what I use while solving.