From boland@sci.kun.nl Sun Sep 24 19:44:45 1995 Return-Path: Received: from wn1.sci.kun.nl by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA10253; Sun, 24 Sep 95 19:44:45 EDT Received: from canteclaer.sci.kun.nl by wn1.sci.kun.nl via canteclaer.sci.kun.nl [131.174.132.34] with SMTP id AAA21239 (8.6.10/2.13) for ; Mon, 25 Sep 1995 00:44:43 +0100 Message-Id: <199509242344.AAA21239@wn1.sci.kun.nl> To: "Cube Lovers List" Subject: Re: Order problems In-Reply-To: Your message of "Sun, 24 Sep 95 18:35:36 -0400." Date: Mon, 25 Sep 95 00:44:40 +0100 From: Michiel Boland Jerry wrote: >I would be curious to hear how you are doing your search. It is >trivial to see how to calculate the order of a particular >position. However, it is not obvious to me how to find a >position of a particular order. I hope it is not the case that >it is in the archives and I just haven't seen it. I use a simple brute-force method, that is, I compute the order of each transform and the number of quarter turns. If there is already a transform with that order & number of qt, I forget all about it and go to the next transform. I have the C source available for anyone who wants to peek at it. Note that (almost) all transforms start with UxRx, since you have to twist two adjacent faces in order to get something with order other than 1, 2 or 4. That saves a bit of time. On my PC, i finished all transforms of length 6 (quarter- and half turns), and did some of length 7. Fortunately, as I mentioned earlier, I managed to get it to work on a somewhat faster machine, and am now waiting for the results of that. I am searching all transforms of 10 quarter turns or less. A process with order 110 must have an even number of quarter turns, since the permutation on the edges has to be even (the only possibility is to have an 11-cycle on the edges, which is an even permutation). Therefore, since there are no processes with order 110 with 6 or less quarter turns, this proves that the one of length 8 is indeed the shortest possible. Cheers, -- Michiel Boland University of Nijmegen The Netherlands