From mouse@collatz.mcrcim.mcgill.edu Mon Sep 25 07:07:11 1995 Return-Path: Received: from Collatz.McRCIM.McGill.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA27224; Mon, 25 Sep 95 07:07:11 EDT Received: (root@localhost) by 3544 on Collatz.McRCIM.McGill.EDU (8.6.12 Mouse 1.0) id HAA03544; Mon, 25 Sep 1995 07:06:43 -0400 Date: Mon, 25 Sep 1995 07:06:43 -0400 From: der Mouse Message-Id: <199509251106.HAA03544@Collatz.McRCIM.McGill.EDU> To: boland@sci.kun.nl Subject: Re: Order problems Cc: cube-lovers@ai.mit.edu >> I would be curious to hear how you are doing your search. [...] > 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. This sounds to me as though you're assuming that all transforms with a given order are equivalent as far as deriving further transforms of other orders go. That is, if you find that a given transform X of length L has order N, it sounds as though you're assuming that there is no need to store any other transforms of length L and order N. I'm not convinced this is justified. If you've found X of (say) length L and order N, and then find a different Y of length L and order N, I can't see any justification for the assumption that you can prune the entire subtree below Y, because if the cycle decompsition of Y is different from that of X, they may behave entirely differently when followed by more twists, even though they have the same order. der Mouse mouse@collatz.mcrcim.mcgill.edu