From mouse@collatz.mcrcim.mcgill.edu Mon Feb 13 18:30:35 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 AA10510; Mon, 13 Feb 95 18:30:35 EST Received: (root@localhost) by 11948 on Collatz.McRCIM.McGill.EDU (8.6.8.1 Mouse 1.0) id SAA11948 for cube-lovers@ai.mit.edu; Mon, 13 Feb 1995 18:30:32 -0500 Date: Mon, 13 Feb 1995 18:30:32 -0500 From: der Mouse Message-Id: <199502132330.SAA11948@Collatz.McRCIM.McGill.EDU> To: cube-lovers@ai.mit.edu Subject: Re: Re: superflip in quarter turn metric In response to a note of mine, >> A search treegiving distances from Start calculates d(I,IY) for all >> positions IY in the domain of inquiry. With an X-rooted tree, >> distances are of the form d(X,XZ) for all positions XZ in the domain >> of inquiry. In general, it is not the case that d(I,IY)=d(X,XY). whereupon what's-his-name :-) responds > In this notation, it is certainly true that > d(,) = d(,). This is because each process that > transforms to the state , will also transform to , > and likewise each process that transforms to will also > transform to . This is what I was trying to say in the message that started this: that one is building a tree of all move sequences no longer than N, which is to say a certain subset of permutations of the cube. But these permutations can be applied to arbitrary positions just as well as as they can be to Start. Any Cubist knows this; it's the basis for many of the common solving macros: that a process that (say) swaps RF and RB, and TF and TB, can be used to swap whatever cubies happen to be in those cubicles, even if they aren't the RF/RB/TF/TB cubies. der Mouse mouse@collatz.mcrcim.mcgill.edu