From news@nntp-server.caltech.edu Fri Dec 16 23:24:15 1994 Return-Path: Received: from piccolo.cco.caltech.edu by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA01947; Fri, 16 Dec 94 23:24:15 EST Received: from gap.cco.caltech.edu by piccolo.cco.caltech.edu with ESMTP (8.6.7/DEI:4.41) id UAA19585; Fri, 16 Dec 1994 20:24:06 -0800 Received: by gap.cco.caltech.edu (8.6.7/DEI:4.41) id RAA16788; Fri, 16 Dec 1994 17:06:30 -0800 To: mlist-cube-lovers@nntp-server.caltech.edu Path: txr From: txr@alumni.caltech.edu (Tim Rentsch) Newsgroups: mlist.cube-lovers Subject: Re: Cyclic Decomposition Date: 17 Dec 1994 01:06:24 GMT Organization: California Institute of Technology, Pasadena Lines: 29 Message-Id: <3ctdig$gci@gap.cco.caltech.edu> References: <9412162233.AA27627@ducie.ptc.com> Nntp-Posting-Host: alumni.caltech.edu X-Newsreader: NN version 6.5.0 #4 (NOV) mreid@ptc.com (michael reid) writes: >unfortunately, this estimate is too optimistic. the number of positions >within 10 face turns of start is more like 2.6 x 10^11. An upper bound for number of positions reachable after 10 turns is 18 * 12**9 which is 92,876,046,336. Admittedly this number is closer to 2.6e11 than 1e10, but the number is an upper bound. It seems to me I remember reading that the limiting branching factor (for q+h turns) is about 9.5 and is reached rather quickly. The value of 18 * 12 * 12 * 12 * 9.5**6 is 22,864,298,166.0 (according to 'bc'), which should be within reach of brute force algorithms. Unfortunately this approach requires several hundred gigabytes of disk space but that could be spread out over lots of physical machines (parallelizing could also result in speeding up the computation). Anyone know where we could find 1000 machines with a few hundred megabytes free each? Well, maybe not just yet. But soon. regards, Tim Rentsch