From news@nntp-server.caltech.edu Fri Oct 20 17:28:13 1995 Return-Path: Received: from chamber.cco.caltech.edu by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA17025; Fri, 20 Oct 95 17:28:13 EDT Received: from gap.cco.caltech.edu by chamber.cco.caltech.edu with ESMTP (8.6.12/DEI:4.41) id OAA13153; Fri, 20 Oct 1995 14:28:02 -0700 Received: by gap.cco.caltech.edu (8.6.7/DEI:4.41) id OAA17076; Fri, 20 Oct 1995 14:27:28 -0700 To: mlist-cube-lovers@nntp-server.caltech.edu Path: whuang From: whuang@cco.caltech.edu (Wei-Hwa Huang) Newsgroups: mlist.cube-lovers Subject: Re: Old question about 2 adj edges Date: 20 Oct 1995 21:27:27 GMT Organization: California Institute of Technology, Pasadena Lines: 30 Message-Id: <46947v$gl9@gap.cco.caltech.edu> References: <199510201629.SAA01720@nukkekoti.cs.hut.fi> Nntp-Posting-Host: accord.cco.caltech.edu X-Newsreader: NN version 6.5.0 #12 (NOV) Mikko Haapanen writes: >This reminds me another old question: 3x3x3 are told to have about 4 >trillion (or whatever) different positions. How many of these positions are >'solved cube' but with different centerpiece combinations? Once i had 3x3x3 >with 6 different pictures (picture/side). Friends asked me to solve it. When >i was completed, they laughed at me and pointed the bottom center piece, >which was out of orientation (i can't remember how many of centers were out >of order). Actually, I think the 4 "trillion" estimate is ignoring the center orientation. Let's see: 8! corner positions x 3^7 corner orientations x 12!/2 edge positions x 2^11 edge orientations = 4.325x10^19 Well, forty-three quadrillion. Five center orientations force the sixth, so multiply your number by 4^5 to get the answer 4.429x10^22 positions, counting center piece orientations. That's 44 quintillion. Whew. I remember when I solved the 5x5x5 cube (finally), someone asked me if I had solved the "invisible" 3x3x3 inside it. I'm not sure I even want to think of trying to solve that. I'll work on the 3x3x3x3 first. :P -- int m,u,e=0;float l,_,I;main() {for(;e<1863; putchar((++e>924&&952> e?60-m:u) ["\n ude.hcetlac.occ@gnauhw ]"])) for(u=_=l=0;(m=e%81) <80&&I*l+_*_ <6&&25>++u;_=2*l*_+e/81*.09-1,l=I)I=l*l-_*_-2+.035*m;}