From mark.longridge@canrem.com Fri Oct 20 02:32:34 1995 Return-Path: Received: from itchy.crso.com (itchy.canrem.com) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA05992; Fri, 20 Oct 95 02:32:34 EDT Received: by canrem.com (PCB-UUCP 1.1f) id 1F9CFB; Fri, 20 Oct 95 02:24:41 -0500 To: cube-lovers@life.ai.mit.edu Reply-To: CRSO.Cube@canrem.com Sender: CRSO.Cube@canrem.com Subject: Cube Verification From: mark.longridge@canrem.com (Mark Longridge) Message-Id: <60.1255.5834.0C1F9CFB@canrem.com> Date: Fri, 20 Oct 95 02:22:00 -0500 Organization: CRS Online (Toronto, Ontario) In Jerry's message from Date: Mon, 16 Oct 1995 23:08:02 -0400 (EDT) Subject: The Correctness of Large Seaches > In light of the above discussion, I thought it might be appropriate > to summarize some background about my larger searches. I want to > indicate which ones of them seem pretty well verified, and which ones > of them might benefit from further study. > > - I believe this one is ok. I ran the q turn case > with and without conjugacy classes. Upon > expanding the conjugacy classes, the results > matched the results without conjugacy classes. > Also, the results matched results posted by > Mark Longridge as far as they went (although > my anomaly with corners-only suggests that > such matching doesn't prove very much). Well, I did get up to 12 q turns deep ;-) Good enough for 2 half deep searches... But there is another possible verification method by counting the number of even positions and odd positions and totalling them. Analysis of < U, R > group on 3x3x3 cube by Parity -------------------------------------------------- Even Positions Odd Positions -------------- ------------- 0 1 1 4 2 10 3 24 4 58 5 140 6 338 7 816 8 1,970 9 4,756 10 11,448 11 27,448 12 65,260 13 154,192 14 360,692 15 827,540 16 1,851,345 17 3,968,840 18 7,891,990 19 13,659,821 20 18,471,682 21 16,586,822 22 8,039,455 23 1,511,110 24 47,351 25 87 ---------- ---------- 36,741,600 36,741,600 This is almost Cube Philosophy... how can we be certain about the true nature of God's Algorithm? How can we be certain our cube databases are completely accurate? I suppose it is not really a big problem as long as the various cube programs all agree, and a human observer executes such processes on a real cube. -> Mark <-