From @mail.uunet.ca:mark.longridge@canrem.com Tue Aug 9 15:17:23 1994 Return-Path: <@mail.uunet.ca:mark.longridge@canrem.com> Received: from seraph.uunet.ca ([142.77.1.1]) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA02832; Tue, 9 Aug 94 15:17:23 EDT Received: from portnoy.canrem.com ([198.133.42.251]) by mail.uunet.ca with SMTP id <86930-4>; Tue, 9 Aug 1994 15:17:13 -0400 Received: from canrem.com by portnoy.canrem.com (4.1/SMI-4.1) id AA15464; Tue, 9 Aug 94 15:14:38 EDT Received: by canrem.com (PCB-UUCP 1.1f) id 1A9A39; Tue, 9 Aug 94 13:57:35 -0400 To: cube-lovers@life.ai.mit.edu Reply-To: CRSO.Cube@canrem.com Sender: CRSO.Cube@canrem.com Subject: < U, R> Group From: mark.longridge@canrem.com (Mark Longridge) Message-Id: <60.783.5834.0C1A9A39@canrem.com> Date: Tue, 9 Aug 1994 01:48:00 -0400 Organization: CRS Online (Toronto, Ontario) Well I decided to pull a "Jerry Byran" and take another look at some cube results, plus take a look at some new groups. Analysis of the 3x3x3 squares group ----------------------------------- (h only) branching Moves Deep arrangements factor loc max (h only) 0 1 -- 0 1 6 6 0 2 27 4.5 0 3 120 4.444 0 4 519 4.325 0 5 1,932 3.722 0 6 6,484 3.356 1 (6 X pattern) 7 20,310 3.132 0 8 55,034 2.709 65 9 113,892 2.069 1,482 10 178,495 1.567 7,379 11 179,196 1.004 25,980 12 89,728 0.501 50,320 13 16,176 0.180 11,328 14 1,488 0.092 912 15 144 0.096 144 ------- ------ 663,552 97,611 Analysis of the 3x3x3 group ---------------------------------- branching Moves Deep arrangements (q only) factor 0 1 -- 1 4 4 2 10 2.5 3 24 2.4 4 58 2.416 5 140 2.413 6 338 2.414 7 816 2.414 8 1,970 2.414 program starts to really bog down after this... I leave it to Jerry or Dan to check my results. I checked up to 2 moves deep by hand and verified 10 different positions. What I don't understand is how Jerry manages to look at so many cube positions: On full 3x3x3 cube, 7 100,803,036 13.231 (new) Using 10 bytes to store a single cube position would still need over 1 billion bytes, or am I missing something? I also used GAP (quite a good program) to calculate the size of < U1, R1 > on the magic dodecahedron: 7,999,675,084,800. Once again, I welcome any verification. -> Mark <-