From mark.longridge@canrem.com Sun Dec 3 20:32:36 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 AA27214; Sun, 3 Dec 95 20:32:36 EST Received: by canrem.com (PCB-UUCP 1.1f) id 201705; Sun, 3 Dec 95 20:17:41 -0500 To: cube-lovers@life.ai.mit.edu Reply-To: CRSO.Cube@canrem.com Sender: CRSO.Cube@canrem.com Subject: & G From: mark.longridge@canrem.com (Mark Longridge) Message-Id: <60.1261.5834.0C201705@canrem.com> Date: Sun, 3 Dec 95 20:09:00 -0500 Organization: CRS Online (Toronto, Ontario) A while back Jerry asked.... > Finally, pick any cube X in . We know > |X| in G <= |X| in . Can anybody find a cube X such that > |X| in G < |X| in ? Well, we basically know the answer is yes. There are elements in which require less moves if we use all the generators of G. To be more specific, look the 6 twist pattern in which requires 22 q turns: ^^^^^^^^^^ >> Equivalent to (U1 R1)^35= (R1 U1)^35 & Shift Invariant >> UR11 = U2 R1 U1 R1 U1 R3 U1 R3 U1 R3 U2 R1 U1 R1 U1 R3 U1 R3 U1 R3 After a bit of computer cubing I found: p183 6 Twist R1 U3 R2 U3 R1 D3 U3 R1 U3 R3 D2 R3 U3 R1 D3 U3 (18 q, 16 q+h moves) ^^^^^ I'll spare everyone all the gory details. I'm certain there are all sorts of other examples, but here is one case where we can save 4 q turns. It may be of some small interest to see which of the two processes can be executed more rapidly by the human hand. -> Mark <-