From cube-lovers-errors@oolong.camellia.org Wed Jun 25 13:29:10 1997 Return-Path: cube-lovers-errors@oolong.camellia.org Received: from oolong.camellia.org (localhost [127.0.0.1]) by oolong.camellia.org (8.6.12/8.6.12) with SMTP id NAA08775; Wed, 25 Jun 1997 13:29:10 -0400 Precedence: bulk Errors-To: cube-lovers-errors@oolong.camellia.org Date: Wed, 25 Jun 1997 18:11:31 BST From: David Singmaster Computing & Maths South Bank Univ To: cube-lovers@ai.mit.edu Message-ID: <009B651B.AC285B40.328@vax.sbu.ac.uk> Subject: Pilloff's query about 5^3; Korf's method. I've been away and have just seen email for late May and early June. Pilloff asks about getting the parity of the edges correct on the 5^3. As he notes, the commutators cannot solve this. Examining the basic moves, one sees that the rotation of a inner face changes the parity of the edges while conserving the parity of some pieces, but not of others. However, the pieces whose parity is not conserved are the pieces next to the centre and there are four apparently identical copies of these, so one can simulate an exchange by a 3-cycle with two pieces the same. Hence one wants to apply a rotation of an inner face. What one does is to move the two edges into the same inner face. Then rotate the face. Then make a 3-cycle of the edges. This produces an exchange of edges - and rather messes up the centre pieces. Then put things back. The edges go A B C D to D A B C to B A C D. Because this is relatively easy to do, but messes up the centres, I normally do the edges and corners first and then put centres in place. Re: Korf. Someone has said it reminds them of alpha-beta pruning. It reminds me of branch and bound search. Both are older names for the general process of using information about the remainder of the problem to estimate the number of steps for a solution via a partial solution. Going back to Pilloff's query, I have several methods in my files for exchanging two edges without moving anything else (I think, but that seems to contradict what I said about parities??) DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk