From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 19 17:34:05 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA07769 for ; Mon, 19 Apr 1999 17:34:05 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 19 Apr 1999 15:13:27 +0100 From: David Singmaster To: jbryan@pstcc.cc.tn.us Cc: cube-lovers@ai.mit.edu Message-Id: <009D6DFF.A3A1ABCB.24@ice.sbu.ac.uk> Subject: RE: Re : Re: Inventing your own techniques The technique of solving the cube by use of commutators and conjugates is what most people worked out in the early days. However, I can testify that it took us some time to realise that one could use second level commutation. That is, FRF'R' = [F,R] only affects seven pieces, but in fact it only affects one piece in the L face, so taking the commutator with the L face produces a 3-cycle of corners. Likewise [F,R]^2 only twists one corner in the L face and combining it with turns of L allows you to twist three corners the same way or two corners opposite ways. 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