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Date: Mon, 19 Apr 1999 15:13:27 +0100
From: David Singmaster <david.singmaster@sbu.ac.uk>
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
X-MDaemon-Deliver-To: cube-lovers-outbound@mc.lcs.mit.edu

	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