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Date: Fri, 14 Jun 1996 16:35:18 BST
From: David Singmaster Computing & Maths South Bank Univ <david.singmaster@sbu.ac.uk>
To: cube-lovers@ai.mit.edu
Message-Id: <009A3D97.EFAEB000.1938@vax.sbu.ac.uk>
Subject: Storage of cube positions

	Responding to Rubin Shai has made me think of an idea which may have
been discussed already.
	I was wondering if one could reduce the storage required to represent
a position or pattern.  In my notation, one basically records the movement
of each facelet.  However, if  UR -> RB  and we know that the UR piece is moving
to the RB place, then we only need to record the  U -> R  part of the motion.
In order to know which piece is moving, number all the 54 facelets.  Suppose
the facelets of UR are 1,2 in order, and the facelets of RB are  11,12 in order.
Then recording that  1 -> 11  completely describes the movement  UR -> RB.
	So we only need to record the movement of one of the facelets of
each piece - the others have to follow.  Hence we can describe the position
of the cube by a vector of 20 numbers in the range 1 .. 54.
	Of course, one has to pay for this - the composition of movements will
be more complex.  But if storage is your problem rather than time, it may be
worth it.
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  @vax.sbu.ac.uk