From mreid@ptc.com  Tue Feb 13 16:14:27 1996
Return-Path: <mreid@ptc.com>
Received: from poster (poster.ptc.com) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA01056; Tue, 13 Feb 96 16:14:27 EST
Received: from ducie.ptc.com by poster (5.x/SMI-SVR4-NN)
	id AA28288; Tue, 13 Feb 1996 16:09:42 -0500
Message-Id: <9602132109.AA28288@poster>
Received: by ducie.ptc.com
	(1.38.193.4/16.2.nn) id AA12740; Tue, 13 Feb 1996 16:40:40 -0500
Date: Tue, 13 Feb 1996 16:40:40 -0500
From: michael reid <mreid@ptc.com>
To: cube-lovers@ai.mit.edu
Subject: Re:  Group/graph status?
Cc: rcs@cs.arizona.edu

rich schroeppel asks

> Has anyone tabulated the number of positions are reachable (from the
> initial cube) in one move, two moves, etc.?  Is the diameter of the
> graph known?

first note that there are two common ways to define a "move",
any twist of a face (face turn metric), or any 90 degree turn
of a face (quarter turn metric).

jerry bryan was counting (and storing) positions close to start
on magnetic tape.  he gave figures for positions within 7 face
turns on july 19, 1994 and positions within 11 quarter turns on
february 4, 1995.  (jerry, how many reels of tape did this take?)

the diameter isn't known.  the best lower bounds are 20 face turns,
or 24 quarter turns, both from considering the position "superflip".
the best upper bounds are 29 face turns, or 42 quarter turns.

mike