Date: 12 Aug 1980 0823-PDT
From: Davis at OFFICE-3
Subject: The Spratt Wrench
To:   greenberg at MIT-MULTICS
cc:   cube-lovers at MIT-MC

Thanks for sharing the wrench with us.  It is a truly wonderful tool.
Another question I had had is now answered.  It was basically:  Once I
get near the end of a solution, I often have more than one set of
edge flips to do.  Is there some scheme which will easily allow me to
do more than one.  After staring at how the wrench works it is clear
that in many cases, with one or two preliminary flips, or flips between
the applications of the two halves of the wrench, wonderous things can
be accomplished.

Also, having worked on my own for quite awhile, and being more of a
mathematician than a computer scientist, I decided that a standard
rotation was CCW, and most of my algorithms favor turns in that direction.
In converting the wrench to my own particular quirks (I can't turn things
CW very well anymore), I discovered that essentially any combination of
F and F', and of Q and Q' work just fine.  In other words, if "f" stands
for F or F' and "q" stands for Q or Q', then (fq)^4 (qf)^4 is a wrench.
(Better leave f and q fixed through the whole transformation, however.)

This next comment is off the subject, but I had been meaning to ask it
for some time.  I have one of the white cubes, and after reading the
message some time ago about underwater cubing, my cube "accidentally"
fell into a pool too.  Well, the white ones float, which I found very
annoying.  Does anyone know if the specific gravity of the hungarian
or Ideal cubes is greater than 1?  I'm also not so sure that I would
recommend that others try to teach their cubes to swim -- mine now
has a disturbing squeak as it turns -- I fear that something has rusted
inside.
Tom Davis
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