From: CSD.VANDERSCHEL
Subject: Re: "Monoflips"
To: ACW at MIT-AI
cc: CSD.VANDERSCHEL
In-Reply-To: Your message of 15-Aug-80 1927-PDT

When I offered my monoflip, I tried to make it clear that I was
claiming no superlatives except, perhaps, that of conceptual
simplicity.  Nor can I claim originality, for I recently noticed that
Singmaster lists essentially the same move I thought of in his first
supplement.  It is presented as FUD'LLUUDDR and attributed to David
Seal.  (Besides, if I claimed originality, it would refute my claim
of obviousness.)

You indicated that you believe 22 qtw is the best one can do for a
diflip.  The only sense I know of in which your claim could be valid
would be a diflip generated by a monoflip and its inverse, where that
monoflip preserves the set of cubies in a face.
B'UUBBUB'U'B'UUFRBR'F' is a 16 qtw process that flips a pair of
adjacent edges, and Singmaster attributes it to Morwen
Thistlethwaite's computer program.

The simplest mono-ops are those that preserve the set of cubies in a
center-slice.  For example, FF could be viewed as a monoswap of the
right and left front edge cubies in the horizontal center-slice.  If
we denote by "S" a quarter turn of that slice, then FFSFFS' will
produce any three cycle you might like of edge cubies in the slice
while leaving the rest of the cube intact.  It also becomes more clear
how FFSSFFSS produces the well-known double swap through opposing
faces.

U'FR'UF' is a 5 qtw monoflip that Singmaster attributes to Frank
Barnes.  It preserves the set of cubies in the RL center-slice.  I
think it is clear how it works and that you could not possibly do it
in fewer moves.  Using this monoflip, you can generate a 14 qtw diflip
for an opposing pair of edge cubies.  I still prefer the move I
thought of because I seem to be less likely to make a mistake using
it, it is more readily adapted to any pair of edge cubies, and it is
about as easy to perform.

				David Vanderschel
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