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From: whuang@ugcs.caltech.edu (Wei-Hwa Huang)
Subject: Algorithm for the Antislice Group
Date: 4 May 1999 14:11:57 GMT
Organization: California Institute of Technology, Pasadena
Message-Id: <7gmv7d$ncj@gap.cco.caltech.edu>
In a small fit of playing around last week, I finally worked out a
method of solving the Antislice Group.
Of course, God's Algorithm is known, but since it's pretty hard for
me to memorize it, here's mine.
For those of you that don't know, the antislice group is all
configurations that the cube can be in, provided that the only
move you make is FB, with rotations and reflections.
So, with fixed centers, the only allowed moves are FB, RL, and UD.
I'll abbreviate these to F, R, and U. I'll even use the "clockwise
quarter turn" metric, which means that F' = FFF is three moves, not one.
Okay. The algorithm has four steps:
A. Get the cube to be a subset of the half-face turn group.
(up to 4 moves)
B. Match the corners.
(up to 6 moves)
C. "HOt HOt HOt" (double-slice group).
(up to 12 moves)
D. Solve the cube.
(up to 6 moves)
This is a maximum of 28 moves. In practice, one can often avoid future
extra moves by modifying the algorithm slightly.
A. Get the cube to be a subset of the half-face turn group.
This means that the UD faces only contain the UD colors, the FB faces
only contain the FB colors, and the RL faces only contain the RL colors.
Here's how to do it:
A0. Pick any set of colors on opposite face centers. Let's call it the
color "grud". (For instance, if blue is opposite white on the solved cube,
"grud" can mean "blue or white".) We'll try to solve "grud" first.
A1. Find a face with grud at the corners and reorient the cube
so that it is the U face.
A2. If the U center is grud but none of the U edges are grud, perform
R, repeat step A1, and go to step A5.
A3. If the U center is not grud but all of the U edges are grud, then
either the F center is grud or the R center is grud. If the F center is
grud, perform F; if the R center is grud, perform R. Then repeat step
A1 and go to step A5.
A4. If the U center is grud and two of the U edges are grud (so there
is a grud "H" shape on the U side), then either F has two grud edges or
R has two grud edges. If the former, perform F; if the latter, perform R.
Then repeat step A1 and go to step A6.
A5. If the U center is not grud, two of the U edges are grud, and
every face has some grud on it, perform U and go to step A7.
A6. If the U center is not grud and none of the U edges are grud,
either the F center is grud or the R center is grud. If the F center is
grud, perform F; if the R center is grud, perform R. Then repeat step
A1 and go to step A7.
A7. If the U center is not grud, two of the U edges are grud, and
either F or R does not have grud on it, then perform F or R (whichever
one did not have grud on it), repeat step A1, and go to step A8.
A8. The U face should now be all grud. If the other four faces are
"unsolved" (have colors of adjacent faces), perform U and it should
be solved.
B. Match the corners.
In other words, does each face have four corners of the same color? If so,
go on to step C. Otherwise, at least one face will have four corners of
the same color. Orient the cube so that it is the U face, and
then perform FRFRFR. This should match the corners.
C. "HOt HOt HOt" (double-slice group)
This step is to get rid of any face that looks like an "H" (all one color
except for two opposite edges), an "O" (all one color except for the
center), or a "t" (all one color except for the corners). This may
have to be done up to three times, and after they are removed
the cube should be in the double-slice group.
Orient the cube so that the top face is "HOt". Then, perform FRRF.
Repeat until no faces are "HOt".
D. Solve the cube.
The cube should now be in a very easy to solve state, if not already solved
already. If the cube is not already solved, there must be some
corner which does not match an edge next to it. Orient the cube so
that said corner is the UFR corner and the edge is the RU edge. Then,
perform FF. Repeat until the cube is solved.
--
Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
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