Newsgroups: rec.puzzles
From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Date: 1997/02/05
Subject: Re: Question about Rubik's Cube Spoiler

eff...@worldaccess.nl (Feico Nater) writes:

[ "Lance S. Hopenwasser" asks how to solve the face center twists on
  Rubik's cube. ]

> I understand that you cube is just like Rubik, except that the centers
> of each side have marks.
> I made such a cube myself, by making each face two-colored.

I wonder how much you played with it, since the procedures you give
for solving it do not work.

> Spoiler follows----------------------------
> 1. Make sure the top is correct.
> 2. Make sure the centers of the front, back, left and right are correct.
> 2a How to turn the center of the front plane without affecting the top?
> 2b Turn front 180 degrees
> 2c Turn bottom 180 degrees
> 2d Trun front as needed
> 2e Turn bottom 180 degrees
> 2f Turn front 180 degrees
> 3. Move the cubicles on the four edges into position.
> I hope this is helpful so far.

If your step 3 procedures for moving the edge cubies mess up the face
twist, you might have to go back to step 2, and never reach solution.
My methods for solving face center twist avoid this problem, because
they do not leave any cubies out of position.

> If a center cublicle is turned clockwise, there is always another
> center cubicle turned anticlockwise,

Wrong.  You could have two face centers rotated in the same directon,
or one center rotated 180 degrees, without any others rotated.  In
half the face center positions, the total face center rotation will
be 180 degrees (modulo 360 degrees), so it is hard to imagine how you
could use this procedure without noticing the problem.

> Here is a procedure to turn a number of center cublicles:
> 1. Turn right plane clockwise
> 2. Turn horizontal equator anti clockwise
> Repeat seven times. Eight times in all.

That will not rotate any face center an odd multiple of 90 degrees.
So even if your analysis were correct, this would not be a solution to
the position in which one face center is rotated 90 degrees clockwise
and another is rotated 90 degrees anticlockwise.

The method I found sixteen years ago for solving face centers is at

  http://www.math.rwth-aachen.de/~mschoene/Cube-Lovers/
  Dan_Hoey__The_Supergroup_--_Part_3__A_Super-H_and_Spoilers.html

and is also available as part of

  ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-1.gz

if you prefer FTP.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil