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From: whuang@ugcs.caltech.edu (Wei-Hwa Huang)
Subject: Re: Method for Solving the Professor's Cube (5x5x5)
Date: 2 Dec 1998 18:21:22 GMT
Organization: California Institute of Technology, Pasadena
Message-Id: <7440f2$q5v@gap.cco.caltech.edu>
References:
Han Wen writes:
>For those brave souls who would like to conquer this beast, the
>following solution may provide some enlightenment. It's a layers
>solution, in contrast to the corners-first solution that I have seen
>posted on various web sites. Good luck to you. The Professor's Cube
>is a truly challenging puzzle.
>______________________________________________________
>Method for Solving the Professor's Cube (5x5x5)
[snip]
Well, since we're sharing solutions, here's my solution to the 5x5x5:
First, a preliminary exercise that
should be mastered before the solution is attempted:
Let's ignore all the corners and all the cubies adjacent or
diagonally adjacent to the corners. (In other words, ignore the
"supercorners," where "super" is a prefix meaning "two layers deep.")
Ignore the centers, too. Paint all of them black, if you want. :-)
Now, all we have left are the 12 "superedges." Each superedge is
composed of a normal edge piece and two attached edge centers. Or,
in other words, each of the 24 edge centers are attached to
an edge piece face. In a normal messed-up cube, these edge
centers will not match their edge piece faces. Our goal in this
exercise will be to match all the edge centers with their edge piece
faces.
Note that superface turns never destroy an edge center pairing.
Now, consider the following sequence of moves:
1. Rotate any face (NOT superface) 180 degrees.
2. Turn any center slice (as much as you want).
3. Rotate the same face in step 1 180 degrees.
(i.e., perform the inverse move of step 1.)
Now, if you chose the center slice to be parallel to the face,
obviously this sequence doesn't do anything. Ditto for when you
turned the center slice some multiple of 360 degrees.
In all other cases, this will essentially perform two swaps of
edge centers. Step 1 swaps two pairs of edge centers all around the
face, but one of those swaps gets undone by Step 3. Step 2
moves the other pair out of the way and puts another pair in its
place to be swapped again. So, if you choose wisely, you can
increase the number of correctly matched edge center pairs by this
move.
Many of these moves, interspersed with superface turns, will
allow you to match all the edge center pairs. Practice this on
your cube.
Thus ends the preliminary exercise. Note that all the moves in
the exercise do not disturb the individual supercorners (well, one
move does for a bit, but then it undoes the damage) but does change
their orientation with respect to each other.
Now, the solution!
Step 1. Ignore the superedges and the centers. You now have what
is equivalent to a 4x4x4. Solve it.
Step 2. Match the edge centers with the edges as detailed in the
preliminary exercise.
Step 3. You now have a cube with correct supercorners (as done in
step 1) and correct superedges (as done is step 2). This means
that your cube is equivalent to a 3x3x3, using only superface
turns. Solve it.
Step 4. Tada! Your 5x5x5 is now solved.
--
Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
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