Date: Fri, 20 Oct 95 09:18:20 -0400
From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >
```On 10/20/95 at 13:00:30 Mikko Haapanen said:
```

I want to ask if somebody can tell me how to flip 2 adj. edges (and nothing
else) in 4x4x4 cube?

That reminds me of a question I have been meaning to ask for a long time.
But first here is some context, involving some reminisces about when
I first figured out how to solve the cube.

After buying my first cube, it took me about a week to figure out how
to solve everything except two edges cubies which were flipped. It took
me about another week to figure out how to unflip them. Since then, I have
discovered that about half the time, my method of solution yields two
flipped edge cubies which have to be unflipped, and about half the time
it doesn't. Fair enough -- 50-50 chance, I guess. (When I am in
practice, I can see the flipped edge cubies coming, and can compensate
as a part of the process of getting the last few edge cubies in place,
but I am seldom really in practice.)

The 4x4x4 was a little tougher. It took me about a week to figure out
how to solve everything except two edge cubies which were exchanged.
It took me about another year(!) to figure out how to exchange them.

On the 3x3x3, I solve the corners first, then the edges. I use the
same general method on the 4x4x4, except that there are four face
centers (if you can call them that) on each face to deal with. So
I solve the corners first, which establishes a frame of reference.
Then, I solve the face centers with respect to the frame of reference
established by the corners. Finally, I solve the edges. All the
operators are identical or similar to the ones I use for the 3x3x3.

For the longest time, I thought that a parity argument made one
exchange of the edges impossible, and I was just sure that somebody
was taking my cube apart and putting it back together when I wasn't
looking. I went through two or three cycles of taking it apart
myself and putting it back together in Start, scrambling it, and
trying to solve it, all in one sitting, before I was convinced that
you really could have just one exchange of the edges.

What I didn't see originally was that there could be invisible
movement of the face centers to compensate for the "bad parity" of
the edges. I am very poor at solving the 4x4x4, but here is how I
do it. When I get the "bad parity", I make one slice move (doesn't
disturb the corners), and then solve the face centers again without
simply undoing the once slice move and without worrying about the
edges. Then, upon solving the edges the second time, there is
"good parity" and all is well.

Finally, here is my question. On the 4x4x4, I get "bad parity" darn
near every time. Why isn't it 50-50 like the situation I have with
flips on the 3x3x3?

``` = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)                        (304) 293-5192
Associate Director, WVNET                            (304) 293-5540 fax