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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 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU