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### Rubik's Cube

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Date: 02/18/99 at 23:31:58
From: Connie
Subject: Rubiks Cube

As I was going over my information, I came across Edge Mover #1 and #2,
two-corner swap, three-corner shuffle, and edge-flipper left and right.
Do they help me solve the layers of the big cube? Can you please
briefly explain what they are? They seem very confusing, but I bet you
know them.

Thanks for the terminology and your time.
```

```
Date: 02/20/99 at 20:51:40
From: Doctor Rick
Subject: Re: Rubiks Cube

I don't know these terms, but I can understand what some of them are.

It's fairly easy to get the first cubies in the right place, because
you do not have to worry about how you mess up, say, the bottom face
of the cube while you get the rest right. But once you have most of
the cubies in place, you need to know some sequences of turns that
move just a few cubies (and just the ones you need to move!) without
messing up any others.

That is where the kinds of sequences you have named come in. Each is a
sequence of turns; most are fairly long sequences. For instance, one
three-corner shuffle that I found, when expressed in my notation
(which I think I got from a Scientific American article), is

FRBR'F'RB'R': exchanges the positions of 3 corners

Another swaps two pairs of corners. Maybe that is your "two corner
swap." It can be proven mathematically that it is impossible to swap
just two corners, but you can swap two pairs of corners. I also have
sequences of moves that exchange three edge cubies, or two pairs of
edge cubies.

Once the cubies are all in place, you may still need to flip some of
them where they are. There are sequences of moves that twist 3 corner
cubies, or that twist 2 cubies in opposite directions, or that flip
two edge cubies. Here is one that flips a pair of edge cubies:

LU'FL'UFB'R'UF'RU'BF'

If you still don't have a cube to try these sequences on, I cannot
really make it less confusing. I hope this helps.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/

For links to sites with Rubik's cube information, see the May 10, 1999
issue of the Math Forum Internet News:

- Doctor Sarah, The Math Forum
http://mathforum.org/dr.math/
```
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