Regarding swapping two edges on Square-1.
You prompt me to write about something I have been meaning to get around
to for a long time.
Long ago I found a way to swap two edges using a complicated sequence.
After considerable unsuccessful effort to improve the solution, I bought
Richard Snyders amazing book "Turn to 1" from Puzzletts.
( HTTP://WWW.PUZZLETTS.COM/ ) His solution is essentially the same as
mine. His method of documentation obscures what is really going on and
consequently it would be very hard to memorize. The principal is
straight forward and follows these steps.
Move all the edge pieces to the same side in an orderly sequence.
Turn the side that has all corner pieces, one position.
Retrace all the moves that brought the edge pieces to the same side.
Fix any thing that got messed up in the process. (this is what I call
Snyder's solution optimizes the process to minimize the collateral damage
but any variation on the steps listed above will work.
On a related subject....
How to get the puzzle into the shape of a cube after initial scrambling.
Snyders book shows pictures of all possible scrambled shapes. Each has
instructions for making a few turns and the next diagram to refer to.
This process may be optimal for getting it into a cube shape but it is
nearly impossible to memorize.
I am sure everyone who works with the puzzle learns some shapes that are
close to the cube shape but it may seem nearly impossible to generally
solve in any orderly way. Well consider the following strategy:
Collect all the edge pieces on the same side. They can all be side by
side in what Snyder calls the Hoofprint pattern or in the Moon pattern
that has two groups of four edges on the same side. Then move half of
the edges to the opposite side. Then move half of the edges from the top
to the bottom and half of the edges from the bottom to the top, but do so
in a way that separates them into groups of two. You are then with a
couple of twist of making a cube.
The beauty of the strategy is that to obtain perfect final symmetry, you
first take it to a position of maximum asymmetry. Every turn after that
keeps it symmetric.
This method will not generally be the optimum solution but it is straight
forward and easily learned.
I said this is related to the previous subject of swapping two edges
because both require reaching a position will all the edge pieces on one
side. I might not have ever found the method for swapping two edges if I
had not first adopted this method for getting it into a cube shape first.
While I am sending out a message let me recommend that everyone include
their mail address when the send a message. Recently a couple of
messages did not. I would have send the author a personal message
answering a simple question but didnt want to bother everyone else. One
such question was about obtaining 3x3x3 cubes. They are available in
many chain toy stores including "The Game Keeper" and "LearningSmith".
Most puzzles are available from Puzzletts also.
I also notice that several local stores are carrying Rubiks Magic again.
The colors are different than the originals.
In 1982 a Worlds Fair was held in Knoxville Tenn. USA.. At the enterance
to the Hungarian pavalion was a Rubik's Cube about 4 feet on a side
mounted on a pedistal. At that time a Rubik's Cube was a universially
near Washington D.C.