I, too, gave myself Square One for Christmas, and I, too, would love to
exchange some useful moves. Here are three that I use. I need some more!

-- Rodney Hoffman
Hoffman.El_Segundo@Xerox.com
or rodney@oxy.edu

------------------------------------------------------

Conventions used in these descriptions:

* These moves start and end in a cube shape. I always hold the
logo to my left, with the two faces which can rotate in front
and back. That means the plane of the 180-degree twist is
perpendicular to my face, angling from upper right to lower left.
The "front" face is the one I'm looking directly at.

* "the smallest increment" as in "Turn the front face cw
the smallest increment". This means the smallest amount
that permits the big 180-degree twist that must follow.
Note that the angle of turn is not always the same! Sometimes
"the smallest increment" turn is truly the smallest possible
increment, that is, the width of an edge piece. At other
times, it may be the width of a corner piece (much larger),
or even two or three piece's widths combined.

* "to match" as in "Turn the back face to match".
This means the front and back faces remain aligned with one
another.

* "Now do the 180-degree twist." I move the right half 180
degrees, holding the left half fixed. The logo stays fixed
in position and orientation, never moving.

* To help in describing the effects of these moves, I will
refer to the pieces by number, as follows. Here I have
numbered the pieces clockwise from the upper left corner
piece on the front face. I have numbered the back face
similarly, ** as if looking straight through to it **,
that is, piece 9 is directly beneath piece 1, piece 10
is directly beneath piece 2, etc.:

Front Face               Back Face

       1   2   3                9  10  11
8       4               16      12
7   6   5               15  14  13

------------------------------------------------------

(1) Swaps all 8 corner pieces diagonally directly across in pairs, staying on
the same faces (front and back). In my numbering scheme, this move swaps 1
with 5, 3 with 7, 9 with 13, and 11 with 15.

(a) Turn the front face cw the smallest increment.
Turn the back face to match. Now do the 180-degree twist.

(b) Turn the front face ccw the smallest increment.
Turn the back face to match. Now do the 180-degree twist.

(c) Repeat the (a)(b) combination three times.

Note: This entire move, repeated twice, is, of course, an identity.

------------------------------------------------------

(2) Swaps all 8 edge pieces directly across in pairs, staying on the same faces
(front and back). In my numbering scheme, this move swaps 2 with 6, 4 with 8,
10 with 14, and 12 with 16.

(a) Turn the front face cw the smallest increment.
Turn the back face to match. Now do the 180-degree twist.

(b) Repeat (a) six times.

(c) Turn the front and back faces 180 degrees.

Note: This entire move, repeated twice, is, of course, an identity.

------------------------------------------------------

(3) Although this move itself is simple to describe, its effect is not. It
moves four pieces (two large and two small) from the front to the back, and
vice-versa.

It's easiest to just give a map of the changes:

BEFORE:     Front Face               Back Face

       1   2   3                9  10  11
8       4               16      12
7   6   5               15  14  13

AFTER:      Front Face               Back Face

      11  6  13                9  10   3
8     12               16       2
7 14   1               15   4   5

(Because the back face is never turned in this move, its pieces 9, 10, 15, and
16 always stay fixed. They are on the immobile half of the back face, the half
not moved during the 180-degree twists.)

(a) Turn the front face cw the smallest increment.
Do not turn the back face at all.
Now do the 180-degree twist.

(b) Turn the front face ccw the smallest increment.
Do not turn the back face at all.
Now do the 180-degree twist.

(c) Repeat the (a)(b) combination three times.

Note: This entire move, repeated five times, is an identity.

------------------------------------------------------