Ronnie,

It's been so long since I've messed around with my 4x4x4 that
I can't answer your question directly, however when I
see descriptions for the method in which people solve the
4x4x4 it is usually different from the way I first solved
it:

What I did was to pair up the middle two edgies, and the
four central face cubes. There are few enough restraints
that this is not too hard to do for someone who has never
touched a 4x4x4 cube. One then has a cube like with faces
similar to the following:

r b b g
y o o b
y o o b
r y y w

One can then "pretend" it is a 3x3x3 cube and then solve it.
Unfortunately you will occasionally end up in an orbit of the
"pseudo-3x3x3" that is impossible to solve. Oh well... scramble
it and try it again.

Using this technique I was able to solve a scrambled 4x4x4 cube within an
hour or so of when I set my hands on one. Needless to say, this is NOT a
good technique for solving a 4x4x4 cube if one is interested only in the
4x4x4. In fact I suspect it is a pretty awful algorithm, especially since
you frequently end up in an unsolveable orbit using your standard 3x3x3
techniques. But it is a useful trick for maximizing the hard work one used in
learning the 3x3x3.

As most people who have a 4x4x4 realize, if you never make any twists of a
solved 4x4x4 cube except along the center, you of course have a 2x2x2. And
as I described, if you only make moves 1-deep, it is equivalent to a 3x3x3,
and of course it is also a 4x4x4.

Tom Miller
tomgm@physics.purdue.edu