Interesting post, I can see this is consuming your very being at the
moment. (and I fully understand). Firstly, I'd like to agree with your
comment at the bottom, about the edge permutation (and it being
independent of this rest of the cube) - the 4x4 rocks!
Anyway, you made mention of a 'cage' method, which I haven't heard of
before. Could this be where you do the centers last? My original
method was just this, but I found it was a bit touch-and-go, however,
doing it this way, I could correct the parity errors (at least the
orientation one, not sure on the other one, my 4x4 is kaputt) before
they occured (and no, this was not elegant). At the time I thought
this method (even if it was 'beginners') was awful. A shame to leave
the privacy of my room, so to speak. As the cubes get larger, the
centers first method becomes increasingly applicable (and efficient),
but for the 4x4 is there promise with this cage method I wonder? If
so, I might have to have another look!
Cheers, happy cubing!
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