I just wanted to thank everyone who gave me some insight as to how to go
about attacking the parity problem in Square-1. It was, indeed as I
thought, a parity issue like the double flipped edges in the 4x4x4, and not
just some oversight on my part. Ron, your tips were particularily helpful.
I didn't have to buy any books or anything, and I can now solve it every
time. I've got to go find a new puzzle now.