Ah, Rubik's Cube once more.
I loved it, actually I own several of them. Some more facts:
Prof. Rubik created the cube for his students to prove that he solved the problem of the independently moving layers. We were all amazed, like Ed was, to see that it can be done.
The puzzle-aspect originates from adding the six colours to the sides of the cube.
There is a special position that allows you to take the cube apart without breaking anything - starting with one cubicle. It is possible to re-assemble it in a wrong way: so it can never be solved. That's because there are basically 2 different topological configurations given the coloured cubicles. Those two configurations have none of the "views" of the cube in common, so the "solved" cube belongs to only one of them.
Official competions started with a "solved" cube being turned randomly by a judge a given number of times. Normally that given number was 13. So if you think about that, it was always possible, theoretically, to move it back by no more than 13 moves. No one found those moves in time of course.
Official analysis shows that there is a maximum to the number of moves each position is "away" from the zero position. I don't remember it by head for certain, but I seem to remember that number was 53 or so. Perhaps I'm wrong here.
The general solutions given by most books are based on moves necessary to move a single cubicle from position a to (proper) position b, without disturbing already correctly placed cubicles. Of course that leads to many redundant moves.
While you're using this sort of instructions, you most probably start moving the cube farther away from it's solved position instead of getting closer (strictly speaking).
One can try for a fundamental solution for each position. I once wrote an "total analysis" version of a Rubik's Cube solving program using Turbo Pascal. Unfortunately it could only go as deep as 6 moves in about 2 minutes (and needed a time factor of 12 for each further move). Recently, I wrote a Visual Basic version of the program, but it can only solve ... 8 moves in 11 minutes (on a much faster PC). So, we still need C++ or machine code as well as a faster computer.
The puzzle with the rings, known as Rubik's Magic, constitutes a "trick". You cannot solve it until you realize the funny outcome. (I leave it at that, not to spoil it for those who are wanting to give it a try.)
Cees