Thank you, for your quick response!vysarge wrote:Hello thedentist! This seems like an interesting project.
I know a bit about the Rubik's cube, so hopefully I'll be able to help.
I looked over the project design, and I noticed some interesting features.
1) When solving a Rubik's cube, it's necessary to move both the corner and edge pieces to the correct positions, as the center pieces can't really be moved. In a solved Rubik's cube, what has to be true about the corner pieces? If you have a mixed-up Rubik's cube, you might be able to make some progress by using Move Sequence #2 to make the corner pieces match the center ones on each face. (Does this make sense? For example, if you have a white center piece, you'd have to get all of the corners with white sides on the top of the cube, then you'd have to get those corners' sides to match.) You might be able to make some progress by looking at how Move Sequence #2 affects the corners of an unsolved cube, and how it could be used for a cube with only two corners out of place, or only three corners out of place. At this stage, I wouldn't worry too much about the edge pieces.
2) After you figure out how to solve the corners, the rest is manipulating the edges. Move Sequence #1 actually switches edge pieces from one edge to another; you could use it when edges are entirely out of place. Move Sequence #3 just flips edge pieces. So, could you make progress by trying to get the edge pieces in the correct places first, then flipping them until the cube is solved?
In general, one of the main strategies that you may have run across is to do the corners first, then the edges. I think that for an algorithm, especially if you're stuck, this could be a good place to start from.
Hope this helped, and good luck- if this isn't quite clear, or you have more questions, do ask!
vysarge wrote:You're welcome!
I think that solving one face at a time might not be the best way to attack the problem- as you said, there's always the issue of messing up what you've already done. Rather, by combining uses of the sequence in different orientations, might you be able to invent combination sequences that only modify two or four corners? For example, if you do the sequence once, then rotate the cube 90 degrees and try again, what is the result?
(If you get really stuck, you could always try searching for a corners-first solving method online to get some inspiration.)
For flipping, take note of the fact that "Repeating [Move Sequence #2] fifteen times restores the cube to it's original position." Since there are five corners involved and the movement makes a loop, repeating the sequence five times restores each corner to its original place- but not its original orientation. So doing the sequence five times should flip the corners, while keeping them in the same places.
Hope this helped! (And again, any more questions/etc, just ask!)
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