How can the top part be solved without looking at the other parts? I'm confused :)
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Because the game only allows 180-degree rotations, it’s impossible for any given face to be anywhere but on either the correct face or the opposite face.
I actually was going to allow for 90-degree rotations originally, but the math needed for rendering that was too difficult for my barely-passed-linear-algebra brain, and then later I realized that it would have made the game too hard to play anyway. The number of possible cube states with 180-degree rotations is a tiny fraction of the total number of possible states of a real cube.