Considering a single side of a standard 3x3 Rubik's Cube, are all possible color combinations attainable? Or are there certain combinations that can only be made by breaking apart the device or moving stickers?
I know there are unsolvable cubes when considering all 6 faces, but within a solvable cube, are all color combinations attainable on a single face?
To put another way, if I randomly selected the color for each of the 9 squares on one side, could standard solved cube always be shuffled in such a way that one of its faces contained that configuration?
Note: I don't know the answer, and I'm simply curious; it seems a mixture of Math and Rubik's Cube knowledge.