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I've always wondered, what is the number of possible permutations of the Rubik's cube such that any two adjacent stickers has a different color. By a permutation I mean a configuration of the cube that can be achieved from the solved cube by only using the legal moves.

An obvious example is the superflip. This picture below is an example of a configuration which fails to fulfill the requirement.

enter image description here

I don't actually have any clue on how one might go about solving such a question and that's why I'm asking.

Extra question: This might be too vague question but it would be interesting to know if solving such cube as described above, takes more moves than one which has adjacent pieces with same color.

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