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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Any permutation of the 8 corner cubies is ...

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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Any permutation of the 8 corner cubies is possible (8! positions), and 7 of the cubies can be independently rotated (37 positions). There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 24. This is derived from the fact all 24 possible positions and orientations of the first corner are equivalent because of the lack of face centers. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles have fixed centers which identify the cube's spatial orientation.