Pocket Cube court affirmed the judgment that Rubik's 2×2×2 Pocket Cube infringed Nichols's patent, but overturned the judgment on Rubik's 3×3×3 Cube. Any permutation of the eight corners is possible (8! positions), and seven of them can be independently rotated (3 positions). There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 24. This is because all 24 possible positions and orientations of the first corner are equivalent due to the lack of fixed centers. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles
Multimagic cube Multimagic cube In mathematics, a "P"-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their "k"-th power for 1 ≤ "k" ≤ "P". Thus, a magic cube is bimagic when it is 2-multimagic, and trimagic when it is 3-multimagic, tetramagic when it is 4-multimagic. A "P"-multimagic cube is said to be semi-perfect if the "k"-th power cubes are perfect for 1 ≤ "k" < "P", and the "P"-th power cube is semiperfect. If all "P" of the power cubes are perfect, the multimagic cube is said to be perfect. The first known