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
Helicopter Cube number of permutations is reduced to 24!/(4!) arrangements. The reducing factor comes about because there are 24 (4!) ways to arrange the four pieces of a given colour. This is raised to the sixth power because there are six colours. This gives a total number of permutations of The expanded number is (approximately trillion or 12 trilliard on the long scale or 12 sextillion on the short scale) To count non-cube positions, we need to count all the possible shapes (ignoring the colours). Counting those shapes is tricky, since sometimes moves are blocked purely due to the shape of the