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
Happy Cube The basic challenge of the Happy Cubes puzzles is to construct a single perfect cube from the 6 pieces of a single puzzle which share the same color scheme and texture. A subsequent challenge to this is to fit the pieces back into the 2-dimensional frame from which they came. With the presence of more than one puzzle available, pieces of several different cube puzzles can be joined together to make up larger and more complex structures other than the basic 6 faced cube. Some structures are more difficult to construct than others and the more pieces available, the easier