Professor's Cube the Eastsheen 5×5×5 and the V-Cube 5 are designed with different mechanisms in an attempt to remedy the fragility of the original design. There are 98 pieces on the exterior of the cube: 8 corners, 36 edges, and 54 centers (48 movable, 6 fixed). Any permutation of the corners is possible, including odd permutations, giving 8! possible arrangements. Seven of the corners can be independently rotated, and the orientation of the eighth depends on the other seven, giving 3 (or 2,187) combinations. There are 54 centers. Six of these (the center square of each face) are fixed in position. The
Combination puzzle can be achieved by randomly placing the coloured stickers on the cube, but not all of these can be achieved by manipulating the cube rotations. Similarly, not all the combinations that are mechanically possible from a disassembled cube are possible by manipulation of the puzzle. Since neither unpeeling the stickers nor disassembling the cube is an allowed operation, the possible operations of rotating various faces limit what can be achieved. Although a mechanical realization of the puzzle is usual, it is not actually necessary. It is only necessary that the rules for the operations are defined. The puzzle can be