Rubik's Revenge - Solutions

Solutions

There are several methods that can be used to solve a Rubik's Revenge. The most common method is reduction, so called because it effectively reduces the 4x4x4 to a 3x3x3. Cubers first group the centre pieces of common colours together, then pair edges that show the same two colours. Once this is done, turning only the outer layers of the cube allows it to be solved like a 3×3×3 cube. However, certain positions that cannot be solved on a standard 3×3×3 cube may be reached. There are two possible problems not found on the 3x3x3. The first is two edge pieces reversed on one edge, resulting in the colours for that edge not matching the rest of the cubies on either face:

Notice that these two edge pieces are swapped. The second is two edge pairs being swapped with each other:

These situations are known as parity errors. These positions are still solvable; however, special algorithms must be applied to fix the errors.

Some methods are designed to avoid the parity errors described above. For instance, solving the corners and edges first and the centres last would avoid such parity errors. Once the rest of the cube is solved, any permutation of the centre pieces can be solved. Note that it is possible to apparently exchange a pair of face centres by cycling 3 face centres, two of which are visually identical.

Direct solving of a 4x4x4 is uncommon, but possible, with methods such as K4. Doing so mixes a variety of techniques and is heavily reliant on commutators for the final steps.