Rubiks Revenge/Layer Method
From charlesreid1
This page covers a solution algorithm for the 4x4 Rubiks Cube, a.k.a. Rubiks Revenge.
Solution Algorithm Steps
The layer method of solving the 4x4 happens in the following order:
1. Centers: Solve the four center faces (ensure the faces are correctly oriented relative to one another)
2. Double Edges: Solve the 12 double edges so that each double edge cubie matches its neighbor
3. Solve the 3x3: Apply 3x3 algorithms to solve the cube (the cube is in a pseudo-3x3 state at this point - the two double edge pieces can be thought of as a single edge piece, and the four center faces can be thought of as a single center face)
4. Last layer parity: At this point, all layers except the last layer are solved. The last layer parity can either be odd (arrangements that can occur on the 3x3 cube, so no new algorithms are needed) or even (arrangements that can only occur on the 4x4 cube, so new algorithms are needd).
4a. Odd Parity: If the last layer parity of the 4x4 cube is odd, that means the top layer can only be arranged in ways that are equivalent to a 3x3 cube (the top layer can have a white square, a white L, a white I, or a white cross). The same algorithms that work for the 3x3 cube will also work for the 4x4 cube.
4b. Even Parity: If the last layer parity of the 4x4 cube is even, that means the cube will reach states that are unreachable on a 3x3 cube, so new algorithms are needed. The even parity scenario occurs in the form of a single pair of inverted double edge cubies (i.e., the double edge cubies are at the correct edge, but the colors are inside-out; equivalent to a T configuration on the top layer).
5. Last Layer Corners: The corners of the last layer also splits into an even parity and odd parity situation. If we consider the corner cubies on a 3x3 cube, we discover that we can ever only have zero, three, or four corner cubies swapped from their correct corners. On a 4x4, however, we can have zero, two, three, or four corner cubies swapped. The case of only two corner cubies swapped can only occur if the cube has an even number of pieces on each side.
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