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# Rubiks Revenge

4x4 Rubiks Cube

## Solution Procedure

I use a modified "beginner's method" to solve the 4x4. This involves reducing the 4x4 to a 3x3, solving the 3x3, then dealing with parity issues in the last step.

### Step 1: Centers

Start by aligning the four cubies in the center of each face. White/yellow, blue/green, and red/orange are all on opposite faces. Line up four of the six faces in any order, but when lining up the last two faces, make sure you have things oriented correctly! Red is to the right of green, etc.

### Step 2: Align Double-Edges

Next step is to align the two cubies in each double-edge so that they have the same color and orientation.

Start by aligning the four double-edges on the top of the cube, then align the next four double-edges on the bottom of the cube.

The last four double-edges can be aligned as well, but will require a slightly different algorithm to keep from undoing the double-edges that are already oriented.

### Step 3: Solve the 3x3

At this point, things get a little easier. Now that the centers are a solid color and the double edges are all matching, the two middle cubies of the 4x4 cube can be treated as a single cubie, turning the 4x4 cube into a 3x3 cube. You can now quickly solve the bottom three layers of the 4x4 cube by simply applying 3x3 algorithms (line up the cross on the bottom, arrange the corners, then align the middle two layers.

### Step 4: Last Layer Double-Edges

The last layer is where things diverge from the 3x3 cube.

When solving the cross on the last layer of a 3x3 cube, there are 4 possible configurations. These four configurations can be cycled through by repeatedly applying a single algorithm. The four configurations are:

• A single square (four squares) on the top is in-place
• Three squares (eight squares) on the top are in place (forming an L shape)
• Three squares (eight squares) on the top are in place (forming an I shape)
• Five squares (twelve squares) on the top are in place (forming a cross)

This arrangement will occur some of the time on the 4x4 (this is the "easy case" - solving the 4x4 is exactly like solving the 3x3, no new algorithms required).

Rubiks Revenge: Parity Situations Occurring On 4x4 Or 3x3
Center Square Configuration: Eight-Square L Configuration: Eight-Square I Configuration: Twelve-Square Cross Configuration:

On the 4x4 cube, there are two sets of configurations. The first set are the four configurations listed above, that occur on the 3x3. The same 3x3 algorithms can be applied to the 4x4 as to the 3x3. However, the second set of configurations is:

• Ten squares on the top are in place (forming a T shape)
• Six squares on the top are in place (forming an incomplete I shape)

The same algorithm that cycles through the four configurations on the 3x3 can be applied to these configurations on the 4x4 to switch between them. Depending on the orientation of the cube, the T shape can be permuted into another T shape, the incomplete I shape can be permuted into another incomplete I shape, or the T and incomplete I can be turned into one or the other.

You can always get to the T shape from an incomplete I shape. There is an algorithm that fixes the one side of the T shape that is not oriented correctly. This is the situation where there is a single double-edge that is "inside out."

Rubiks Revenge: Parity Situations Occurring On 4x4 Only
Single Dedge Inside-Out (T configuration): Three Dedges Inside-Out (Incomplete I configuration):

### Step 5: Last Layer Corners

When solving the corners of the last layer of a 3x3 cube, only two situations can occur:

• All four corners have the correct matching colors, and simply need to be re-oriented to solve the cube.
• One of the four corners has the correct matching colors, and three corners need to be swapped/cycled.

However, in a 4x4 cube, because there are an even number of cubies, you can end up with one additional situation:

• All four corners have the correct matching colors, and simply need to be re-oriented to solve the cube.
• One of the four corners has the correct matching colors, and three corners need to be swapped/cycled.
• Two of the four corners have the correct matching colors, and two corners need to be swapped/cycled.

The case of two swapped corners requires a special algorithm.

Rubiks Revenge Corner Situations
Two Swapped Corners and a Swapped Dedge: Two Swapped Corners:

## Algorithms

### Last Layer Algorithms

Parity Algorithms
Fix Two Swapped Corners: Start with the cube oriented with the two swapped corners on the top-left and top-right corners of the front face. Then execute the algorithm:
```R U' R B2 L' D L B2 R2 U
2R2 F2 2R2 f2 2R2 2F2
```
Fix Single Inside-Out Dedge: Start with the cube oriented with the inside-out dedge at the top of the front face. Then execute the algorithm (broken into pieces to make it easier to remember):
```r' D' 2U' u'
r 2F r'
u
r 2F' r' 2F'
u'
2F u 2F
2U D r
```