## Solution Procedure

### The Layer Method

The layer method solves the 5x5 by reducing it to a 3x3, and applying the layer method to solve the 3x3 cube.

The short version:

1. Solve center crosses

2. Solve center faces

3. Align triple edges (tredges)

4. Correct tredge orientation

5. Solve the 3x3

## Algorithms Cheat Sheet

### Tredge Fix

tredge = triple edge

Tredge Fix (Inversion) Algorithm
Fix one tredge whose middle piece has inverted colors: This algorithm should be applied once all triple edges have the colors of all three pieces oriented correctly, except for one triple edge.

Start with the cube oriented such that the tredge with the inverted colors joins the front (F) and upper (U) face of the cube. (This tredge is the cube's "forehead".)

Now execute the Tredge Fix (Inversion) algorithm:

```(Rr)2   B2   U2
(Ll)    U2
(Rr)'   U2
(Rr)    U2
F2      (Rr)
F2      (Ll)'
B2      (Rr)2
```

## Mathematical Representation

Like the 3x3 and 4x4 cubes, the 5x5 cube can be represented using a tuple, with one entry in the tuple per face of the cube.

The 3x3 cube has 3^2 = 9 faces per side, for a total of 6 x 9 = 54 faces, so the state of any 3x3 cube can be represented using a 54-uple.

The 4x4 cube has 4^2 = 16 faces per side, for a total of 6 x 16 = 96 faces, so the state of any 4x4 cube can be represented using a 96-uple.

The 5x5 cube has 5^2 = 25 faces per side, for a total of 6 x 25 = 150 faces, so we can write the state of any 5x5 cube using a 150-uple.

For general information on the mathematical representation of the cube:

For information specific to the 5x5 cube: