# Solving A 5x5 Rubix Cube

Solving the 5x5 cube is similar (but slightly easier) than solving the 4x4. The process is the same but there are fewer edge cases.

The steps are

- Reduce it to a 3x3 by
- Solving the center
- Solving the edges
- Handle any edge parity

- Solve the 3x3

## Center Solve

The center solve is the exact same as a 4x4, just a litle bigger.

- Solve the white square
- Solve the opposite side (yellow square)
- Solve any of the remaining sides
- Solve the adjacent side (it could be any side, but it’s just easier to solve the adjacent side since it means less flipping the cube around)
- Solve the remaining two sides in one go

# Edges

## Free Slicing

To speed things up you can use the “free slicing” method. Which pretty much means you solve 8 of the edges w/out making sure you get the center squares resolved after each pass. This just speeds up the process. Once you have 8 out of the 12 edges solved, you put them at the top and bottom and then resolve the center squares. After this, you can solve the remaining 4 edges the “normal” way: one block at a time and always bringing the square faces back to solved after every move.

## Flipping an edge

In order to pair up an edge you may need to flip one of the edge pieces. For example, you would want to flip the orange/blue piece in the top right with the bottom right red/green piece. This will let you slot in the blu/orange piece in the next move.

```
🔲|🔲🔲🔲🔲🔲|🔲 🔲|🔲🔲🔲🔲🔲|🔲
🟦|🟧🔲🔲🔲🟧|🟦 🟦|🟧🔲🔲🔲🟥|🟩
🟦|🟧🔲🔲🔲🟥|🟩 ==> 🟦|🟧🔲🔲🔲🟥|🟩
🟨|🟩🔲🔲🔲🟥|🟩 🟨|🟩🔲🔲🔲🟦|🟧
🔲|🔲🔲🔲🔲🔲|🔲 🔲|🔲🔲🔲🔲🔲|🔲
```

The algorithm for this is

```
R U R` F R` F` R
```

## Parity

```
⚪|🟨🟨🟦🟨🟨|⚪ ⚪|🟨🟨🟨🟨🟨|⚪
———————————————————— ———————————————————
🟧|🟦🟦🟨🟦🟦|🟥 🟧|🟦🟦🟦🟦🟦|🟥
🟧|🟦🟦🟦🟦🟦|🟥 🟧|🟦🟦🟦🟦🟦|🟥
🟧|🟦🟦🟦🟦🟦|🟥 ==> 🟧|🟦🟦🟦🟦🟦|🟥
🟧|🟦🟦🟦🟦🟦|🟥 🟧|🟦🟦🟦🟦🟦|🟥
🟧|🟦🟦🟦🟦🟦|🟥 🟧|🟦🟦🟦🟦🟦|🟥
```

Either of the below algorithms will solve this problem. Pick whichever you like best.

### Algorithm 1

```
Rw U2 x Rw U2 Rw U2 3Rw' U2
Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
```

### Algorithm 2

```
Rm' U2 Lm F2
Lm' F2 Rm2 U2
Rm U2 Rm' U2
F2 Rm2 F2
```

## Reading the diagrams

In the diagrams above I use the following conventions.

- The 🔲 square is used to denote a square we don’t care about
- The ⚪ is just a spacer. It means nothing and is only there so everything else lines up.
- The
`|`

is used to denote the side edge of the cube. Something to the left of a`|`

is on a different face than the square to the right of it. - The — is used to denote the top edge of the cube. Something above the — is on a different face than the square below it.

## Note on notation

Some of the notation for 5x5 is slightly different than the 4x4 or 3x3

`Rw`

means “right wide” or the two rightmost columns.`3Rw`

means the 3 right most columns`Rm`

means the “right middle” column. So it’s rotating just the single column between the center colum and the right face.`Lm`

means the “left middle” column.`x`

means to rotate the entire cube so the bottom is now the front and the front is now the top. The two sides (left and right) do not change.