## Vandenbergh-Harris Last Slot

VHLS (Vandenbergh-Harris Last Slot) is a method for solving the last F2L pair in which you already have a connected or separated pair (the cases that can be solved in 3 moves) while also orienting the last layer edges. This will result in only OLLs in which the edges are already oriented, so you could use one of the 7 OLLs with the edges already oriented or you could use COLL and end with an EPLL. It also increases the odds of an OLL skip from 1/216 to 1/27. These are also the first cases you should learn if you're interested in learning full ZBLS. Honestly, I think the best use for many of these is in one-handed solving to get an easier alg in the next step for only a couple extra moves.

These are the 32 F2L cases for the last slot and the algorithms I use for them. These algorithms appear EXACTLY as I perform them when I am solving the last layer, in speedcubing notation with rotations included in the algorithm. It should be noted that these are the algorithms that I find easiest to perform. However, you may find other algorithms better-suited for your own hands, so it is recommended to try many different algorithms for the same situation to find which one works best for your own style of cubing.

In each diagram, yellow is the color of the upper face. A yellow "bar" indicates that the last layer color is facing that direction in that location. Grey denotes that a particular piece is not oriented correctly.

### Connected Pair

Name | Diagram | Algorithm | Comments |

ALL | [U] (R U' R') |
This is the most basic case. | |

UL | [U] F' (L' U' L F) |
This is a pretty easy case. | |

UF | (R' F R F') |
This is called the sledgehammer. | |

UB | y [U] F (R U') (R' F') |
This one is pretty quick. | |

UFUL | (R' U' F U) (R2 U') (R' F') |
This one is a bit too long to be practical. I will usually just do a sledgehammer or regular insertion here. | |

UFUB | (R' F) (R2 U R' U' F') |
This one is not great, but it's still decently fast. | |

UBUL | y [U2] (F U') (R U') (R' F') |
This one is a bit too long to be practical. I will usually just do a sledgehammer or regular insertion here. | |

NONE | y (R' F' R) U2 (M' U' M) |
This case is pretty neat because it turns what would be a nasty no edges OLL case into a nice case with all edges oriented and it's a pretty fast alg. |

### Mirrored Connected Pair

Name | Diagram | Algorithm | Comments |

ALL | [Dw'] (L' U L) |
These are just the mirrors of the above cases. | |

UB | [Dw'] F (R U R' F') |
These are just the mirrors of the above cases. | |

UR | (F R' F' R) |
These are just the mirrors of the above cases. | |

UL | [U'] F' (L' U) (L F) |
These are just the mirrors of the above cases. | |

UBUR | y (L U F' U') (L2' U) (L F) |
These are just the mirrors of the above cases. | |

URUL | y (L F') (L2' U' L U F) |
These are just the mirrors of the above cases. | |

UBUL | [U2] (F' U) (L' U) (L F) |
These are just the mirrors of the above cases. | |

NONE | (L F L') U2 (M' U M) |
These are just the mirrors of the above cases. |

### Split Pair

Name | Diagram | Algorithm | Comments |

ALL | (R U R') |
This is just the standard insertion. | |

UF | (R U') (R' U2') (R' F R F') |
This one is a bit too long to be practical. I will usually just do a regular insertion here. | |

UL | (R U2') (R' U') (R' F R F') |
Here you just make the pair, restore the cross, and sledgehammer the pair in. | |

UR | [Dw'] (L' U2' L) Dw (R U' R') |
Here you just make the pair, restore the cross, and sledgehammer the pair in. | |

URUL | (R U2) y (R U') (R' F') |
This one is a bit too long to be practical. I will usually just do a regular insertion here. | |

UFUL | [U2] (R U) y (R U') (R' U' F') |
This one is a bit too long to be practical. I will usually just do a regular insertion here. | |

UFUR | (R U) y (R U R' U') F' |
This one is a bit too long to be practical. I will usually just do a regular insertion here. | |

NONE | (R' D') (L F' L' D) (R2 U R') |
This case is neat to know, but I don't use it too often. I usually just use it in one-handed solving to avoid the much longer cases with no edges oriented. |

### Mirrored Split Pair

Name | Diagram | Algorithm | Comments |

ALL | y (L' U' L) |
These are just the mirrors of the above cases. | |

UB | y (L' U2) (L U) (L F' L' F) |
These are just the mirrors of the above cases. | |

UR | y (L' U) (L U2) (L F' L' F) |
These are just the mirrors of the above cases. | |

UF | [U] (R U2 R') d' (L' U L) |
These are just the mirrors of the above cases. | |

UFUB | y (L' U2') y' (L' U) (L F) |
These are just the mirrors of the above cases. | |

UFUR | y [U2] (L' U') y' (L' U) (L U) F |
These are just the mirrors of the above cases. | |

UBUR | y (L' U') y' (L' U' L U F) |
These are just the mirrors of the above cases. | |

NONE | y (L D) (R' F R D') (L2' U' L) |
These are just the mirrors of the above cases. |