#### Athefre

##### Member

- Joined
- Jul 25, 2006

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- 1,218

There is a method that has a lot of potential, yet the community seems to be overlooking it. How does the method work? Below are the steps:

This is a step that has been proven by many Roux users over the years. The 1x2x3 block on the left places pieces in the area where the left hand is holding the cube. This removes any necessity to check there for pieces later in the solve and reduces the rest of the solve to the use of mostly the right hand.

This step has also proven by the Roux method. Building the 1x2x2 further reduces blindspots while efficiently taking care of a corner and two of the edges surrounding it.

This is the big start of the potential of the method. A natural trait of the cube is that corners can sometimes require a lot of moves to solve. When solving a single corner using any method, and once some level of restriction is reached, just solving a single corner requires 3-4 moves in some cases. But if we solve all five corners at once in this method, they can all be completed in even fewer moves than something like CMLL which solves four corners instead of five. L5C is also the big start of the high level of required effort. There are 614 algorithms for full L5C. However, there are people learning ZBLL now so 614 isn't much more to learn and such a high algorithm count may be expected in our search for advanced methods. The L5C algorithms are also very short on average at 9.00 moves when SL5C is used.

I have developed full L5C and a new type of L5C called SL5C. I think SL5C is the way to go with this method. With SL5C, the algorithms are designed to freely end in one of five possible end states - U* R' away from solved, U* R' U, U* R' U', U* R' U2, or the solved state. This reduces the number of moves required to solve the corners and takes advantage of the natural interconnection between L5C and L7E. The edges are free to be solved when the corners are in those pseudo states and the pseudo state of the corners can be undone while solving the edges. Currently the SL5C algorithms have been created by removing the last U* R' turns from any L5C algorithms that ended with those two turns. The SL5C algorithms can be even better once an algorithm generator is able to solve to any set of input states and not just the solved state.

This is the other area where the method can show its potential. Instead of reducing to six edges as in Corners First related methods or Roux, here seven edges are being solved. It is similar to the L5C situation where solving more pieces at once can be done efficiently if done correctly. It is also a difficult aspect of the method. It will likely require a lot of practice to become proficient at solving the edges. There have been several L7E methods developed by me, Joseph Briggs, Jason Wong, Julien Adam, and Eric Fattah. Below are some of the methods:

- FB
- 1x2x2 on the right
- L5C
- L7E

**Move Count**- FB: 7
- 1x2x2: 8
- SL5C: 9.75
- L7E: 17

**FB**This is a step that has been proven by many Roux users over the years. The 1x2x3 block on the left places pieces in the area where the left hand is holding the cube. This removes any necessity to check there for pieces later in the solve and reduces the rest of the solve to the use of mostly the right hand.

**1x2x2**This step has also proven by the Roux method. Building the 1x2x2 further reduces blindspots while efficiently taking care of a corner and two of the edges surrounding it.

**L5C**This is the big start of the potential of the method. A natural trait of the cube is that corners can sometimes require a lot of moves to solve. When solving a single corner using any method, and once some level of restriction is reached, just solving a single corner requires 3-4 moves in some cases. But if we solve all five corners at once in this method, they can all be completed in even fewer moves than something like CMLL which solves four corners instead of five. L5C is also the big start of the high level of required effort. There are 614 algorithms for full L5C. However, there are people learning ZBLL now so 614 isn't much more to learn and such a high algorithm count may be expected in our search for advanced methods. The L5C algorithms are also very short on average at 9.00 moves when SL5C is used.

I have developed full L5C and a new type of L5C called SL5C. I think SL5C is the way to go with this method. With SL5C, the algorithms are designed to freely end in one of five possible end states - U* R' away from solved, U* R' U, U* R' U', U* R' U2, or the solved state. This reduces the number of moves required to solve the corners and takes advantage of the natural interconnection between L5C and L7E. The edges are free to be solved when the corners are in those pseudo states and the pseudo state of the corners can be undone while solving the edges. Currently the SL5C algorithms have been created by removing the last U* R' turns from any L5C algorithms that ended with those two turns. The SL5C algorithms can be even better once an algorithm generator is able to solve to any set of input states and not just the solved state.

**L7E**This is the other area where the method can show its potential. Instead of reducing to six edges as in Corners First related methods or Roux, here seven edges are being solved. It is similar to the L5C situation where solving more pieces at once can be done efficiently if done correctly. It is also a difficult aspect of the method. It will likely require a lot of practice to become proficient at solving the edges. There have been several L7E methods developed by me, Joseph Briggs, Jason Wong, Julien Adam, and Eric Fattah. Below are some of the methods:

**My L7E method****EO + FR edge then L6EP****An alternate L6EP reduction method****FR + Arrow****Another L6EP reduction method****WaterRoux L7E**

**Reducing the number of L5C cases**- The 42 method: 42 is the sibling of the method being presented in this post. In 42, instead of using full L5C, a U layer corner is positioned above the 1x2x2 then brought to the bottom layer with an R turn. Then the remaining four corners on the U layer are solved relative to the U layer corner that was placed with the 1x2x2. This is called CCMLL and requires just 42 algorithms. They are also the same algorithms as would be used for CMLL, but slightly shorter if the empty edge slot in the right side 1x2x3 is ignored. The number of required algorithms is greatly reduced, but at the expense of more difficult corner recognition. There is also a slightly higher movecount due to the need to have an extra corner attached to the 1x2x2 and the CCMLL algorithms are a little longer than SL5C. If you want fewer corner cases, 42 may be the method to use.
- CPFB: If early corner permutation is used, L5C is reduced to 104 algorithms. The algorithms would be slightly shorter than full L5C, but there is an increase in FB move count when CP is added.
- A few moves can be used to ensure that the DFR corner is oriented or positioned a specific way. Examples would be permuting DFR and learning CLL and TCLL. Or orienting the corner a specific way on the U layer and learning the 162 algorithms for those situations.
- Two look versions of L5C can be used, at the expense of a higher move count. OL5C and PL5C is provided in the L5C document.

Last edited: Jan 16, 2023