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The 3x3 method that no one is talking about: High Effort, High Potential

Athefre

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Jul 25, 2006
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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:
  1. FB
  2. 1x2x2 on the right
  3. L5C
  4. L7E
The idea for this method has been mentioned a couple of times, but the proposers have always abandoned it. Probably for the same reasons that some may view the method as not good or not worth it. L5C requires memorizing a lot of algorithms (614) and L7E is difficult and currently not 100% optimized. Yet I believe that the method has a very high level of potential. So I have spent the last year developing it. I developed every L5C algorithm, an alternate version of L5C called SL5C, iterative EO for L7E, a complete L7E method, and I have put a lot of time into analyzing and comparing the method with other related methods.

Move Count
  • FB: 7
  • 1x2x2: 8
  • SL5C: 9.75
  • L7E: 17
That's 41.75 moves. If an advanced L7E method is developed, that would be a reduction of around two moves. If any of the four possible right side 1x2x2 blocks is built in step 2 and the pseudo corner recognition is learned, that's a reduction of potentially another two moves. SL5C can also be further reduced by probably around a move using software that can generate solutions for an input state. Users can also improve their blockbuilding skills. There is already an instance of Fahmi averaging 6.5 moves for FB in a speedsolving average of 100. This means that averaging 37-38 moves in speedsolves is possible without having to learn thousands of algorithms.

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:
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.
 
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My main concern with a method like this is the sheer alg count and recognition. While 600+ algs isn't impossible, it's far out of reach for the average cuber. And unless there's something I'm missing, L5C and L7E sound like an incredible pain to recognize, especially if you were implementing pseudo blocks and color neutrality.

Still would be interested to see how this method could be developed if people started using it, as I do believe efficiency is the future of cubing.
 

ruffleduck

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I just can't see how this is an improvement over its obvious brother, Roux. L5C and L7E have significantly worse recognition than their Roux counterparts, CMLL and L6E. L5C may barely be able to compare to CMLL from what I see, but L7E just can't compare to L6E, which is only 2-gen and around 6 moves more efficient. I don't see how just skipping SBLS (a very fast algset that can very smoothly be looked ahead into) justifies all of these issues.
 

OreKehStrah

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My main concern with a method like this is the sheer alg count and recognition. While 600+ algs isn't impossible, it's far out of reach for the average cuber. And unless there's something I'm missing, L5C and L7E sound like an incredible pain to recognize, especially if you were implementing pseudo blocks and color neutrality.

Still would be interested to see how this method could be developed if people started using it, as I do believe efficiency is the future of cubing.
Over time I don't think L5C would be that bad recognition wise. After all, it's the same thing as 2x2 LS, which we have seen 2x2 solvers use.
 

Athefre

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I just can't see how this is an improvement over its obvious brother, Roux. L5C and L7E have significantly worse recognition than their Roux counterparts, CMLL and L6E. L5C may barely be able to compare to CMLL from what I see, but L7E just can't compare to L6E, which is only 2-gen and around 6 moves more efficient. I don't see how just skipping SBLS (a very fast algset that can very smoothly be looked ahead into) justifies all of these issues.
I don't think L5C is really a problem. We have lookahead to see the DFR corner. Then from there it's only a matter of looking at three corners. So there isn't a big difference in recognition compared to CMLL. The biggest negative is the number of cases.

L7E however is the big unknown. No one has practiced the step enough to help determine the best way. Depending on the method used, it is also R r U M instead of LSE's simple M and U. Move count wise you still maintain the same low ~17 moves and the same overall ~41 moves even if you just insert the FR edge after L5C then do LSE.

The biggest benefit of the method seems to be the 4-5 move advantage over Roux. But the two unproven steps need use and analysis to determine their worth.
 

artless1der

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Feb 8, 2020
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It's nice to have something to occupy one's time and mind,
but
I solved my RS3M Super Ball-Core like 20x before I finished reading all of this. . .
only had to use 1×2×23 algs to do it to bóöt
GL and GN
 

efattah

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Feb 14, 2016
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I do like this method, but I do agree that the L5C recognition mid-solve is a problem. This is why I always go back to the WaterRoux variant, where top cubers can theoretically one-look first-block AND all the remaining corners. There are two paths to that:
1. Mentally solve FB, and the BDR corner (in your head), and see the L5C case in inspection
2. Mentally solve FB, and BOTH the FDR + BDR corners, and see CMLL inspection

Obviously #1 requires seeing fewer moves ahead but requires the 614 algorithm L5C set. Method #2 requires seeing more moves ahead but only requires 42 algorithms.

I am still dumbfounded how 2x2 solvers can inspect 4 solutions in a single inspection period. Despite my inability to understand that, it does mean that it is possible that a true expert could see FB + the 2x2 back right block all in the inspection, thus, seeing the L5C case in their mind. They would then reach L7E in 1-look, which puts them (compared to CFOP) in an XXXCross similar state, except it would be every solve. I have heard MANY Roux solvers who often solve first block and the back 2x2 block in inspection, but when doing this I do not think they are seeing the corner orientations since that is not required. So it isn't too much past that. I would LOVE it if a top Roux solver on this forum could just TRY for an hour to solve FB + the back 2x2 right block AND predict the corners case-- even if it takes 60 seconds of focused inspection. If it can be done in 60 seconds of inspection, then maybe with more practice, 15 seconds.

Another thing that is not mentioned here is the luck advantage. Putting the cube in an L7E state where your L7E method is flexible (like LMCF style), there are three edges that can be solved by luck (UR, UL, FR). If any one of them is solved by luck, which will be OFTEN, you really only have to finish with L6E.
 
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