LL - The Last Layer

Because edge orientation is solved during EOLine and preserved during F2L, the last layer edges will always be oriented. This provides great number of options, ranging from a simple 20 algorithm 2-look system, all the way up to a 1-look system with up to 493 algorithms to learn.

Contents

• OCLL/PLL
• COLL/EPLL
• OCELL/CPLL
• ZBLL
• ZZLL
• Winter Variation
• ZZ-CT
• MGLS
• Blah's Method

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• OCLL/PLL: This orients the last layer corners in one step (OCLL), then permutes the last layer corners and edges simultaneously in the final step (PLL). This is similar to Fridrich's OLL/PLL last layer, but much fewer OLL algorithms are required since the last layer edges are already oriented. OCLL requires a minimum of 6 algorithms and PLL requires a minimum of 14, giving a total of 20 algorithms for both steps. The average move count is 7.93 for OCLL and 11.21 for PLL which gives a total of 19.14 moves average.^[10] Using partial corner control during insertion of the last 1x1x2 block eliminates the H and Pi OCLL cases, allowing even fewer moves and faster algs during OCLL or COLL.
  
  Algorithms:
  • speedsolving.com wiki: OCLL
  • speedsolving.com wiki: PLL
  • AlgDB.Net PLL
  • speedsolving.com: Partial Corner Control
  
  
  
• COLL/EPLL (ZZ-VH): This orients and permutes the last layer corners (without affecting edge orientation) in one step, then permutes the last layer edges in the final step. This may be preferred since it has a lower move count than OCLL/PLL, and is regarded by some to have easier case recognition. Learning COLL/EPLL is also a useful intermediate step to learning ZZLL or ZBLL. COLL has 40 cases to recognise, solvable by 25 algs min. EPLL is just 4 cases (and only 3 algs if U-perm is mirrored) - a total of 28 for the whole LL. COLL is 9.78 moves average, and EPLL is 8.75 average, yielding a move count of 18.53 (slightly fewer than OCLL/PLL).^[10]
  Algorithms:
  • COLL on the Algorithm Database
  • Lars Vandenbergh's COLL Page
  • Bob Burton's COLL Page
  • speedcubing.com: COLL Page
  
  
  
• OCELL/CPLL: This orients the last layer corners, while permuting the last layer edges (without affecting edge orientation) in one step, then permutes the last layer corners in the final step. The advantage of using this method is that the majority of algorithms (all of OCELL) can be done 2-gen (turning only two sides). This may give it an advantage over COLL in OH (one-handed) cubing. Like COLL there are 40 cases to recognise, solvable by 25 algs min. Again CPLL is just 4 cases, 2/3^rds of which are A-perm. The remaining cases are E-Perm, H-Perm and a 1 in 12 chance of CPLL-skip. The average move count for OCELL with 2-gen algs is 12.10, and for CPLL it's 9.17. In total that gives 22.01 moves on average, including AUF. ^[10]
  Algorithms:
  • speedsolving.com: OCELL 2-gen algorithms and move count statistics
  
  
  
• ZBLL (ZZ-a): Often labelled as the holy grail of speed cubing, this method completes the last layer by orienting the corners and permuting the corners and edges, all in one step. It involves 494 distinct cases, and requires learning a minimum of 177 algorithms assuming mirrors and inverses are applied. Completing the last layer has an average move count of 12.08, which is a significant advantage over the 2-look options.^[10]
  Algorithms:
  • ZBLL algs on SpeedSolving.com Wiki (complete set)
  • Bernard Helmstetter's ZBLL algs
  • Chris Hardwick's ZBLL Page
  • Jason Baum's ZBLL Page
  • Lars Petrus's ZBLL Page (warning: many java applets!)

F2LL

During the final stages of F2L it's possible to manipulate the last layer cubies to reduce the number of LL cases. This partial solving of LL during F2L is called F2LL. The following are examples of F2LL options:

• ZZLL (ZZ-b or Phasing): Involves permuting two opposite LL edges during insertion of the final 1x1x2 F2L block. It is a relatively lightweight technique, using an estimated average of ~2 moves. It reduces the number of LL cases from 494 to only 167, enabling completion in one step with knowledge of 80 algorithms. Phasing also serves as a useful transition between COLL/EPLL and full ZBLL.
  Further info:
  • Michal Hordecki's ZZLL algorithms
  • Michal Hordecki's Phasing algorithms
  • James Stuber's ZZLL algorithms
  • speedsolving.com: Phasing Explained
  
  
  
• Winter Variation (WV): This orients the LL corners during insertion of the final 1x1x2 F2L block, reducing the last layer to just PLL. It involves 27 cases and is said to have a lower average move count than OCLL/PLL.
  Algorithms:
  • Sarah Strong's WV Algs
  • Winter Variation on Cyotheking
  • Sebastien Felix's WV Page
  • Winter Variation Article
  
  
  
• ZZ-CT: The first step (TSLE) orients all corners during insertion of the final F2L edge. During this step the final F2L corner is not placed, and may end up in the top layer. TSLE has 108 cases, all solvable with 2-gen algorithms. The second step (TTLL) is similar to PLL, except the final F2L corner is also being placed. It has 72 cases, and is said to have recognition and execution similar to PLL.
  Further Info:
  • TSLE Algorithms
  • TTLL Algorithms
  • ZZ-CT Thread
  • ZZ-CT Article
  
  
  
• MGLS: On the last F2L slot only the edge is placed. The CLS part of the MGLS method then orients the LL corners, while simultaneously placing the final D-face corner. This leaves only PLL to complete the cube. There are a total of 105 cases to recognise, solvable by a minimum of 56 algorithms, in an average of ~9.5 moves. It's possible to reduce the number of CLS algs required if the D-face corner is also placed along with its edge, but not necessarily oriented. This results in a subset of MGLS cases called EJF2L, solvable with a total of 16 fast 2-gen algorithms.
  Algorithms:
  • Lucas Garron's MGLS Page
  • Cubefreak MGLS Section
  • YouTube: EJF2L Tutorial
  • YouTube: EJF2L Cases
  
  
  
• Blah's Method: This de-orients the LL corners during insertion of the final 1x1x2 F2L block, allowing completion of LL in one-step using a reduced subset of ZBLL.^[7]
  
  

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Last updated: 7^th August 2016