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Last Layer

2017-09-18T20:39:44Z

ChandlerSch: Fixed two spelling issues.

[[Image:LL higlight.jpg|thumb|160px|The Last Layer]]

The term ''Last Layer'' (normally abbreviated as '''LL''', also called '''Last Slice''') refers to the complete movable "slice" of a twisty puzzle which is the last to be solved in a [[Layer-By-Layer]] method. The '''Last Layer''' (normally abbreviated as '''LL''') is the layer that must be solved on a [[cube]] when all of the other layers have already been finished. All pieces of the last layer can move together.

Last layer is different from a Last [[face]]. Rather than just including the stickers of the last side of a twisty puzzle, the last layer includes all of the stickers on all of the pieces of the last slice.

== Confusion with the Top Layer ==

[[Image:Top layer.gif|thumb|160px|Top Layer]]

Last Layer is often confused with the Top Layer (U layer). Indeed, most of [[Layer-By-Layer]] methods (as [[CFOP]]) solve the Top Layer at the end of the solve. In those methods, the Top Layer and the Last Layer are the same.

== Last Layer methods ==

{{Main Article|Article=Last Layer methods}}

Thus any last layer steps will be the last few steps of a method. The last layer is very often found with a prefix that refers to what part of the last layer is being solved in the particular [[method]], such [[OLL]] (orienting the pieces), [[PLL]] (permuting the pieces), or [[CxLL]] (solving the corners).

There is no practical method that solves a completely scrambled last layer in one step every time, because there are far too many cases to learn (although the [[ZBLL]] method, which solves the last layer when edges are already oriented, is close to this level of difficulty): not counting inverses or mirrored positions, there are a total of 1,211 cases. Because of this, the last layer is always solved in multiple steps. The number of steps is counted in numbers of [[looks]] (the number of separate algorithms needed to finish the cube). The vast majority of [[speedcuber]]s today use a two-look last layer (2LLL): possible ways to do this include [[OLL]]/[[PLL]] and [[CLL]]/[[ELL]].

== See also ==

* [[Layer-By-Layer]]
* [[Layer]]
* [[F2L]]
* [[First Layer]]
* [[OLL]]/[[PLL]]
* [[CxLL]]/[[ELL]]
* [[ZBLL]]
* [[Algorithm Database]]
* [[Intuitive solving]]

== Links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/solutions_tout.html List of algorithms to solve the last layer in one step]

[[Category:Terminology]]

PLL

2017-09-18T20:38:44Z

ChandlerSch: /* External links */ Grammar

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=[[Hans Dockhorn]], [[Anneke Treep]], [[Jessica Fridrich]]
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''PLL''' is the acronym for '''Permutation of the Last Layer'''. Permutation of the [[Last Layer]] is the last step of many speedsolving methods. In this step, the pieces on the top layer have already been oriented ([[OLL]]) so that the top face has all the same color, and they can now be moved into their solved positions. There are 21 PLLs (13 if you count mirrors and inverses as being the same) and each one is named after a letter. The following page gives a list of all of the PLLs, along with a picture and a list of common [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|T Permutation]] (or 'T perm') swaps the UL and UR edges, as well as the UFR and UBR corners. If you like, try out all of the available algorithms for a case to see which one feels the fastest to you - the same algorithm may not be the fastest for everyone, and shorter algorithms are not always faster than longer ones. PLL is a subgroup of [[ZBLL]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognizing PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==Permutations of Corners Only==
This is also known as [[CPLL]] (Corner Permute Last Layer). There is one more case in this group, the X-PLL but that is the same alg as [[H-PLL]] + U2, see [[EPLL]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|F2 B2 D F2 B2 R U R' U' R' F R2 U' R' U' R U R' F B2 D' F2 B2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL|vidurl=http://www.youtube.com/watch?v=4hxXyedEvoE}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U (R' U R' U' R) U' R2 D (U' R' U R) D'|PLL}}
{{Alg|(y2) F2' D (R' U R' U' R) D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|(R U R' U' R') U F (R U R U' R') F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R (F' L' F U) R' U' (F' L F' L')|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u (R' U R U' R) u' R2'|PLL}}
{{Alg|R' U' R B2 D (L' U L U' L) D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u (R' U R U' R) u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}
{{Alg|R' U' R U D' R2 U R' U R U' R U' R2 D|PLL|vidurl=http://www.youtube.com/watch?v=M6RDFenst9g}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' (R U' R U R') u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' (R U' R U R') u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' (R U' R U R') U R2 (D' U R U' R' D)|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|B2 L2 U' B2 D B2 D' R2 U M2 F2 (x2)|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' (R U' R' U R') u R2|PLL}}
{{Alg|(y2) R U R' F2 D' (L U' L' U L') D F2|PLL}}
{{Alg|(y2) L U2 L' U F' (L' U' L U L) F U (L' U' L' U L)|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|(B' U F') U2 (B U' B') U2 (F B U')|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R' U L') U2 (R U' R') U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L' U R') U2 (L U' L') U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L' U R') (z) R2 (U R' U') R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R U' R' U' R U R' F' R U R' U' R' F R U F'|Alg.2|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|(B U' F) U2 (B' U B) U2 (F' B' U)|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L U' R) U2 (L' U L) U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U' L) U2 (R' U R) U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U' L) (z') L2 (U' L U) L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 (R' U' R) U2 L' (U R' U') L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 (L U L') B2 (R D' R D) R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 (R U R') F2 (L D' L D) L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 (R U R') b2 (R U' R U) l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) (L U' L U) r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r (U' L U) r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 (U' L' U) r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|R2 U F U F' R2 F U' F' R2 U' R2 U'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U') l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(y') (R U2 R' U' R U' R')(R U R' U' R' F R2 U' R' U' R U R' F')(R U R' U R U2 R')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]
{{Alg|R U R' U' R' F R F' R' F R F' U' F' U F U'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') (R' F R F')2 (y') (x') F' (R' F R F') (x) (y)|Alg.10(v1)|cube=3x3x3&stage=PLL}}

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

[[Category:3x3x3 last layer substeps]]
[[Category:Acronyms]]
[[Category:Algorithms]]

__NOTOC__

CFOP method

2017-09-18T20:32:37Z

ChandlerSch: /* The Steps */ Fixed a grammar issue.

{{Method Infobox
|name=CFOP
|image=Fridrich_method.gif
|proposers=[[David Singmaster]] [[René Schoof]] [[Jessica Fridrich]] [[Hans Dockhorn]] [[Anneke Treep]]
|year=1981
|anames=Fridrich Method
|variants=[[CLL]]/[[ELL]], [[VH]], [[ZB]], [[MGLS-F]]
|steps=4 (Cross, F2L, OLL, PLL)
|algs=Total: 78 to 119 F2L: 0 to 41 Full 2LLL: 78 (OLL: 57, PLL: 21)
|moves=~55
|purpose=
* [[Speedsolving]]
* [[Speed BLD]]
* [[One-Handed Solving]]
* [[Solving with Feet]]
}}

{{Method Header
|listofsteps=[[Cross|'''C'''ross]] -> [[F2L|'''F'''2L]] -> [[OLL|'''O'''LL]] -> [[PLL|'''P'''LL]]
|description=[[CFOP|'''CFOP''']] is the most frequently used [[speedsolving]] [[method]] for the [[3x3x3 cube]].
}}

'''CFOP''' (''Cross, F2L, OLL, PLL'', pronounced C-F-O-P or C-fop) is a 3x3 speedsolving method proposed by several cubers around 1981. It is also known as the '''Fridrich Method''' after its popularizer, [[Jessica Fridrich]]. In part due to Fridrich's publication of the method on her website in 1995, CFOP has been the most dominant 3x3 speedcubing method since around 2000, with it and its variants used by the vast majority of the top speedcubers such as [[Feliks Zemdegs]], [[Max Park]], [[Sebastian Weyer]], [[Mats Valk]], etc.

== Origin and Naming Dispute ==

Jessica Fridrich is often erroneously credited as the sole inventor of CFOP. In reality, many developments were made in the early '80s by other cubers who have contributed to the method in its current form. The constituent techniques and their original proposers are as follows:
* [[Cross]]: [[David Singmaster]]
* [[F2L]] (4x corner + edge pairs): [[René Schoof]]
* [[OLL]]/[[PLL]]: [[Hans Dockhorn]], [[Anneke Treep]], with many algorithms developed by [[Jessica Fridrich]]

During the resurgence in speedcubing's popularity in the late '90s and early 2000s, there was a general lack of information on the sport. Fridrich's website offered a vast wealth of information for those entering the sport, including a full description of CFOP with complete lists of algorithms. As a result, many who learned from her website began to call this method the "Fridrich Method," which explains the common use of the term today.

Several high-profile cubers have long disputed this terminology; [[Ron van Bruchem]], famously, has publicly written that he will never call CFOP the "Fridrich Method." This issue has become well-advertised within the cubing community around the year 2008, likely because of this. The term "CFOP" has since seen increasing usage compared to back then, also in part motivated by efforts to standardize terminology in method classification, and is now seen, commonly, as "Fridrich Method."

While some cubers still insist on the term "CFOP," Fridrich's contribution to the popularization of the method is undeniable, and many others accept the term "Fridrich Method" as established terminology and a perfectly valid synonym for "CFOP."

== The Steps ==
CFOP can be viewed as an advanced version of a [[Layer-By-Layer]] method. In particular, it combines some steps of the said method into one by using many more algorithms. Here, we outline pure CFOP without any additional trick. Also, the cube is commonly solved with the white side on top for the cross, yellow on the bottom for the cross, and opposite for the other steps. However, it is NOT required.

{|
|| [[File:Cross 2.jpg|120px|Cross|link=Cross]]
| valign="top" | '''[[Cross]]'''

Make a cross on one side by solving all edges of a given face. A
Make sure to align the edges with the second-layer centers.

It is recommended that you solve the cross on the bottom face and that you become familiar doing the cross with all colors; not just one.
|}

{|
|| [[File:F2Linfo.png|120px|F2L|link=F2L]]
| valign="top" | '''[[F2L]] (First Two Layers)'''

Fill in the four '''slots''' between the cross pieces, one slot at a time. Each slot is filled by inserting a corner and its corresponding edge simultaneously. Most of the 41 cases have reasonable intuitive solutions. The completion of this step leaves one with just the last layer, typically placed on top.
|}

{|
|| [[File:OLLinfo.png|120px|OLL|link=OLL]]
| valign="top" | '''[[OLL]] (Orientation of the Last Layer)'''

Make the entire top side (the last layer) of the cube a solid color. 57 nontrivial cases.

''Those new to [[OLL]] break up the step into two. This greatly reduces the number of cases; [[2-look OLL]] has 9 cases. However, note that this is a few seconds slower''
|}

{|
|| [[File:PLLinfo.jpg|120px|PLL|link=PLL]]
| valign="top" | '''[[PLL]] (Permutation of the Last Layer)'''

Finally, you finish the cube by permuting the top layer of the cube. 21 nontrivial cases.

''Those new to [[PLL]] break up the step into two. This greatly reduces the number of cases; [[2-look PLL]] has 6 cases. However, note that this is a few seconds slower''
|}

== Pros ==

* '''Easy to learn''' - CFOP is widely considered to be the easiest method to learn, as it transitions easily from beginner's methods.
* '''Doesn't require a large understanding of how the cube works''' - Due to the lack of blockbuilding or edge orientation needed in CFOP, the method relies more on pattern recognition and algorithms. Although the cross and F2L are solved intuitively, they are more straightforward than the blockbuilding with Roux or the edge orientation and blockbuilding with ZZ.
* '''Is by far the most researched method''' - As CFOP is the most widely used method and has been for many years, there has been far more research done on CFOP than any other method, which means more resources, a larger variety of algorithms to choose from, and more community members to assist and give advice. All world records for the 3x3 Rubik's Cube since 2003 have been set with CFOP.
*'''Statistically the fastest speedsolving method''' - Statistically speaking, CFOP has proven to currently be the fastest method, despite the move count. As of June 1, 2016, the top four speedsolvers in 3x3 average use the method, as well as the top fifteen speedsolvers in 3x3 single.

== Cons ==

* '''Algorithms''' - CFOP with 4 Look last layer makes a total of 16 algorithms (10 2-look OLL algs and 6 2-look PLL algs). Full CFOP has 57 OLLs and 21 PLLs for a total of 78 algorithms. If a person learned one full CFOP alg a day (OLL and PLL), it would take a bit over 2 and a half months to learn all of them.
* '''Move count''' - CFOP has a slightly higher average movecount than that of ZZ and much higher movecount compared to Roux.
* '''Reliance on Inspection''' - CFOP relies on the use of inspection time, in order for the cross (and the first pair, depending on how advanced the user is) to be solved quickly. In instances where there is no inspection time, such as big cube solves where one must transition between the cube's reduction and 3x3x3 steps, this can be a drawback as the cross has to be done on the fly rather than being planned out. Although this may be the case, CFOP is still the most popular choice for the 3x3x3 stage on big cubes as the planning and execution of a Roux or ZZ solve is typically more difficult than doing CFOP.
* '''Difficulty of Cross''' - Planning the cross during inspection can take a while to master. It requires a fair amount of experience, similar to planning the first block with Roux or the EOLine with ZZ.

== See also ==
* [[Cross]]
* [[F2L]]
* [[OLL]]/[[PLL]]
* [[4LLL]]
* [[CFCE]]
* [[ZZ]]
* [[Roux]]

{{F2L}}

{{OLL}}

{{PLL}}

== External links ==

* [http://solvethecube.110mb.com/ Joël van Noort's tutorial]
* [http://erikku.er.funpic.org/rubik/Fridrich.html Erik Akkersdijk's tutorial]
* [http://www.cubefreak.net/cfop/ Shotaro Makisumi's tutorial]
* [http://www.ws.binghamton.edu/fridrich/cube.html Jessica's Homepage]
* [http://www.youtube.com/watch?v=k-xbcAMfWwM Badmephisto's Intuitive F2L Tutorial]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=2322 Fridrich Method] - info on its origin.
* [http://algdb.net/ All the CFOP algs that you can think off]

[[Category:3x3x3 methods]]
[[Category:3x3x3 speedsolving methods]]
[[Category:SpeedBLD Methods]]
[[Category:Acronyms]]

CFOP method

2017-09-18T20:32:16Z

ChandlerSch: /* Cons */ Fixed two grammar issues

{{Method Infobox
|name=CFOP
|image=Fridrich_method.gif
|proposers=[[David Singmaster]] [[René Schoof]] [[Jessica Fridrich]] [[Hans Dockhorn]] [[Anneke Treep]]
|year=1981
|anames=Fridrich Method
|variants=[[CLL]]/[[ELL]], [[VH]], [[ZB]], [[MGLS-F]]
|steps=4 (Cross, F2L, OLL, PLL)
|algs=Total: 78 to 119 F2L: 0 to 41 Full 2LLL: 78 (OLL: 57, PLL: 21)
|moves=~55
|purpose=
* [[Speedsolving]]
* [[Speed BLD]]
* [[One-Handed Solving]]
* [[Solving with Feet]]
}}

{{Method Header
|listofsteps=[[Cross|'''C'''ross]] -> [[F2L|'''F'''2L]] -> [[OLL|'''O'''LL]] -> [[PLL|'''P'''LL]]
|description=[[CFOP|'''CFOP''']] is the most frequently used [[speedsolving]] [[method]] for the [[3x3x3 cube]].
}}

'''CFOP''' (''Cross, F2L, OLL, PLL'', pronounced C-F-O-P or C-fop) is a 3x3 speedsolving method proposed by several cubers around 1981. It is also known as the '''Fridrich Method''' after its popularizer, [[Jessica Fridrich]]. In part due to Fridrich's publication of the method on her website in 1995, CFOP has been the most dominant 3x3 speedcubing method since around 2000, with it and its variants used by the vast majority of the top speedcubers such as [[Feliks Zemdegs]], [[Max Park]], [[Sebastian Weyer]], [[Mats Valk]], etc.

== Origin and Naming Dispute ==

Jessica Fridrich is often erroneously credited as the sole inventor of CFOP. In reality, many developments were made in the early '80s by other cubers who have contributed to the method in its current form. The constituent techniques and their original proposers are as follows:
* [[Cross]]: [[David Singmaster]]
* [[F2L]] (4x corner + edge pairs): [[René Schoof]]
* [[OLL]]/[[PLL]]: [[Hans Dockhorn]], [[Anneke Treep]], with many algorithms developed by [[Jessica Fridrich]]

During the resurgence in speedcubing's popularity in the late '90s and early 2000s, there was a general lack of information on the sport. Fridrich's website offered a vast wealth of information for those entering the sport, including a full description of CFOP with complete lists of algorithms. As a result, many who learned from her website began to call this method the "Fridrich Method," which explains the common use of the term today.

Several high-profile cubers have long disputed this terminology; [[Ron van Bruchem]], famously, has publicly written that he will never call CFOP the "Fridrich Method." This issue has become well-advertised within the cubing community around the year 2008, likely because of this. The term "CFOP" has since seen increasing usage compared to back then, also in part motivated by efforts to standardize terminology in method classification, and is now seen, commonly, as "Fridrich Method."

While some cubers still insist on the term "CFOP," Fridrich's contribution to the popularization of the method is undeniable, and many others accept the term "Fridrich Method" as established terminology and a perfectly valid synonym for "CFOP."

== The Steps ==
CFOP can be viewed as an advanced version of a [[Layer-By-Layer]] method. In particular, it combines some steps of the said method into one by using many more algorithms. Here, we outline pure CFOP without any additional trick. Also, the cube is commonly solved with the white side on top for the cross, yellow on bottom for the cross, and opposite for the other steps. However, it is NOT required.

{|
|| [[File:Cross 2.jpg|120px|Cross|link=Cross]]
| valign="top" | '''[[Cross]]'''

Make a cross on one side by solving all edges of a given face. A
Make sure to align the edges with the second-layer centers.

It is recommended that you solve the cross on the bottom face and that you become familiar doing the cross with all colors; not just one.
|}

{|
|| [[File:F2Linfo.png|120px|F2L|link=F2L]]
| valign="top" | '''[[F2L]] (First Two Layers)'''

Fill in the four '''slots''' between the cross pieces, one slot at a time. Each slot is filled by inserting a corner and its corresponding edge simultaneously. Most of the 41 cases have reasonable intuitive solutions. The completion of this step leaves one with just the last layer, typically placed on top.
|}

{|
|| [[File:OLLinfo.png|120px|OLL|link=OLL]]
| valign="top" | '''[[OLL]] (Orientation of the Last Layer)'''

Make the entire top side (the last layer) of the cube a solid color. 57 nontrivial cases.

''Those new to [[OLL]] break up the step into two. This greatly reduces the number of cases; [[2-look OLL]] has 9 cases. However, note that this is a few seconds slower''
|}

{|
|| [[File:PLLinfo.jpg|120px|PLL|link=PLL]]
| valign="top" | '''[[PLL]] (Permutation of the Last Layer)'''

Finally, you finish the cube by permuting the top layer of the cube. 21 nontrivial cases.

''Those new to [[PLL]] break up the step into two. This greatly reduces the number of cases; [[2-look PLL]] has 6 cases. However, note that this is a few seconds slower''
|}

== Pros ==

* '''Easy to learn''' - CFOP is widely considered to be the easiest method to learn, as it transitions easily from beginner's methods.
* '''Doesn't require a large understanding of how the cube works''' - Due to the lack of blockbuilding or edge orientation needed in CFOP, the method relies more on pattern recognition and algorithms. Although the cross and F2L are solved intuitively, they are more straightforward than the blockbuilding with Roux or the edge orientation and blockbuilding with ZZ.
* '''Is by far the most researched method''' - As CFOP is the most widely used method and has been for many years, there has been far more research done on CFOP than any other method, which means more resources, a larger variety of algorithms to choose from, and more community members to assist and give advice. All world records for the 3x3 Rubik's Cube since 2003 have been set with CFOP.
*'''Statistically the fastest speedsolving method''' - Statistically speaking, CFOP has proven to currently be the fastest method, despite the move count. As of June 1, 2016, the top four speedsolvers in 3x3 average use the method, as well as the top fifteen speedsolvers in 3x3 single.

== Cons ==

* '''Algorithms''' - CFOP with 4 Look last layer makes a total of 16 algorithms (10 2-look OLL algs and 6 2-look PLL algs). Full CFOP has 57 OLLs and 21 PLLs for a total of 78 algorithms. If a person learned one full CFOP alg a day (OLL and PLL), it would take a bit over 2 and a half months to learn all of them.
* '''Move count''' - CFOP has a slightly higher average movecount than that of ZZ and much higher movecount compared to Roux.
* '''Reliance on Inspection''' - CFOP relies on the use of inspection time, in order for the cross (and the first pair, depending on how advanced the user is) to be solved quickly. In instances where there is no inspection time, such as big cube solves where one must transition between the cube's reduction and 3x3x3 steps, this can be a drawback as the cross has to be done on the fly rather than being planned out. Although this may be the case, CFOP is still the most popular choice for the 3x3x3 stage on big cubes as the planning and execution of a Roux or ZZ solve is typically more difficult than doing CFOP.
* '''Difficulty of Cross''' - Planning the cross during inspection can take a while to master. It requires a fair amount of experience, similar to planning the first block with Roux or the EOLine with ZZ.

== See also ==
* [[Cross]]
* [[F2L]]
* [[OLL]]/[[PLL]]
* [[4LLL]]
* [[CFCE]]
* [[ZZ]]
* [[Roux]]

{{F2L}}

{{OLL}}

{{PLL}}

== External links ==

* [http://solvethecube.110mb.com/ Joël van Noort's tutorial]
* [http://erikku.er.funpic.org/rubik/Fridrich.html Erik Akkersdijk's tutorial]
* [http://www.cubefreak.net/cfop/ Shotaro Makisumi's tutorial]
* [http://www.ws.binghamton.edu/fridrich/cube.html Jessica's Homepage]
* [http://www.youtube.com/watch?v=k-xbcAMfWwM Badmephisto's Intuitive F2L Tutorial]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=2322 Fridrich Method] - info on its origin.
* [http://algdb.net/ All the CFOP algs that you can think off]

[[Category:3x3x3 methods]]
[[Category:3x3x3 speedsolving methods]]
[[Category:SpeedBLD Methods]]
[[Category:Acronyms]]

CFOP method

2017-09-18T20:31:16Z

ChandlerSch: /* Pros */ Fixed a grammar issue.

{{Method Infobox
|name=CFOP
|image=Fridrich_method.gif
|proposers=[[David Singmaster]] [[René Schoof]] [[Jessica Fridrich]] [[Hans Dockhorn]] [[Anneke Treep]]
|year=1981
|anames=Fridrich Method
|variants=[[CLL]]/[[ELL]], [[VH]], [[ZB]], [[MGLS-F]]
|steps=4 (Cross, F2L, OLL, PLL)
|algs=Total: 78 to 119 F2L: 0 to 41 Full 2LLL: 78 (OLL: 57, PLL: 21)
|moves=~55
|purpose=
* [[Speedsolving]]
* [[Speed BLD]]
* [[One-Handed Solving]]
* [[Solving with Feet]]
}}

{{Method Header
|listofsteps=[[Cross|'''C'''ross]] -> [[F2L|'''F'''2L]] -> [[OLL|'''O'''LL]] -> [[PLL|'''P'''LL]]
|description=[[CFOP|'''CFOP''']] is the most frequently used [[speedsolving]] [[method]] for the [[3x3x3 cube]].
}}

'''CFOP''' (''Cross, F2L, OLL, PLL'', pronounced C-F-O-P or C-fop) is a 3x3 speedsolving method proposed by several cubers around 1981. It is also known as the '''Fridrich Method''' after its popularizer, [[Jessica Fridrich]]. In part due to Fridrich's publication of the method on her website in 1995, CFOP has been the most dominant 3x3 speedcubing method since around 2000, with it and its variants used by the vast majority of the top speedcubers such as [[Feliks Zemdegs]], [[Max Park]], [[Sebastian Weyer]], [[Mats Valk]], etc.

== Origin and Naming Dispute ==

Jessica Fridrich is often erroneously credited as the sole inventor of CFOP. In reality, many developments were made in the early '80s by other cubers who have contributed to the method in its current form. The constituent techniques and their original proposers are as follows:
* [[Cross]]: [[David Singmaster]]
* [[F2L]] (4x corner + edge pairs): [[René Schoof]]
* [[OLL]]/[[PLL]]: [[Hans Dockhorn]], [[Anneke Treep]], with many algorithms developed by [[Jessica Fridrich]]

During the resurgence in speedcubing's popularity in the late '90s and early 2000s, there was a general lack of information on the sport. Fridrich's website offered a vast wealth of information for those entering the sport, including a full description of CFOP with complete lists of algorithms. As a result, many who learned from her website began to call this method the "Fridrich Method," which explains the common use of the term today.

Several high-profile cubers have long disputed this terminology; [[Ron van Bruchem]], famously, has publicly written that he will never call CFOP the "Fridrich Method." This issue has become well-advertised within the cubing community around the year 2008, likely because of this. The term "CFOP" has since seen increasing usage compared to back then, also in part motivated by efforts to standardize terminology in method classification, and is now seen, commonly, as "Fridrich Method."

While some cubers still insist on the term "CFOP," Fridrich's contribution to the popularization of the method is undeniable, and many others accept the term "Fridrich Method" as established terminology and a perfectly valid synonym for "CFOP."

== The Steps ==
CFOP can be viewed as an advanced version of a [[Layer-By-Layer]] method. In particular, it combines some steps of the said method into one by using many more algorithms. Here, we outline pure CFOP without any additional trick. Also, the cube is commonly solved with the white side on top for the cross, yellow on bottom for the cross, and opposite for the other steps. However, it is NOT required.

{|
|| [[File:Cross 2.jpg|120px|Cross|link=Cross]]
| valign="top" | '''[[Cross]]'''

Make a cross on one side by solving all edges of a given face. A
Make sure to align the edges with the second-layer centers.

It is recommended that you solve the cross on the bottom face and that you become familiar doing the cross with all colors; not just one.
|}

{|
|| [[File:F2Linfo.png|120px|F2L|link=F2L]]
| valign="top" | '''[[F2L]] (First Two Layers)'''

Fill in the four '''slots''' between the cross pieces, one slot at a time. Each slot is filled by inserting a corner and its corresponding edge simultaneously. Most of the 41 cases have reasonable intuitive solutions. The completion of this step leaves one with just the last layer, typically placed on top.
|}

{|
|| [[File:OLLinfo.png|120px|OLL|link=OLL]]
| valign="top" | '''[[OLL]] (Orientation of the Last Layer)'''

Make the entire top side (the last layer) of the cube a solid color. 57 nontrivial cases.

''Those new to [[OLL]] break up the step into two. This greatly reduces the number of cases; [[2-look OLL]] has 9 cases. However, note that this is a few seconds slower''
|}

{|
|| [[File:PLLinfo.jpg|120px|PLL|link=PLL]]
| valign="top" | '''[[PLL]] (Permutation of the Last Layer)'''

Finally, you finish the cube by permuting the top layer of the cube. 21 nontrivial cases.

''Those new to [[PLL]] break up the step into two. This greatly reduces the number of cases; [[2-look PLL]] has 6 cases. However, note that this is a few seconds slower''
|}

== Pros ==

* '''Easy to learn''' - CFOP is widely considered to be the easiest method to learn, as it transitions easily from beginner's methods.
* '''Doesn't require a large understanding of how the cube works''' - Due to the lack of blockbuilding or edge orientation needed in CFOP, the method relies more on pattern recognition and algorithms. Although the cross and F2L are solved intuitively, they are more straightforward than the blockbuilding with Roux or the edge orientation and blockbuilding with ZZ.
* '''Is by far the most researched method''' - As CFOP is the most widely used method and has been for many years, there has been far more research done on CFOP than any other method, which means more resources, a larger variety of algorithms to choose from, and more community members to assist and give advice. All world records for the 3x3 Rubik's Cube since 2003 have been set with CFOP.
*'''Statistically the fastest speedsolving method''' - Statistically speaking, CFOP has proven to currently be the fastest method, despite the move count. As of June 1, 2016, the top four speedsolvers in 3x3 average use the method, as well as the top fifteen speedsolvers in 3x3 single.

== Cons ==

* '''Algorithms''' - CFOP with 4 Look last layer makes a total of 16 algorithms (10 2-look OLL algs and 6 2-look PLL algs). Full CFOP has 57 OLLs and 21 PLLs for a total of 78 algorithms. If a person learned one full CFOP alg a day (OLL and PLL), it would take a bit over 2 and a half months to learn all of them.
* '''Move count''' - CFOP has a slightly higher average movecount than that of ZZ and much higher movecount compared to Roux.
* '''Reliance on Inspection''' - CFOP relies on use of inspection time, in order for the cross (and first pair, depending on how advanced the user is) to be solved quickly. In instances where there is no inspection time, such as big cube solves where one must transition between the cube's reduction and 3x3x3 steps, this can be a drawback as the cross has to be done on the fly rather than being planned out. Although this may be the case, CFOP is still the most popular choice for the 3x3x3 stage on big cubes as the planning and execution of a Roux or ZZ solve is typically more difficult than doing CFOP.
* '''Difficulty of Cross''' - Planning the cross during inspection can take a while to master. It requires a fair amount of experience, similar to planning the first block with Roux or the EOLine with ZZ.

== See also ==
* [[Cross]]
* [[F2L]]
* [[OLL]]/[[PLL]]
* [[4LLL]]
* [[CFCE]]
* [[ZZ]]
* [[Roux]]

{{F2L}}

{{OLL}}

{{PLL}}

== External links ==

* [http://solvethecube.110mb.com/ Joël van Noort's tutorial]
* [http://erikku.er.funpic.org/rubik/Fridrich.html Erik Akkersdijk's tutorial]
* [http://www.cubefreak.net/cfop/ Shotaro Makisumi's tutorial]
* [http://www.ws.binghamton.edu/fridrich/cube.html Jessica's Homepage]
* [http://www.youtube.com/watch?v=k-xbcAMfWwM Badmephisto's Intuitive F2L Tutorial]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=2322 Fridrich Method] - info on its origin.
* [http://algdb.net/ All the CFOP algs that you can think off]

[[Category:3x3x3 methods]]
[[Category:3x3x3 speedsolving methods]]
[[Category:SpeedBLD Methods]]
[[Category:Acronyms]]

CFOP method

2017-09-18T20:30:49Z

ChandlerSch: /* The Steps */ Fixed a grammar issue.

{{Method Infobox
|name=CFOP
|image=Fridrich_method.gif
|proposers=[[David Singmaster]] [[René Schoof]] [[Jessica Fridrich]] [[Hans Dockhorn]] [[Anneke Treep]]
|year=1981
|anames=Fridrich Method
|variants=[[CLL]]/[[ELL]], [[VH]], [[ZB]], [[MGLS-F]]
|steps=4 (Cross, F2L, OLL, PLL)
|algs=Total: 78 to 119 F2L: 0 to 41 Full 2LLL: 78 (OLL: 57, PLL: 21)
|moves=~55
|purpose=
* [[Speedsolving]]
* [[Speed BLD]]
* [[One-Handed Solving]]
* [[Solving with Feet]]
}}

{{Method Header
|listofsteps=[[Cross|'''C'''ross]] -> [[F2L|'''F'''2L]] -> [[OLL|'''O'''LL]] -> [[PLL|'''P'''LL]]
|description=[[CFOP|'''CFOP''']] is the most frequently used [[speedsolving]] [[method]] for the [[3x3x3 cube]].
}}

'''CFOP''' (''Cross, F2L, OLL, PLL'', pronounced C-F-O-P or C-fop) is a 3x3 speedsolving method proposed by several cubers around 1981. It is also known as the '''Fridrich Method''' after its popularizer, [[Jessica Fridrich]]. In part due to Fridrich's publication of the method on her website in 1995, CFOP has been the most dominant 3x3 speedcubing method since around 2000, with it and its variants used by the vast majority of the top speedcubers such as [[Feliks Zemdegs]], [[Max Park]], [[Sebastian Weyer]], [[Mats Valk]], etc.

== Origin and Naming Dispute ==

Jessica Fridrich is often erroneously credited as the sole inventor of CFOP. In reality, many developments were made in the early '80s by other cubers who have contributed to the method in its current form. The constituent techniques and their original proposers are as follows:
* [[Cross]]: [[David Singmaster]]
* [[F2L]] (4x corner + edge pairs): [[René Schoof]]
* [[OLL]]/[[PLL]]: [[Hans Dockhorn]], [[Anneke Treep]], with many algorithms developed by [[Jessica Fridrich]]

During the resurgence in speedcubing's popularity in the late '90s and early 2000s, there was a general lack of information on the sport. Fridrich's website offered a vast wealth of information for those entering the sport, including a full description of CFOP with complete lists of algorithms. As a result, many who learned from her website began to call this method the "Fridrich Method," which explains the common use of the term today.

Several high-profile cubers have long disputed this terminology; [[Ron van Bruchem]], famously, has publicly written that he will never call CFOP the "Fridrich Method." This issue has become well-advertised within the cubing community around the year 2008, likely because of this. The term "CFOP" has since seen increasing usage compared to back then, also in part motivated by efforts to standardize terminology in method classification, and is now seen, commonly, as "Fridrich Method."

While some cubers still insist on the term "CFOP," Fridrich's contribution to the popularization of the method is undeniable, and many others accept the term "Fridrich Method" as established terminology and a perfectly valid synonym for "CFOP."

== The Steps ==
CFOP can be viewed as an advanced version of a [[Layer-By-Layer]] method. In particular, it combines some steps of the said method into one by using many more algorithms. Here, we outline pure CFOP without any additional trick. Also, the cube is commonly solved with the white side on top for the cross, yellow on bottom for the cross, and opposite for the other steps. However, it is NOT required.

{|
|| [[File:Cross 2.jpg|120px|Cross|link=Cross]]
| valign="top" | '''[[Cross]]'''

Make a cross on one side by solving all edges of a given face. A
Make sure to align the edges with the second-layer centers.

It is recommended that you solve the cross on the bottom face and that you become familiar doing the cross with all colors; not just one.
|}

{|
|| [[File:F2Linfo.png|120px|F2L|link=F2L]]
| valign="top" | '''[[F2L]] (First Two Layers)'''

Fill in the four '''slots''' between the cross pieces, one slot at a time. Each slot is filled by inserting a corner and its corresponding edge simultaneously. Most of the 41 cases have reasonable intuitive solutions. The completion of this step leaves one with just the last layer, typically placed on top.
|}

{|
|| [[File:OLLinfo.png|120px|OLL|link=OLL]]
| valign="top" | '''[[OLL]] (Orientation of the Last Layer)'''

Make the entire top side (the last layer) of the cube a solid color. 57 nontrivial cases.

''Those new to [[OLL]] break up the step into two. This greatly reduces the number of cases; [[2-look OLL]] has 9 cases. However, note that this is a few seconds slower''
|}

{|
|| [[File:PLLinfo.jpg|120px|PLL|link=PLL]]
| valign="top" | '''[[PLL]] (Permutation of the Last Layer)'''

Finally, you finish the cube by permuting the top layer of the cube. 21 nontrivial cases.

''Those new to [[PLL]] break up the step into two. This greatly reduces the number of cases; [[2-look PLL]] has 6 cases. However, note that this is a few seconds slower''
|}

== Pros ==

* '''Easy to learn''' - CFOP is widely considered to be the easiest method to learn, as it transitions easily from beginner's methods.
* '''Doesn't require a large understanding of how the cube works''' - Due to the lack of blockbuilding or edge orientation needed in CFOP, the method relies more on pattern recognition and algorithms. Although the cross and F2L are solved intuitively, they are more straightforward than the blockbuilding with Roux or the edge orientation and blockbuilding with ZZ.
* '''Is by far the most researched method''' - As CFOP is the most widely used method, and has been for many years, there has been far more research done on CFOP than any other method, which means more resources, a larger variety of algorithms to choose from, and more community members to assist and give advice. All world records for the 3x3 Rubik's Cube since 2003 have been set with CFOP.
*'''Statistically the fastest speedsolving method''' - Statistically speaking, CFOP has proven to currently be the fastest method, despite the move count. As of June 1, 2016, the top four speedsolvers in 3x3 average use the method, as well as the top fifteen speedsolvers in 3x3 single.
== Cons ==

* '''Algorithms''' - CFOP with 4 Look last layer makes a total of 16 algorithms (10 2-look OLL algs and 6 2-look PLL algs). Full CFOP has 57 OLLs and 21 PLLs for a total of 78 algorithms. If a person learned one full CFOP alg a day (OLL and PLL), it would take a bit over 2 and a half months to learn all of them.
* '''Move count''' - CFOP has a slightly higher average movecount than that of ZZ and much higher movecount compared to Roux.
* '''Reliance on Inspection''' - CFOP relies on use of inspection time, in order for the cross (and first pair, depending on how advanced the user is) to be solved quickly. In instances where there is no inspection time, such as big cube solves where one must transition between the cube's reduction and 3x3x3 steps, this can be a drawback as the cross has to be done on the fly rather than being planned out. Although this may be the case, CFOP is still the most popular choice for the 3x3x3 stage on big cubes as the planning and execution of a Roux or ZZ solve is typically more difficult than doing CFOP.
* '''Difficulty of Cross''' - Planning the cross during inspection can take a while to master. It requires a fair amount of experience, similar to planning the first block with Roux or the EOLine with ZZ.

== See also ==
* [[Cross]]
* [[F2L]]
* [[OLL]]/[[PLL]]
* [[4LLL]]
* [[CFCE]]
* [[ZZ]]
* [[Roux]]

{{F2L}}

{{OLL}}

{{PLL}}

== External links ==

* [http://solvethecube.110mb.com/ Joël van Noort's tutorial]
* [http://erikku.er.funpic.org/rubik/Fridrich.html Erik Akkersdijk's tutorial]
* [http://www.cubefreak.net/cfop/ Shotaro Makisumi's tutorial]
* [http://www.ws.binghamton.edu/fridrich/cube.html Jessica's Homepage]
* [http://www.youtube.com/watch?v=k-xbcAMfWwM Badmephisto's Intuitive F2L Tutorial]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=2322 Fridrich Method] - info on its origin.
* [http://algdb.net/ All the CFOP algs that you can think off]

[[Category:3x3x3 methods]]
[[Category:3x3x3 speedsolving methods]]
[[Category:SpeedBLD Methods]]
[[Category:Acronyms]]

VLS

2017-09-18T20:29:15Z

ChandlerSch: /* Pros */ Fixed a grammar issue.

{{Substep Infobox
|name=VLS
|image=ols.png
|proposers=[[Mats Valk]], [[Rowe Hessler]], [[Lucas Winter]]
|year=[[WV]]: 2005 The rest of VLS: 2013
|anames=VRLS, RLS
|variants=[[WV]], UF, UL, UB, UFUL, ULUB, UFUB, all edges misoriented
|subgroup=
|algs=432 (216 excluding mirrors)
|moves=9.74
|purpose=
* [[Speedsolving]]
* [[FMC]]
|previous=[[VLS]] setup or third [[F2L]] pair
|next=[[PLL]]
}}

'''VLS''', short for '''Valk Last Slot''', is a subset of [[OLS]]. The VLS substep solves the last F2L [[pair]], if the edge and corner are already [[pair]]ed in the [[LL|last layer]] and can be inserted using [U]RU'R', and also skips [[OLL]] which is the third step used in the widely popular [[CFOP]] method. VLS can be used in [[speedsolving]] or [[FMC]] to decrease move count.

==History==
A portion of VLS was previously completed and published in 2005 by [[Lucas Winter]]. The portion created by him is commonly known throughout the cubing community as [[Winter Variation]], or WV, and is one of the subsets in VLS.

The rest of VLS was later generated by speedcuber [[Mats Valk]] in 2009. He had used them somewhat often in his solves, however, he did not publish them for the public and it was not commonly known that Mats used an [[OLS]] method. A few years later in 2013, [[Rowe Hessler]] had unintentionally come up with the same idea. He generated and published all of the [[algorithms]] for the last slot method on his [http://rowe.cubing.net/rls/ website], calling them "RLS" for Rowe Last Slot. Mats had later found out that Rowe had come up with the same idea and contacted him about it. They agreed to create [http://www.youtube.com/channel/UCOvpCbHRg9NSQce3is8MGNw a YouTube channel] that, for a short time, made videos about VLS cases and Rowe also created [https://www.speedsolving.com/forum/threads/ols-vls-hls-algorithms-by-mats-valk-and-rowe-hessler.44642/ a forum post] introducing the method, now calling it VLS. One year later in 2014, Rowe also created [[algdb]] pages for VLS algorithms, finally calling them "VRLS" for Valk-Rowe Last Slot, however most people still know it today by the name VLS.

==Learning Approach==
There are 8 subsets under VLS. They are named after which edges are misoriented if the F2L pair is on the right and is facing towards the solver. Note that there are mirrored cases which still fall under their unmirrored subsets. These subsets includes [[WV]], UF, UL, UB, UFUL, ULUB, UFUB, and all edges. Each of these subsets include 54 algorithms, if mirrors are counted as separate cases. It is usually recommended to first learn [[WV]] and then the rest of VLS in whatever order you choose. Learn the placement of the stickers meant to be on the top face, like with [[OLL]].

==Pros==
* Move count is decreased by about 4 moves compared to normally doing the last [[F2L]] pair, then [[OLL]].
* It requires less [[look ahead]] if implemented into solves, compared to doing the last F2L pair and OLL. So, although it only saves 4 moves, decreased look ahead can help reduce your solve times.
* Increased chance of a last layer skip.

==Cons==
* There are a total of 432 algorithms, including mirrors.
* Because of the first point, this means that if the solver were to learn full VLS, it would likely take at least a year if 1 algorithm was learned per day.

==See Also==
*[[OLS]]
*[[HLS]]
*[[VHLS]]
*[[ZBLS]]
*[[OLL]]
==External Links==
*[https://www.speedsolving.com/forum/threads/ols-vls-hls-algorithms-by-mats-valk-and-rowe-hessler.44642/ The original forum post introducing VLS and HLS]
*[http://rowe.cubing.net/rls/ All of Rowe Hessler's VLS algorithms]
*[http://www.youtube.com/channel/UCOvpCbHRg9NSQce3is8MGNw Mats Valk and Rowe Hessler's abandoned OLS YouTube channel]
[[Category:3x3x3 last slot substeps]]

VLS

2017-09-18T20:28:50Z

ChandlerSch: /* Learning Approach */ Fixed a grammar issue (yes, this is correct)

{{Substep Infobox
|name=VLS
|image=ols.png
|proposers=[[Mats Valk]], [[Rowe Hessler]], [[Lucas Winter]]
|year=[[WV]]: 2005 The rest of VLS: 2013
|anames=VRLS, RLS
|variants=[[WV]], UF, UL, UB, UFUL, ULUB, UFUB, all edges misoriented
|subgroup=
|algs=432 (216 excluding mirrors)
|moves=9.74
|purpose=
* [[Speedsolving]]
* [[FMC]]
|previous=[[VLS]] setup or third [[F2L]] pair
|next=[[PLL]]
}}

'''VLS''', short for '''Valk Last Slot''', is a subset of [[OLS]]. The VLS substep solves the last F2L [[pair]], if the edge and corner are already [[pair]]ed in the [[LL|last layer]] and can be inserted using [U]RU'R', and also skips [[OLL]] which is the third step used in the widely popular [[CFOP]] method. VLS can be used in [[speedsolving]] or [[FMC]] to decrease move count.

==History==
A portion of VLS was previously completed and published in 2005 by [[Lucas Winter]]. The portion created by him is commonly known throughout the cubing community as [[Winter Variation]], or WV, and is one of the subsets in VLS.

The rest of VLS was later generated by speedcuber [[Mats Valk]] in 2009. He had used them somewhat often in his solves, however, he did not publish them for the public and it was not commonly known that Mats used an [[OLS]] method. A few years later in 2013, [[Rowe Hessler]] had unintentionally come up with the same idea. He generated and published all of the [[algorithms]] for the last slot method on his [http://rowe.cubing.net/rls/ website], calling them "RLS" for Rowe Last Slot. Mats had later found out that Rowe had come up with the same idea and contacted him about it. They agreed to create [http://www.youtube.com/channel/UCOvpCbHRg9NSQce3is8MGNw a YouTube channel] that, for a short time, made videos about VLS cases and Rowe also created [https://www.speedsolving.com/forum/threads/ols-vls-hls-algorithms-by-mats-valk-and-rowe-hessler.44642/ a forum post] introducing the method, now calling it VLS. One year later in 2014, Rowe also created [[algdb]] pages for VLS algorithms, finally calling them "VRLS" for Valk-Rowe Last Slot, however most people still know it today by the name VLS.

==Learning Approach==
There are 8 subsets under VLS. They are named after which edges are misoriented if the F2L pair is on the right and is facing towards the solver. Note that there are mirrored cases which still fall under their unmirrored subsets. These subsets includes [[WV]], UF, UL, UB, UFUL, ULUB, UFUB, and all edges. Each of these subsets include 54 algorithms, if mirrors are counted as separate cases. It is usually recommended to first learn [[WV]] and then the rest of VLS in whatever order you choose. Learn the placement of the stickers meant to be on the top face, like with [[OLL]].

==Pros==
* Move count is decreased by about 4 moves compared to normally doing the last [[F2L]] pair, then [[OLL]].
* It requires less [[look ahead]], if implemented into solves, compared to doing the last F2L pair and OLL. So, although it only saves 4 moves, decreased look ahead can help reduce your solve times.
* Increased chance of a last layer skip.

==Cons==
* There are a total of 432 algorithms, including mirrors.
* Because of the first point, this means that if the solver were to learn full VLS, it would likely take at least a year if 1 algorithm was learned per day.

==See Also==
*[[OLS]]
*[[HLS]]
*[[VHLS]]
*[[ZBLS]]
*[[OLL]]
==External Links==
*[https://www.speedsolving.com/forum/threads/ols-vls-hls-algorithms-by-mats-valk-and-rowe-hessler.44642/ The original forum post introducing VLS and HLS]
*[http://rowe.cubing.net/rls/ All of Rowe Hessler's VLS algorithms]
*[http://www.youtube.com/channel/UCOvpCbHRg9NSQce3is8MGNw Mats Valk and Rowe Hessler's abandoned OLS YouTube channel]
[[Category:3x3x3 last slot substeps]]

VLS

2017-09-18T20:28:02Z

ChandlerSch: /* History */ Fixed a grammar issue.

{{Substep Infobox
|name=VLS
|image=ols.png
|proposers=[[Mats Valk]], [[Rowe Hessler]], [[Lucas Winter]]
|year=[[WV]]: 2005 The rest of VLS: 2013
|anames=VRLS, RLS
|variants=[[WV]], UF, UL, UB, UFUL, ULUB, UFUB, all edges misoriented
|subgroup=
|algs=432 (216 excluding mirrors)
|moves=9.74
|purpose=
* [[Speedsolving]]
* [[FMC]]
|previous=[[VLS]] setup or third [[F2L]] pair
|next=[[PLL]]
}}

'''VLS''', short for '''Valk Last Slot''', is a subset of [[OLS]]. The VLS substep solves the last F2L [[pair]], if the edge and corner are already [[pair]]ed in the [[LL|last layer]] and can be inserted using [U]RU'R', and also skips [[OLL]] which is the third step used in the widely popular [[CFOP]] method. VLS can be used in [[speedsolving]] or [[FMC]] to decrease move count.

==History==
A portion of VLS was previously completed and published in 2005 by [[Lucas Winter]]. The portion created by him is commonly known throughout the cubing community as [[Winter Variation]], or WV, and is one of the subsets in VLS.

The rest of VLS was later generated by speedcuber [[Mats Valk]] in 2009. He had used them somewhat often in his solves, however, he did not publish them for the public and it was not commonly known that Mats used an [[OLS]] method. A few years later in 2013, [[Rowe Hessler]] had unintentionally come up with the same idea. He generated and published all of the [[algorithms]] for the last slot method on his [http://rowe.cubing.net/rls/ website], calling them "RLS" for Rowe Last Slot. Mats had later found out that Rowe had come up with the same idea and contacted him about it. They agreed to create [http://www.youtube.com/channel/UCOvpCbHRg9NSQce3is8MGNw a YouTube channel] that, for a short time, made videos about VLS cases and Rowe also created [https://www.speedsolving.com/forum/threads/ols-vls-hls-algorithms-by-mats-valk-and-rowe-hessler.44642/ a forum post] introducing the method, now calling it VLS. One year later in 2014, Rowe also created [[algdb]] pages for VLS algorithms, finally calling them "VRLS" for Valk-Rowe Last Slot, however most people still know it today by the name VLS.

==Learning Approach==
There are 8 subsets under VLS. They are named after which edges are misoriented if the F2L pair is on the right and is facing towards the solver. Note that there are mirrored cases which still fall under their unmirrored subsets. These subsets include [[WV]], UF, UL, UB, UFUL, ULUB, UFUB, and all edges. Each of these subsets include 54 algorithms, if mirrors are counted as separate cases. It is usually recommended to first learn [[WV]] and then the rest of VLS in whatever order you choose. Learn the placement of the stickers meant to be on the top face, like with [[OLL]].

==Pros==
* Move count is decreased by about 4 moves compared to normally doing the last [[F2L]] pair, then [[OLL]].
* It requires less [[look ahead]], if implemented into solves, compared to doing the last F2L pair and OLL. So, although it only saves 4 moves, decreased look ahead can help reduce your solve times.
* Increased chance of a last layer skip.

==Cons==
* There are a total of 432 algorithms, including mirrors.
* Because of the first point, this means that if the solver were to learn full VLS, it would likely take at least a year if 1 algorithm was learned per day.

==See Also==
*[[OLS]]
*[[HLS]]
*[[VHLS]]
*[[ZBLS]]
*[[OLL]]
==External Links==
*[https://www.speedsolving.com/forum/threads/ols-vls-hls-algorithms-by-mats-valk-and-rowe-hessler.44642/ The original forum post introducing VLS and HLS]
*[http://rowe.cubing.net/rls/ All of Rowe Hessler's VLS algorithms]
*[http://www.youtube.com/channel/UCOvpCbHRg9NSQce3is8MGNw Mats Valk and Rowe Hessler's abandoned OLS YouTube channel]
[[Category:3x3x3 last slot substeps]]

OLS

2017-09-18T20:25:31Z

ChandlerSch: /* Pros */ Fixed a grammar issue.

{{Substep Infobox
|name=OLS
|image=ols.png
|proposers=[[Mats Valk]] (VLS) [[Rowe Hessler]] (VLS+HLS) [[Lucas Winter]] (WV) [[Chester Lian]] (SV) [[Lucas Garron]] (CLS) [[Shotaro Makisumi]] (CLS) [[Jabari Nuruddin]] (Oriented LS)
|year=[[WV]]: 2005 [[CLS]]: 2006 [[SV]]: 2009 The rest of [[VLS]] + [[HLS]]: 2013 [[Oriented LS]]: 2015
|anames=
|variants=[[VLS]], [[HLS]], [[CLS]], [[Oriented LS]]
|subgroup=
|algs=864 are needed (including mirrors, by using VLS+HLS), however there can be up to 17,712
|moves=
|purpose=
* [[Speedsolving]]
* [[FMC]]
|previous=Third [[F2L]] pair
|next=[[PLL]]
}}

'''OLS''', an acronym for '''Orientation of the Last Slot''', is a last slot method used to skip any [[OLL]] case while simultaneously solving the last [[F2L]] pair. All OLS cases can be solved using one of the [[algorithms]] found in [[VLS]] or [[HLS]]. If the pair cannot be solved using RUR' or RU'R', it can be intuitively changed to be able to do so. For example, if you were to set up this case (RU'R'URU2R'), the pair can be easily changed to an [[HLS]] case by intuitively doing this algorithm (RU2R'U'). However, setup moves and OLS can be done at the same time if the correct algorithms are used. Unfortunately, this would require up to 17,712 algorithms so it is not put into full use by any human. This method is quite helpful with decreasing times once the solver gets used to using the algorithms. Some notable speedsolvers who use parts of this method from time to time include [[Feliks Zemdegs]], [[Seung Hyuk Nahm]], and [[Mats Valk]] to name a few.

==Learning Approach==
As previously stated, OLS is mainly split into two groups: VLS and HLS. These two groups are split into 8 subsets, each, that are based on edge misorientation. The subsets under VLS include [[WV]], UF, UL, UB, UFUL, ULUB, UFUB, and all edges. The subsets under HLS include [[SV]], UF, UL, UR, UFUR, UFUL, ULUR, and all edges. Each of these subsets has 54 algorithms, including mirrors. It is usually recommended to first learn WV, then SV, followed by the rest of VLS, and finally the rest of HLS.

==Pros==
* Move count is decreased by about 4 moves compared to normally doing the last [[F2L]] pair, then [[OLL]].
* It requires less [[look ahead]] if implemented into solves, compared to doing the last F2L pair and OLL. So, although it only saves 4 moves, decreased look ahead can help reduce your solve times.
* Increased chance of a last layer skip.

==Cons==
* There are a total of at least 864 algorithms, including mirrors.
* Because of the first point, this means that if the solver were to learn full [[VLS]] and [[HLS]], it would take over a year to learn if 2 algorithms were learned per day.

==See Also==
*[[VLS]]
*[[HLS]]
*[[VHLS]]
*[[ZBLS]]
*[[OLL]]
==External Links==
*[https://www.speedsolving.com/forum/threads/ols-vls-hls-algorithms-by-mats-valk-and-rowe-hessler.44642/ The original forum post introducing VLS and HLS]
*[http://rowe.cubing.net/rls/ All of Rowe Hessler's VLS algorithms]
*[https://www.speedsolving.com/forum/threads/bindedsas-algorithms.55518/ Jabari Nuruddin's algs (HLS 0 edges and Oriented LS)]