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Corner Orientation

2017-03-12T09:16:57Z

Logiqx: Removed apostrophe from my previous edit

{{Substep Infobox
|name=Corner Orientation
|image=COinfo.png
|proposers=
|year=
|anames=CO
|variants=[[OCLL]]
|subgroup=
|algs=7
|moves=
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
}}
'''Corner Orientation''', abbrevaited '''CO''', the [[orientation]] of a [[cube]]'s [[corner]]s. There are three possible corner cubie orientations. CO is a [[substep]] in many [[method]]s.

For the [[last layer]] of the [[3x3x3 cube]] there are three main variations used for the seven cases of CO, one that is named [[Corner Orientation#Pure CO|pure CO]] wich orients the corners without affecting anything else, not even corner permutation, one preserves edge orientation wich is [[OCLL]] (OLL 21 - 27) and the last variation orients the corners ignoring edges (use any [[OLL]] that twists the same corners for that).

The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named "corner orientation".

'''Algorithms'''; at this page you can find algortihms for two different variations of CO;
* [[Corner Orientation#Pure CO|Pure CO]]: orients corners preserving edge orientation and both corner and edge permutation.
* [[Corner Orientation#OCLL-EPP|OCLL-EPP]]: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).

== See also ==
* [[Orientation]]
* [[Permutation]]
* [[Edge Orientation]]
* [[Corner Permutation]]
* [[OCLL]]
* [[Winter Variation]]
* [[CLS]]
* [[Partial Corner Control]]
= Pure CO =
'''Usage:''' Besides that these cases are a group in [[L4C]], [[L3C]], [[ZBLL]], [[ZZLL]];

[[3OP]] is a [[blindfold method]] that orients the pieces before they are placed into position, the algorithms here solves the corner orientation in at the most 3 steps, first, if needed two pieces, one in the top layer and one in the bottom layer to fix [[orientation parity]] and then 2-4 corners in the top layer and then the same for the bottom layer. ''Algs for pure orientation of the edges can be found at the [[ELL|ELL page]]''.

Any other BLD method, to fix orientation for corners that are in position but unoriented from the scramble (a few setup moves to get the pieces into the same layer may be needed then).

For [[FMC]] to solve the last pieces (but that won't give any WR, better to try some different start of the last layer that gives a easier case in the end).

===Algorithms===
All cases here have long [[algorithm]]s, the H case is actually the worst LL case of them all and the pi case is second worst. The good thing is that all cases are solvable using only two sides (RU [[2-gen]]). There are different sections for different types of algorithms, first is optimal 2-gen followed by 2-gens of any length. All cases can be solved using two or more [[Sune]], the third section is for these combinations (double, anti and mirrors included). Next comes algs optimal in [[Half Turn Metric]], using as many sides that is needed for that (2-6) and the last section is for any other alg that solves the case.

{{Algnote}}

==Two corners unoriented==
Note that the T-twist is the same case as the U-twist if you reorient the cube (for these images that will be z' y2).
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U ===
{{case |image=Pure twist U.jpg
|name=U, [[Headlights]], Superman
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)}}

'''Any other 2-gen:'''
{{Alg|R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)}}

'''Sune combos:'''
{{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}
{{Alg|(R U2 R' U' R U' R') U2 (R' U2 R U R' U R) (U2)}}

'''HTM optimal:'''
{{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}

'''Any other:'''
{{Alg|(x) U2 R' U' R U' R' L' U2 L U L' U L R (x')}}
{{Alg|(z') (U R U' R')2 L' (R U R' U')2 L (z)}}
{{Alg|(y2) (R U R' U')2 L' (U R U' R')2 L}}
{{Alg|(F D' F' R' D' R) U (R' D R F D F') U'}}

|

=== T ===
{{case |image=Pure twist T.jpg
|name=T
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|(U) R2 U' R U' R2 U R2 U R U' R' U' R U R2}}

'''Any other 2-gen:'''
{{Alg|(U2) R U R' U' R' U R U2 R U2 R' U R' U2 R}}
{{Alg|(U2) R' U' R U' R' U2 R U2 R U R' U R U2 R'}}

'''Sune combos:'''
{{Alg|(L' U' L U' L' U2 L) (R U R' U R U2 R')}}
{{Alg|(U2) (R' U' R U' R' U2 R) U2 (R U R' U R U2 R')}}

'''HTM optimal:'''
{{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}

'''Any other:'''
{{Alg|(z') (R U R' U')2 L' (U R U' R')2 L (z)}}
{{Alg|(y2) (U R U' R')2 L' (R U R' U')2 L}}
{{Alg|(R' D R F D F') U (F D' F' R' D' R) U'}}

|-valign="top"
|

=== L ===
{{case |image=Pure twist L.jpg
|name=L, Bowtie
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')}}

'''Any other 2-gen:'''
{{Alg|(U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R}}

'''Sune combos:'''
{{Alg|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}}
{{Alg|(U) F (R U2 R' U' R U' R') U2 (R' U2 R U R' U R) U2 F}}

'''HTM optimal:''' (12 move commutator)
{{Alg|U2 (R' B D2 B' R) U2 (R' B D2 B' R)}}
{{Alg|(F L' D2 L F') U2 (F L' D2 L F') U2}}

'''Any other:'''
{{Alg|R U' R' L' U2 L U L' U L R U2 R' U'}}
{{Alg|y' R' U L U' R U2 y' R' U' R F' R' U R U2}}
{{Alg|(F D' F' R' D' R) U2 (R' D R F D F') U2}}

|
|}

==Three corners unoriented==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== S ===
{{case |image=Pure twist S.jpg
|name=S, Sune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}

'''Any other 2-gen:'''
{{Alg|R U R2 U' R2 U R U R' U' R U R U R U' R' (U)}}
{{Alg|(R U R' U') R' U' R' U' (R U R' U') R2 U2 R2 U2 R' (U')}}

'''Sune combos:'''
{{Alg|(U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)}}

'''HTM optimal:'''
{{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}

'''Any other:'''
{{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }}

|

=== -S ===
{{case |image=Pure twist aS.jpg
|name=-S, Antisune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}

'''Any other 2-gen:'''
{{Alg|R2 U2 R' U2 R' U' R U' R2 U' R U' R2 U' R U' R}}
{{Alg|(U2) R U' R2 U' R U' R' U2 R' U2 R' U' R U' R2 (U)}}

'''Sune combos:'''
{{Alg|(U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)}}

'''HTM optimal:'''
{{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}

'''Any other:'''
{{Alg|U2 R U2 R' U' R U' R d M U2 M' d L2}}

|}

==Four corners unoriented==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== H ===
{{case |image=Pure twist H.jpg
|name=H
|methods=[[L4C]], [[BLD]]
|optimal=16 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R (U)}}
{{Alg|R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2') (R U' R' U') (R U R U) (R U' R)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}

'''Any other:'''
{{Alg|(r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')}}
{{Alg|(r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)}}
{{Alg|(L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')}}
{{Alg|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2}}

|

=== pi ===
{{case |image=Pure twist pi.jpg
|name=pi, Bruno
|methods=[[L4C]], [[BLD]]
|optimal=15 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R' (U)}}
{{Alg|R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')}}

'''Any other 2-gen:'''
{{Alg|(y) R U2 R' U' R U R2 U2 R2 U R2 U R2 U' R' (U')}}
{{Alg|(y') R' U2 R U R' U' R2 U2 R2 U' R2 U' R2 U R (U)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}

'''Any other:'''
{{Alg|(y) R' U' (R' F R F') (R U' R' U) (R' F R F') R U' R' U2 R}}
{{Alg|B (U L U' L') (U L U') L2 (x') U' M' U L U' M (x)}}
{{Alg|(y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'}}
{{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}

|}

= OCLL-EPP =
'''Orientation of the corners of the last layer - edges permutation preserved'''; orients the [[last layer]] corners preserving edge permutation but ignoring corner permutation.

'''Usage'''; to solve the [[last four corners]] in two looks if the edges are solved (3-look [[LLEF]], OCLL-EPP and [[CPLL]], total 26 algs. 4-look [[EO]], [[EP]], OCLL-EPP and CPLL, total 16 algs).

Average movecount is 9.63 turns optimally, CPLL is 9.12 turns optimally wich gives 19 moves on average for solving L4C in 2-looks like this.

===Algorithms===
{{Algnote}}

==Two corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U (EPP) ===
{{case |image=OCLL-EPP U.jpg
|name=U, Headlights, Superman
|methods=2-look [[L4C]]
|optimal=9 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U' R' U2 R' U2 R U R' U R U2 R U2 R' U' R}}
{{Alg|U R U2 R' U' R U' R' U2 R' U2 R U R' U R}}
{{Alg|U R' U2 R U R' U R U2 R U2 R' U' R U' R'}}

'''HTM optimal:'''
{{Alg|R2 D' R U2 R' D R U2 R}}
{{Alg|R2 F2 R' B2 R F2 R' B2 R'}}
{{Alg|(z' y') U2 R2 U' L2 U R2 U' L2 U' (y z)}}

'''Any other:'''
{{Alg|R U2 R2 U L U' R2 U L' U R'}}
{{Alg|R' U2 R F' R' F U2 F' R F}}

|

=== T (EPP) ===
{{case |image=OCLL-EPP T.jpg
|name=T
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R' U R U2 R U2 R' U R' U2 R U2 R U}}
{{Alg|U' R U R' U R U2 R' U2 R' U' R U' R' U2 R}}
{{Alg|U' R' U' R U' R' U2' R U2 R U R' U R U2 R'}}

'''HTM optimal:'''
{{Alg|R' F' R B' R' F R B}}
{{Alg|(x) R' U' R D' R' U R D (x')}}
{{Alg|(x') R' D' R U' R' D R U (x)}}
{{Alg|(y') r U R' U' r' F R F'}}
{{Alg|(y) l U L' U' R' U L U' (x)}}

'''Any other:'''
{{Alg|F U F' R' F U' F' U R U'}}
{{Alg|(y') R U R' U' L' U R U' M' (x')}}

|-valign="top"
|

=== L (EPP) ===
{{case |image=OCLL-EPP L.jpg
|name=L, Bowtie
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R2 U2 R2 U R U' R U R2 U2 R2 U' R' U}}
{{Alg|U2 R' U' R U' R' U R U' R' U R U' R' U2 R}}
{{Alg|U' R U2 R' U' R U R' U' R U R' U' R U' R'}}

'''HTM optimal:'''
{{Alg|R B' R' F R B R' F'}}
{{Alg|(y) F R' F' r U R U' r'}}
{{Alg|(x') U' R U L' U' R' U r}}

'''Any other:'''
{{Alg|U' F U R' U' R F' R' U R}}
{{Alg|R U R U' L' U R' U' M' (x')}}

|
|}

==Three corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== S (EPP) ===
{{case |image=OCLL-EPP S.jpg
|name=S, Sune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}}

'''HTM optimal:'''
{{Alg|R U' L' U R' U' L U}}

'''Any other:'''
{{Alg|!}}

|

=== -S (EPP) ===
{{case |image=OCLL-EPP aS.jpg
|name=-S, Antisune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R U2 R2 U' R2 U' R' U R' U R}}

'''HTM optimal:'''
{{Alg|U' L' U R U' L U R'}}

'''Any other:'''
{{Alg|!}}

|}

==Four corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== H (EPP) ===
{{case |image=OCLL-EPP H.jpg
|name=H
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'}}

'''HTM optimal:'''
{{Alg|R' F2 R2 U2 R' F2 R U2 R2 F2 R U2}}

'''Any other:'''
{{Alg|F (R U R' U')3 F'}}

|

=== pi (EPP) ===
{{case |image=OCLL-EPP pi.jpg
|name=pi, Bruno
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R U R' U R' U' R2 U R' U' R U' R2 U}}

'''HTM optimal:'''
{{Alg|R F' D2 F R' U' R F' D2 F R' U}}

'''Any other:'''
{{Alg|R' U L U' R U L2 U R U' L U R' U2}}
{{Alg|L U' R' U L' U' R2 U' L' U R' U' L U2}}

|}

[[Category:Puzzle theory]]
[[Category:3x3x3 other substeps]]

__NOTOC__

== OLC Algorithms ==

'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.

Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).

Odds of skipping this step are 1/27.

{{Algnote}}

=== OLC 1 ===
Probability 4/27
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[ZZ-reduction]]
|text=
}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|y2 R' U L U' R U L'|OLL}}
{{Alg|U R U' L' U R' U' L|OLL}}

=== OLC 2 ===
Probability 4/27
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|L' U R U' L U R'|OLL}}

=== OLC 3 ===
Probability 2/27
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]], ? [[STM]]
|text=
}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y R U2 R' (U' R U R') U' (R U' R')|OLL}}
{{Alg|R U2 R' F R' F' R F2 L F L' F|OLL}}

=== OLC 4 ===
Probability 4/27
{{case
|image=o22.gif
|name=pi, Bruno, wheel, T-shirt
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|f (R U R' U') F f' (R U R' U') F'|OLL}}
{{Alg|R U2' R2' U' R2 U' R2' U2' R|OLL}}
{{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}

=== OLL 23 ===
Probability 4/27
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}
{{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}
{{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}
{{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}
{{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}

=== OLL 24 ===
Probability 4/27
{{case
|image=o24.gif
|name=T, chameleon, shark, Hammerhead, Little Horse, stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D'|OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}

=== OLL 25 ===
Probability 4/27
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x' L' U' R' U L U' R U|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}

Corner Orientation

2017-03-12T09:13:44Z

Logiqx: Additional Sune combination

{{Substep Infobox
|name=Corner Orientation
|image=COinfo.png
|proposers=
|year=
|anames=CO
|variants=[[OCLL]]
|subgroup=
|algs=7
|moves=
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
}}
'''Corner Orientation''', abbrevaited '''CO''', the [[orientation]] of a [[cube]]'s [[corner]]s. There are three possible corner cubie orientations. CO is a [[substep]] in many [[method]]s.

For the [[last layer]] of the [[3x3x3 cube]] there are three main variations used for the seven cases of CO, one that is named [[Corner Orientation#Pure CO|pure CO]] wich orients the corners without affecting anything else, not even corner permutation, one preserves edge orientation wich is [[OCLL]] (OLL 21 - 27) and the last variation orients the corners ignoring edges (use any [[OLL]] that twists the same corners for that).

The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named "corner orientation".

'''Algorithms'''; at this page you can find algortihms for two different variations of CO;
* [[Corner Orientation#Pure CO|Pure CO]]: orients corners preserving edge orientation and both corner and edge permutation.
* [[Corner Orientation#OCLL-EPP|OCLL-EPP]]: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).

== See also ==
* [[Orientation]]
* [[Permutation]]
* [[Edge Orientation]]
* [[Corner Permutation]]
* [[OCLL]]
* [[Winter Variation]]
* [[CLS]]
* [[Partial Corner Control]]
= Pure CO =
'''Usage:''' Besides that these cases are a group in [[L4C]], [[L3C]], [[ZBLL]], [[ZZLL]];

[[3OP]] is a [[blindfold method]] that orients the pieces before they are placed into position, the algorithms here solves the corner orientation in at the most 3 steps, first, if needed two pieces, one in the top layer and one in the bottom layer to fix [[orientation parity]] and then 2-4 corners in the top layer and then the same for the bottom layer. ''Algs for pure orientation of the edges can be found at the [[ELL|ELL page]]''.

Any other BLD method, to fix orientation for corners that are in position but unoriented from the scramble (a few setup moves to get the pieces into the same layer may be needed then).

For [[FMC]] to solve the last pieces (but that won't give any WR, better to try some different start of the last layer that gives a easier case in the end).

===Algorithms===
All cases here have long [[algorithm]]s, the H case is actually the worst LL case of them all and the pi case is second worst. The good thing is that all cases are solvable using only two sides (RU [[2-gen]]). There are different sections for different types of algorithms, first is optimal 2-gen followed by 2-gens of any length. All cases can be solved using two or more [[Sune]], the third section is for these combinations (double, anti and mirrors included). Next comes algs optimal in [[Half Turn Metric]], using as many sides that is needed for that (2-6) and the last section is for any other alg that solves the case.

{{Algnote}}

==Two corners unoriented==
Note that the T-twist is the same case as the U-twist if you reorient the cube (for these images that will be z' y2).
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U ===
{{case |image=Pure twist U.jpg
|name=U, [[Headlights]], Superman
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)}}

'''Any other 2-gen:'''
{{Alg|R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)}}

'''Sune combos:'''
{{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}
{{Alg|(R U2 R' U' R U' R') U2 (R' U2 R U R' U R) (U2)}}

'''HTM optimal:'''
{{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}

'''Any other:'''
{{Alg|(x) U2 R' U' R U' R' L' U2 L U L' U L R (x')}}
{{Alg|(z') (U R U' R')2 L' (R U R' U')2 L (z)}}
{{Alg|(y2) (R U R' U')2 L' (U R U' R')2 L}}
{{Alg|(F D' F' R' D' R) U (R' D R F D F') U'}}

|

=== T ===
{{case |image=Pure twist T.jpg
|name=T
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|(U) R2 U' R U' R2 U R2 U R U' R' U' R U R2}}

'''Any other 2-gen:'''
{{Alg|(U2) R U R' U' R' U R U2 R U2 R' U R' U2 R}}
{{Alg|(U2) R' U' R U' R' U2 R U2 R U R' U R U2 R'}}

'''Sune combos:'''
{{Alg|(L' U' L U' L' U2 L) (R U R' U R U2 R')}}
{{Alg|(U2) (R' U' R U' R' U2' R) U2 (R U R' U R U2 R')}}

'''HTM optimal:'''
{{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}

'''Any other:'''
{{Alg|(z') (R U R' U')2 L' (U R U' R')2 L (z)}}
{{Alg|(y2) (U R U' R')2 L' (R U R' U')2 L}}
{{Alg|(R' D R F D F') U (F D' F' R' D' R) U'}}

|-valign="top"
|

=== L ===
{{case |image=Pure twist L.jpg
|name=L, Bowtie
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')}}

'''Any other 2-gen:'''
{{Alg|(U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R}}

'''Sune combos:'''
{{Alg|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}}
{{Alg|(U) F (R U2 R' U' R U' R') U2 (R' U2 R U R' U R) U2 F}}

'''HTM optimal:''' (12 move commutator)
{{Alg|U2 (R' B D2 B' R) U2 (R' B D2 B' R)}}
{{Alg|(F L' D2 L F') U2 (F L' D2 L F') U2}}

'''Any other:'''
{{Alg|R U' R' L' U2 L U L' U L R U2 R' U'}}
{{Alg|y' R' U L U' R U2 y' R' U' R F' R' U R U2}}
{{Alg|(F D' F' R' D' R) U2 (R' D R F D F') U2}}

|
|}

==Three corners unoriented==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== S ===
{{case |image=Pure twist S.jpg
|name=S, Sune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}

'''Any other 2-gen:'''
{{Alg|R U R2 U' R2 U R U R' U' R U R U R U' R' (U)}}
{{Alg|(R U R' U') R' U' R' U' (R U R' U') R2 U2 R2 U2 R' (U')}}

'''Sune combos:'''
{{Alg|(U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)}}

'''HTM optimal:'''
{{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}

'''Any other:'''
{{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }}

|

=== -S ===
{{case |image=Pure twist aS.jpg
|name=-S, Antisune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}

'''Any other 2-gen:'''
{{Alg|R2 U2 R' U2 R' U' R U' R2 U' R U' R2 U' R U' R}}
{{Alg|(U2) R U' R2 U' R U' R' U2 R' U2 R' U' R U' R2 (U)}}

'''Sune combos:'''
{{Alg|(U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)}}

'''HTM optimal:'''
{{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}

'''Any other:'''
{{Alg|U2 R U2 R' U' R U' R d M U2 M' d L2}}

|}

==Four corners unoriented==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== H ===
{{case |image=Pure twist H.jpg
|name=H
|methods=[[L4C]], [[BLD]]
|optimal=16 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R (U)}}
{{Alg|R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2') (R U' R' U') (R U R U) (R U' R)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}

'''Any other:'''
{{Alg|(r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')}}
{{Alg|(r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)}}
{{Alg|(L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')}}
{{Alg|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2}}

|

=== pi ===
{{case |image=Pure twist pi.jpg
|name=pi, Bruno
|methods=[[L4C]], [[BLD]]
|optimal=15 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R' (U)}}
{{Alg|R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')}}

'''Any other 2-gen:'''
{{Alg|(y) R U2 R' U' R U R2 U2 R2 U R2 U R2 U' R' (U')}}
{{Alg|(y') R' U2 R U R' U' R2 U2 R2 U' R2 U' R2 U R (U)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}

'''Any other:'''
{{Alg|(y) R' U' (R' F R F') (R U' R' U) (R' F R F') R U' R' U2 R}}
{{Alg|B (U L U' L') (U L U') L2 (x') U' M' U L U' M (x)}}
{{Alg|(y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'}}
{{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}

|}

= OCLL-EPP =
'''Orientation of the corners of the last layer - edges permutation preserved'''; orients the [[last layer]] corners preserving edge permutation but ignoring corner permutation.

'''Usage'''; to solve the [[last four corners]] in two looks if the edges are solved (3-look [[LLEF]], OCLL-EPP and [[CPLL]], total 26 algs. 4-look [[EO]], [[EP]], OCLL-EPP and CPLL, total 16 algs).

Average movecount is 9.63 turns optimally, CPLL is 9.12 turns optimally wich gives 19 moves on average for solving L4C in 2-looks like this.

===Algorithms===
{{Algnote}}

==Two corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U (EPP) ===
{{case |image=OCLL-EPP U.jpg
|name=U, Headlights, Superman
|methods=2-look [[L4C]]
|optimal=9 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U' R' U2 R' U2 R U R' U R U2 R U2 R' U' R}}
{{Alg|U R U2 R' U' R U' R' U2 R' U2 R U R' U R}}
{{Alg|U R' U2 R U R' U R U2 R U2 R' U' R U' R'}}

'''HTM optimal:'''
{{Alg|R2 D' R U2 R' D R U2 R}}
{{Alg|R2 F2 R' B2 R F2 R' B2 R'}}
{{Alg|(z' y') U2 R2 U' L2 U R2 U' L2 U' (y z)}}

'''Any other:'''
{{Alg|R U2 R2 U L U' R2 U L' U R'}}
{{Alg|R' U2 R F' R' F U2 F' R F}}

|

=== T (EPP) ===
{{case |image=OCLL-EPP T.jpg
|name=T
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R' U R U2 R U2 R' U R' U2 R U2 R U}}
{{Alg|U' R U R' U R U2 R' U2 R' U' R U' R' U2 R}}
{{Alg|U' R' U' R U' R' U2' R U2 R U R' U R U2 R'}}

'''HTM optimal:'''
{{Alg|R' F' R B' R' F R B}}
{{Alg|(x) R' U' R D' R' U R D (x')}}
{{Alg|(x') R' D' R U' R' D R U (x)}}
{{Alg|(y') r U R' U' r' F R F'}}
{{Alg|(y) l U L' U' R' U L U' (x)}}

'''Any other:'''
{{Alg|F U F' R' F U' F' U R U'}}
{{Alg|(y') R U R' U' L' U R U' M' (x')}}

|-valign="top"
|

=== L (EPP) ===
{{case |image=OCLL-EPP L.jpg
|name=L, Bowtie
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R2 U2 R2 U R U' R U R2 U2 R2 U' R' U}}
{{Alg|U2 R' U' R U' R' U R U' R' U R U' R' U2 R}}
{{Alg|U' R U2 R' U' R U R' U' R U R' U' R U' R'}}

'''HTM optimal:'''
{{Alg|R B' R' F R B R' F'}}
{{Alg|(y) F R' F' r U R U' r'}}
{{Alg|(x') U' R U L' U' R' U r}}

'''Any other:'''
{{Alg|U' F U R' U' R F' R' U R}}
{{Alg|R U R U' L' U R' U' M' (x')}}

|
|}

==Three corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== S (EPP) ===
{{case |image=OCLL-EPP S.jpg
|name=S, Sune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}}

'''HTM optimal:'''
{{Alg|R U' L' U R' U' L U}}

'''Any other:'''
{{Alg|!}}

|

=== -S (EPP) ===
{{case |image=OCLL-EPP aS.jpg
|name=-S, Antisune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R U2 R2 U' R2 U' R' U R' U R}}

'''HTM optimal:'''
{{Alg|U' L' U R U' L U R'}}

'''Any other:'''
{{Alg|!}}

|}

==Four corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== H (EPP) ===
{{case |image=OCLL-EPP H.jpg
|name=H
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'}}

'''HTM optimal:'''
{{Alg|R' F2 R2 U2 R' F2 R U2 R2 F2 R U2}}

'''Any other:'''
{{Alg|F (R U R' U')3 F'}}

|

=== pi (EPP) ===
{{case |image=OCLL-EPP pi.jpg
|name=pi, Bruno
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R U R' U R' U' R2 U R' U' R U' R2 U}}

'''HTM optimal:'''
{{Alg|R F' D2 F R' U' R F' D2 F R' U}}

'''Any other:'''
{{Alg|R' U L U' R U L2 U R U' L U R' U2}}
{{Alg|L U' R' U L' U' R2 U' L' U R' U' L U2}}

|}

[[Category:Puzzle theory]]
[[Category:3x3x3 other substeps]]

__NOTOC__

== OLC Algorithms ==

'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.

Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).

Odds of skipping this step are 1/27.

{{Algnote}}

=== OLC 1 ===
Probability 4/27
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[ZZ-reduction]]
|text=
}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|y2 R' U L U' R U L'|OLL}}
{{Alg|U R U' L' U R' U' L|OLL}}

=== OLC 2 ===
Probability 4/27
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|L' U R U' L U R'|OLL}}

=== OLC 3 ===
Probability 2/27
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]], ? [[STM]]
|text=
}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y R U2 R' (U' R U R') U' (R U' R')|OLL}}
{{Alg|R U2 R' F R' F' R F2 L F L' F|OLL}}

=== OLC 4 ===
Probability 4/27
{{case
|image=o22.gif
|name=pi, Bruno, wheel, T-shirt
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|f (R U R' U') F f' (R U R' U') F'|OLL}}
{{Alg|R U2' R2' U' R2 U' R2' U2' R|OLL}}
{{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}

=== OLL 23 ===
Probability 4/27
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}
{{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}
{{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}
{{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}
{{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}

=== OLL 24 ===
Probability 4/27
{{case
|image=o24.gif
|name=T, chameleon, shark, Hammerhead, Little Horse, stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D'|OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}

=== OLL 25 ===
Probability 4/27
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x' L' U' R' U L U' R U|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}

Corner Orientation

2017-03-12T09:06:00Z

Logiqx: Added Sune combos

{{Substep Infobox
|name=Corner Orientation
|image=COinfo.png
|proposers=
|year=
|anames=CO
|variants=[[OCLL]]
|subgroup=
|algs=7
|moves=
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
}}
'''Corner Orientation''', abbrevaited '''CO''', the [[orientation]] of a [[cube]]'s [[corner]]s. There are three possible corner cubie orientations. CO is a [[substep]] in many [[method]]s.

For the [[last layer]] of the [[3x3x3 cube]] there are three main variations used for the seven cases of CO, one that is named [[Corner Orientation#Pure CO|pure CO]] wich orients the corners without affecting anything else, not even corner permutation, one preserves edge orientation wich is [[OCLL]] (OLL 21 - 27) and the last variation orients the corners ignoring edges (use any [[OLL]] that twists the same corners for that).

The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named "corner orientation".

'''Algorithms'''; at this page you can find algortihms for two different variations of CO;
* [[Corner Orientation#Pure CO|Pure CO]]: orients corners preserving edge orientation and both corner and edge permutation.
* [[Corner Orientation#OCLL-EPP|OCLL-EPP]]: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).

== See also ==
* [[Orientation]]
* [[Permutation]]
* [[Edge Orientation]]
* [[Corner Permutation]]
* [[OCLL]]
* [[Winter Variation]]
* [[CLS]]
* [[Partial Corner Control]]
= Pure CO =
'''Usage:''' Besides that these cases are a group in [[L4C]], [[L3C]], [[ZBLL]], [[ZZLL]];

[[3OP]] is a [[blindfold method]] that orients the pieces before they are placed into position, the algorithms here solves the corner orientation in at the most 3 steps, first, if needed two pieces, one in the top layer and one in the bottom layer to fix [[orientation parity]] and then 2-4 corners in the top layer and then the same for the bottom layer. ''Algs for pure orientation of the edges can be found at the [[ELL|ELL page]]''.

Any other BLD method, to fix orientation for corners that are in position but unoriented from the scramble (a few setup moves to get the pieces into the same layer may be needed then).

For [[FMC]] to solve the last pieces (but that won't give any WR, better to try some different start of the last layer that gives a easier case in the end).

===Algorithms===
All cases here have long [[algorithm]]s, the H case is actually the worst LL case of them all and the pi case is second worst. The good thing is that all cases are solvable using only two sides (RU [[2-gen]]). There are different sections for different types of algorithms, first is optimal 2-gen followed by 2-gens of any length. All cases can be solved using two or more [[Sune]], the third section is for these combinations (double, anti and mirrors included). Next comes algs optimal in [[Half Turn Metric]], using as many sides that is needed for that (2-6) and the last section is for any other alg that solves the case.

{{Algnote}}

==Two corners unoriented==
Note that the T-twist is the same case as the U-twist if you reorient the cube (for these images that will be z' y2).
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U ===
{{case |image=Pure twist U.jpg
|name=U, [[Headlights]], Superman
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)}}

'''Any other 2-gen:'''
{{Alg|R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)}}

'''Sune combos:'''
{{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}
{{Alg|(R U2 R' U' R U' R') U2 (R' U2 R U R' U R) (U2)}}

'''HTM optimal:'''
{{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}

'''Any other:'''
{{Alg|(x) U2 R' U' R U' R' L' U2 L U L' U L R (x')}}
{{Alg|(z') (U R U' R')2 L' (R U R' U')2 L (z)}}
{{Alg|(y2) (R U R' U')2 L' (U R U' R')2 L}}
{{Alg|(F D' F' R' D' R) U (R' D R F D F') U'}}

|

=== T ===
{{case |image=Pure twist T.jpg
|name=T
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|(U) R2 U' R U' R2 U R2 U R U' R' U' R U R2}}

'''Any other 2-gen:'''
{{Alg|(U2) R U R' U' R' U R U2 R U2 R' U R' U2 R}}
{{Alg|(U2) R' U' R U' R' U2 R U2 R U R' U R U2 R'}}

'''Sune combos:'''
{{Alg|(L' U' L U' L' U2 L) (R U R' U R U2 R')}}
{{Alg|(U2) (R' U' R U' R' U2' R) U2 (R U R' U R U2 R')}}

'''HTM optimal:'''
{{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}

'''Any other:'''
{{Alg|(z') (R U R' U')2 L' (U R U' R')2 L (z)}}
{{Alg|(y2) (U R U' R')2 L' (R U R' U')2 L}}
{{Alg|(R' D R F D F') U (F D' F' R' D' R) U'}}

|-valign="top"
|

=== L ===
{{case |image=Pure twist L.jpg
|name=L, Bowtie
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')}}

'''Any other 2-gen:'''
{{Alg|(U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R}}

'''Sune combos:'''
{{Alg|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}}

'''HTM optimal:''' (12 move commutator)
{{Alg|U2 (R' B D2 B' R) U2 (R' B D2 B' R)}}
{{Alg|(F L' D2 L F') U2 (F L' D2 L F') U2}}

'''Any other:'''
{{Alg|R U' R' L' U2 L U L' U L R U2 R' U'}}
{{Alg|y' R' U L U' R U2 y' R' U' R F' R' U R U2}}
{{Alg|(F D' F' R' D' R) U2 (R' D R F D F') U2}}

|
|}

==Three corners unoriented==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== S ===
{{case |image=Pure twist S.jpg
|name=S, Sune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}

'''Any other 2-gen:'''
{{Alg|R U R2 U' R2 U R U R' U' R U R U R U' R' (U)}}
{{Alg|(R U R' U') R' U' R' U' (R U R' U') R2 U2 R2 U2 R' (U')}}

'''Sune combos:'''
{{Alg|(U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)}}

'''HTM optimal:'''
{{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}

'''Any other:'''
{{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }}

|

=== -S ===
{{case |image=Pure twist aS.jpg
|name=-S, Antisune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}

'''Any other 2-gen:'''
{{Alg|R2 U2 R' U2 R' U' R U' R2 U' R U' R2 U' R U' R}}
{{Alg|(U2) R U' R2 U' R U' R' U2 R' U2 R' U' R U' R2 (U)}}

'''Sune combos:'''
{{Alg|(U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)}}

'''HTM optimal:'''
{{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}

'''Any other:'''
{{Alg|U2 R U2 R' U' R U' R d M U2 M' d L2}}

|}

==Four corners unoriented==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== H ===
{{case |image=Pure twist H.jpg
|name=H
|methods=[[L4C]], [[BLD]]
|optimal=16 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R (U)}}
{{Alg|R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2') (R U' R' U') (R U R U) (R U' R)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}

'''Any other:'''
{{Alg|(r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')}}
{{Alg|(r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)}}
{{Alg|(L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')}}
{{Alg|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2}}

|

=== pi ===
{{case |image=Pure twist pi.jpg
|name=pi, Bruno
|methods=[[L4C]], [[BLD]]
|optimal=15 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R' (U)}}
{{Alg|R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')}}

'''Any other 2-gen:'''
{{Alg|(y) R U2 R' U' R U R2 U2 R2 U R2 U R2 U' R' (U')}}
{{Alg|(y') R' U2 R U R' U' R2 U2 R2 U' R2 U' R2 U R (U)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}

'''Any other:'''
{{Alg|(y) R' U' (R' F R F') (R U' R' U) (R' F R F') R U' R' U2 R}}
{{Alg|B (U L U' L') (U L U') L2 (x') U' M' U L U' M (x)}}
{{Alg|(y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'}}
{{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}

|}

= OCLL-EPP =
'''Orientation of the corners of the last layer - edges permutation preserved'''; orients the [[last layer]] corners preserving edge permutation but ignoring corner permutation.

'''Usage'''; to solve the [[last four corners]] in two looks if the edges are solved (3-look [[LLEF]], OCLL-EPP and [[CPLL]], total 26 algs. 4-look [[EO]], [[EP]], OCLL-EPP and CPLL, total 16 algs).

Average movecount is 9.63 turns optimally, CPLL is 9.12 turns optimally wich gives 19 moves on average for solving L4C in 2-looks like this.

===Algorithms===
{{Algnote}}

==Two corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U (EPP) ===
{{case |image=OCLL-EPP U.jpg
|name=U, Headlights, Superman
|methods=2-look [[L4C]]
|optimal=9 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U' R' U2 R' U2 R U R' U R U2 R U2 R' U' R}}
{{Alg|U R U2 R' U' R U' R' U2 R' U2 R U R' U R}}
{{Alg|U R' U2 R U R' U R U2 R U2 R' U' R U' R'}}

'''HTM optimal:'''
{{Alg|R2 D' R U2 R' D R U2 R}}
{{Alg|R2 F2 R' B2 R F2 R' B2 R'}}
{{Alg|(z' y') U2 R2 U' L2 U R2 U' L2 U' (y z)}}

'''Any other:'''
{{Alg|R U2 R2 U L U' R2 U L' U R'}}
{{Alg|R' U2 R F' R' F U2 F' R F}}

|

=== T (EPP) ===
{{case |image=OCLL-EPP T.jpg
|name=T
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R' U R U2 R U2 R' U R' U2 R U2 R U}}
{{Alg|U' R U R' U R U2 R' U2 R' U' R U' R' U2 R}}
{{Alg|U' R' U' R U' R' U2' R U2 R U R' U R U2 R'}}

'''HTM optimal:'''
{{Alg|R' F' R B' R' F R B}}
{{Alg|(x) R' U' R D' R' U R D (x')}}
{{Alg|(x') R' D' R U' R' D R U (x)}}
{{Alg|(y') r U R' U' r' F R F'}}
{{Alg|(y) l U L' U' R' U L U' (x)}}

'''Any other:'''
{{Alg|F U F' R' F U' F' U R U'}}
{{Alg|(y') R U R' U' L' U R U' M' (x')}}

|-valign="top"
|

=== L (EPP) ===
{{case |image=OCLL-EPP L.jpg
|name=L, Bowtie
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R2 U2 R2 U R U' R U R2 U2 R2 U' R' U}}
{{Alg|U2 R' U' R U' R' U R U' R' U R U' R' U2 R}}
{{Alg|U' R U2 R' U' R U R' U' R U R' U' R U' R'}}

'''HTM optimal:'''
{{Alg|R B' R' F R B R' F'}}
{{Alg|(y) F R' F' r U R U' r'}}
{{Alg|(x') U' R U L' U' R' U r}}

'''Any other:'''
{{Alg|U' F U R' U' R F' R' U R}}
{{Alg|R U R U' L' U R' U' M' (x')}}

|
|}

==Three corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== S (EPP) ===
{{case |image=OCLL-EPP S.jpg
|name=S, Sune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}}

'''HTM optimal:'''
{{Alg|R U' L' U R' U' L U}}

'''Any other:'''
{{Alg|!}}

|

=== -S (EPP) ===
{{case |image=OCLL-EPP aS.jpg
|name=-S, Antisune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R U2 R2 U' R2 U' R' U R' U R}}

'''HTM optimal:'''
{{Alg|U' L' U R U' L U R'}}

'''Any other:'''
{{Alg|!}}

|}

==Four corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== H (EPP) ===
{{case |image=OCLL-EPP H.jpg
|name=H
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'}}

'''HTM optimal:'''
{{Alg|R' F2 R2 U2 R' F2 R U2 R2 F2 R U2}}

'''Any other:'''
{{Alg|F (R U R' U')3 F'}}

|

=== pi (EPP) ===
{{case |image=OCLL-EPP pi.jpg
|name=pi, Bruno
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R U R' U R' U' R2 U R' U' R U' R2 U}}

'''HTM optimal:'''
{{Alg|R F' D2 F R' U' R F' D2 F R' U}}

'''Any other:'''
{{Alg|R' U L U' R U L2 U R U' L U R' U2}}
{{Alg|L U' R' U L' U' R2 U' L' U R' U' L U2}}

|}

[[Category:Puzzle theory]]
[[Category:3x3x3 other substeps]]

__NOTOC__

== OLC Algorithms ==

'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.

Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).

Odds of skipping this step are 1/27.

{{Algnote}}

=== OLC 1 ===
Probability 4/27
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[ZZ-reduction]]
|text=
}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|y2 R' U L U' R U L'|OLL}}
{{Alg|U R U' L' U R' U' L|OLL}}

=== OLC 2 ===
Probability 4/27
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|L' U R U' L U R'|OLL}}

=== OLC 3 ===
Probability 2/27
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]], ? [[STM]]
|text=
}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y R U2 R' (U' R U R') U' (R U' R')|OLL}}
{{Alg|R U2 R' F R' F' R F2 L F L' F|OLL}}

=== OLC 4 ===
Probability 4/27
{{case
|image=o22.gif
|name=pi, Bruno, wheel, T-shirt
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|f (R U R' U') F f' (R U R' U') F'|OLL}}
{{Alg|R U2' R2' U' R2 U' R2' U2' R|OLL}}
{{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}

=== OLL 23 ===
Probability 4/27
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}
{{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}
{{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}
{{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}
{{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}

=== OLL 24 ===
Probability 4/27
{{case
|image=o24.gif
|name=T, chameleon, shark, Hammerhead, Little Horse, stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D'|OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}

=== OLL 25 ===
Probability 4/27
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x' L' U' R' U L U' R U|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}

Corner Orientation

2017-03-12T08:49:26Z

Logiqx: Added some Sune combinations for two corners

{{Substep Infobox
|name=Corner Orientation
|image=COinfo.png
|proposers=
|year=
|anames=CO
|variants=[[OCLL]]
|subgroup=
|algs=7
|moves=
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
}}
'''Corner Orientation''', abbrevaited '''CO''', the [[orientation]] of a [[cube]]'s [[corner]]s. There are three possible corner cubie orientations. CO is a [[substep]] in many [[method]]s.

For the [[last layer]] of the [[3x3x3 cube]] there are three main variations used for the seven cases of CO, one that is named [[Corner Orientation#Pure CO|pure CO]] wich orients the corners without affecting anything else, not even corner permutation, one preserves edge orientation wich is [[OCLL]] (OLL 21 - 27) and the last variation orients the corners ignoring edges (use any [[OLL]] that twists the same corners for that).

The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named "corner orientation".

'''Algorithms'''; at this page you can find algortihms for two different variations of CO;
* [[Corner Orientation#Pure CO|Pure CO]]: orients corners preserving edge orientation and both corner and edge permutation.
* [[Corner Orientation#OCLL-EPP|OCLL-EPP]]: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).

== See also ==
* [[Orientation]]
* [[Permutation]]
* [[Edge Orientation]]
* [[Corner Permutation]]
* [[OCLL]]
* [[Winter Variation]]
* [[CLS]]
* [[Partial Corner Control]]
= Pure CO =
'''Usage:''' Besides that these cases are a group in [[L4C]], [[L3C]], [[ZBLL]], [[ZZLL]];

[[3OP]] is a [[blindfold method]] that orients the pieces before they are placed into position, the algorithms here solves the corner orientation in at the most 3 steps, first, if needed two pieces, one in the top layer and one in the bottom layer to fix [[orientation parity]] and then 2-4 corners in the top layer and then the same for the bottom layer. ''Algs for pure orientation of the edges can be found at the [[ELL|ELL page]]''.

Any other BLD method, to fix orientation for corners that are in position but unoriented from the scramble (a few setup moves to get the pieces into the same layer may be needed then).

For [[FMC]] to solve the last pieces (but that won't give any WR, better to try some different start of the last layer that gives a easier case in the end).

===Algorithms===
All cases here have long [[algorithm]]s, the H case is actually the worst LL case of them all and the pi case is second worst. The good thing is that all cases are solvable using only two sides (RU [[2-gen]]). There are different sections for different types of algorithms, first is optimal 2-gen followed by 2-gens of any length. All cases can be solved using two or more [[Sune]], the third section is for these combinations (double, anti and mirrors included). Next comes algs optimal in [[Half Turn Metric]], using as many sides that is needed for that (2-6) and the last section is for any other alg that solves the case.

{{Algnote}}

==Two corners unoriented==
Note that the T-twist is the same case as the U-twist if you reorient the cube (for these images that will be z' y2).
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U ===
{{case |image=Pure twist U.jpg
|name=U, [[Headlights]], Superman
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)}}

'''Any other 2-gen:'''
{{Alg|R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)}}

'''Sune combos:'''
{{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}

'''HTM optimal:'''
{{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}

'''Any other:'''
{{Alg|(x) U2 R' U' R U' R' L' U2 L U L' U L R (x')}}
{{Alg|(z') (U R U' R')2 L' (R U R' U')2 L (z)}}
{{Alg|(y2) (R U R' U')2 L' (U R U' R')2 L}}
{{Alg|(F D' F' R' D' R) U (R' D R F D F') U'}}

|

=== T ===
{{case |image=Pure twist T.jpg
|name=T
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|(U) R2 U' R U' R2 U R2 U R U' R' U' R U R2}}

'''Any other 2-gen:'''
{{Alg|(U2) R U R' U' R' U R U2 R U2 R' U R' U2 R}}
{{Alg|(U2) R' U' R U' R' U2 R U2 R U R' U R U2 R'}}

'''Sune combos:'''
{{Alg|(L' U' L U' L' U2 L) (R U R' U R U2 R')}}

'''HTM optimal:'''
{{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}

'''Any other:'''
{{Alg|(z') (R U R' U')2 L' (U R U' R')2 L (z)}}
{{Alg|(y2) (U R U' R')2 L' (R U R' U')2 L}}
{{Alg|(R' D R F D F') U (F D' F' R' D' R) U'}}

|-valign="top"
|

=== L ===
{{case |image=Pure twist L.jpg
|name=L, Bowtie
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')}}

'''Any other 2-gen:'''
{{Alg|(U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R}}

'''Sune combos:'''
{{Alg|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}}

'''HTM optimal:''' (12 move commutator)
{{Alg|U2 (R' B D2 B' R) U2 (R' B D2 B' R)}}
{{Alg|(F L' D2 L F') U2 (F L' D2 L F') U2}}

'''Any other:'''
{{Alg|R U' R' L' U2 L U L' U L R U2 R' U'}}
{{Alg|y' R' U L U' R U2 y' R' U' R F' R' U R U2}}
{{Alg|(F D' F' R' D' R) U2 (R' D R F D F') U2}}

|
|}

==Three corners unoriented==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== S ===
{{case |image=Pure twist S.jpg
|name=S, Sune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}

'''Any other 2-gen:'''
{{Alg|R U R2 U' R2 U R U R' U' R U R U R U' R' (U)}}
{{Alg|(R U R' U') R' U' R' U' (R U R' U') R2 U2 R2 U2 R' (U')}}

'''Sune combos:'''
{{Alg|(U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)}}

'''HTM optimal:'''
{{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}

'''Any other:'''
{{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }}

|

=== -S ===
{{case |image=Pure twist aS.jpg
|name=-S, Antisune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}

'''Any other 2-gen:'''
{{Alg|R2 U2 R' U2 R' U' R U' R2 U' R U' R2 U' R U' R}}
{{Alg|(U2) R U' R2 U' R U' R' U2 R' U2 R' U' R U' R2 (U)}}

'''Sune combos:'''
{{Alg|(U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)}}

'''HTM optimal:'''
{{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}

'''Any other:'''
{{Alg|U2 R U2 R' U' R U' R d M U2 M' d L2}}

|}

==Four corners unoriented==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== H ===
{{case |image=Pure twist H.jpg
|name=H
|methods=[[L4C]], [[BLD]]
|optimal=16 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R (U)}}
{{Alg|R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2') (R U' R' U') (R U R U) (R U' R)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}

'''Any other:'''
{{Alg|(r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')}}
{{Alg|(r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)}}
{{Alg|(L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')}}
{{Alg|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2}}

|

=== pi ===
{{case |image=Pure twist pi.jpg
|name=pi, Bruno
|methods=[[L4C]], [[BLD]]
|optimal=15 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R' (U)}}
{{Alg|R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')}}

'''Any other 2-gen:'''
{{Alg|(y) R U2 R' U' R U R2 U2 R2 U R2 U R2 U' R' (U')}}
{{Alg|(y') R' U2 R U R' U' R2 U2 R2 U' R2 U' R2 U R (U)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}

'''Any other:'''
{{Alg|(y) R' U' (R' F R F') (R U' R' U) (R' F R F') R U' R' U2 R}}
{{Alg|B (U L U' L') (U L U') L2 (x') U' M' U L U' M (x)}}
{{Alg|(y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'}}
{{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}

|}

= OCLL-EPP =
'''Orientation of the corners of the last layer - edges permutation preserved'''; orients the [[last layer]] corners preserving edge permutation but ignoring corner permutation.

'''Usage'''; to solve the [[last four corners]] in two looks if the edges are solved (3-look [[LLEF]], OCLL-EPP and [[CPLL]], total 26 algs. 4-look [[EO]], [[EP]], OCLL-EPP and CPLL, total 16 algs).

Average movecount is 9.63 turns optimally, CPLL is 9.12 turns optimally wich gives 19 moves on average for solving L4C in 2-looks like this.

===Algorithms===
{{Algnote}}

==Two corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U (EPP) ===
{{case |image=OCLL-EPP U.jpg
|name=U, Headlights, Superman
|methods=2-look [[L4C]]
|optimal=9 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U' R' U2 R' U2 R U R' U R U2 R U2 R' U' R}}
{{Alg|U R U2 R' U' R U' R' U2 R' U2 R U R' U R}}
{{Alg|U R' U2 R U R' U R U2 R U2 R' U' R U' R'}}

'''HTM optimal:'''
{{Alg|R2 D' R U2 R' D R U2 R}}
{{Alg|R2 F2 R' B2 R F2 R' B2 R'}}
{{Alg|(z' y') U2 R2 U' L2 U R2 U' L2 U' (y z)}}

'''Any other:'''
{{Alg|R U2 R2 U L U' R2 U L' U R'}}
{{Alg|R' U2 R F' R' F U2 F' R F}}

|

=== T (EPP) ===
{{case |image=OCLL-EPP T.jpg
|name=T
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R' U R U2 R U2 R' U R' U2 R U2 R U}}
{{Alg|U' R U R' U R U2 R' U2 R' U' R U' R' U2 R}}
{{Alg|U' R' U' R U' R' U2' R U2 R U R' U R U2 R'}}

'''HTM optimal:'''
{{Alg|R' F' R B' R' F R B}}
{{Alg|(x) R' U' R D' R' U R D (x')}}
{{Alg|(x') R' D' R U' R' D R U (x)}}
{{Alg|(y') r U R' U' r' F R F'}}
{{Alg|(y) l U L' U' R' U L U' (x)}}

'''Any other:'''
{{Alg|F U F' R' F U' F' U R U'}}
{{Alg|(y') R U R' U' L' U R U' M' (x')}}

|-valign="top"
|

=== L (EPP) ===
{{case |image=OCLL-EPP L.jpg
|name=L, Bowtie
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R2 U2 R2 U R U' R U R2 U2 R2 U' R' U}}
{{Alg|U2 R' U' R U' R' U R U' R' U R U' R' U2 R}}
{{Alg|U' R U2 R' U' R U R' U' R U R' U' R U' R'}}

'''HTM optimal:'''
{{Alg|R B' R' F R B R' F'}}
{{Alg|(y) F R' F' r U R U' r'}}
{{Alg|(x') U' R U L' U' R' U r}}

'''Any other:'''
{{Alg|U' F U R' U' R F' R' U R}}
{{Alg|R U R U' L' U R' U' M' (x')}}

|
|}

==Three corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== S (EPP) ===
{{case |image=OCLL-EPP S.jpg
|name=S, Sune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}}

'''HTM optimal:'''
{{Alg|R U' L' U R' U' L U}}

'''Any other:'''
{{Alg|!}}

|

=== -S (EPP) ===
{{case |image=OCLL-EPP aS.jpg
|name=-S, Antisune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R U2 R2 U' R2 U' R' U R' U R}}

'''HTM optimal:'''
{{Alg|U' L' U R U' L U R'}}

'''Any other:'''
{{Alg|!}}

|}

==Four corners==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== H (EPP) ===
{{case |image=OCLL-EPP H.jpg
|name=H
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'}}

'''HTM optimal:'''
{{Alg|R' F2 R2 U2 R' F2 R U2 R2 F2 R U2}}

'''Any other:'''
{{Alg|F (R U R' U')3 F'}}

|

=== pi (EPP) ===
{{case |image=OCLL-EPP pi.jpg
|name=pi, Bruno
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R U R' U R' U' R2 U R' U' R U' R2 U}}

'''HTM optimal:'''
{{Alg|R F' D2 F R' U' R F' D2 F R' U}}

'''Any other:'''
{{Alg|R' U L U' R U L2 U R U' L U R' U2}}
{{Alg|L U' R' U L' U' R2 U' L' U R' U' L U2}}

|}

[[Category:Puzzle theory]]
[[Category:3x3x3 other substeps]]

__NOTOC__

== OLC Algorithms ==

'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.

Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).

Odds of skipping this step are 1/27.

{{Algnote}}

=== OLC 1 ===
Probability 4/27
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[ZZ-reduction]]
|text=
}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|y2 R' U L U' R U L'|OLL}}
{{Alg|U R U' L' U R' U' L|OLL}}

=== OLC 2 ===
Probability 4/27
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|L' U R U' L U R'|OLL}}

=== OLC 3 ===
Probability 2/27
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]], ? [[STM]]
|text=
}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y R U2 R' (U' R U R') U' (R U' R')|OLL}}
{{Alg|R U2 R' F R' F' R F2 L F L' F|OLL}}

=== OLC 4 ===
Probability 4/27
{{case
|image=o22.gif
|name=pi, Bruno, wheel, T-shirt
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|f (R U R' U') F f' (R U R' U') F'|OLL}}
{{Alg|R U2' R2' U' R2 U' R2' U2' R|OLL}}
{{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}

=== OLL 23 ===
Probability 4/27
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}
{{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}
{{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}
{{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}
{{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}

=== OLL 24 ===
Probability 4/27
{{case
|image=o24.gif
|name=T, chameleon, shark, Hammerhead, Little Horse, stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D'|OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}

=== OLL 25 ===
Probability 4/27
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x' L' U' R' U L U' R U|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}

CEOLL

2016-11-27T19:54:40Z

Logiqx: Redirected page to OLLCP

#REDIRECT [[OLLCP]]

CLLEO

2016-11-27T19:53:50Z

Logiqx: Redirected page to OLLCP

#REDIRECT [[OLLCP]]

OCPLL

2016-11-27T19:51:54Z

Logiqx: Redirected page to OLLCP

#REDIRECT [[OLLCP]]

OLLCP-A

2016-11-27T18:37:24Z

Logiqx: Added an info box, tweaked the text and added some links

'''OLLCP-A''', ''corner permutation and edges orientation of the last layer'', an [[experimental method]] for the [[3x3x3 cube]] that [[permute]]s the [[last layer]] [[corner]]s and [[orient]]s the last layer [[edge]]s preserving [[F2L]].

{{Substep Infobox
|name=OLLCP-A
|image=OLLCP.png
|proposers=Various
|year=
|anames=[[OELLCP]], [[CPEOLL]]
|variants=
|subgroup=
|algs=15
|moves=~11
|purpose=
* [[Speedsolving]]
|previous=[[F2L cube state]]
|next=[[LL:EO+CO+CP cube state]]
}}

'''Orientation of Last Layer and Corner Permutation'''
'''OLLCP-A''' is an [[experimental method|experimental]] [[LL]] method which both [[EOLL|orients the last layer edges]] and [[CPLL|permutes the last layer corners]] when the corners are already oriented. Thus after this step only [[EPLL]] remains. It would normally be used as an add on to the [[CFOP]] / [[Fridrich method]] when a [[CO]] skip occurs (1/27 solves) but it may also be used as the second step in a 3-look last layer where the first step is [[OCLL]] (orientation of corners).

OLLCP-A is a subset of [[OLLCP]] (OLL + CP, AKA OCPLL) which is the same as CLLEO (CLL + EO, AKA CEOLL). [[OLLCP]] is an advanced [[LL]] method with 331 cases and solves all of the last layer except [[EPLL]] in one look.

==See also==
* [[OLLCP]]. Advanced LL method which both orients the last layer and solves the corners
* [[CFOP]]. Method which solves the last layer using [[OLL]] and [[PLL]]
* [[CFCE]]. Method which solves the last layer using [[CLL]] and [[ELL]]
* [[EPLL]]. Edge Permutation of the Last Layer which follows OLLCP

== External links ==
* [https://docs.google.com/spreadsheet/ccc?key=0Aq2MYrmu606CdFFuallJVFRDQm9FUm44ekoxbDRwQVE#gid=0 Robert Yau's OLLCP]
* [https://sites.google.com/site/piauscubingsite/3x3x3/ollcp/others Antoine Piau's OLLCP]
* [http://sarah.cubing.net/3x3x3/oellcp Sarah Strong's OELLCP]
* AlgDB.Net: [http://algdb.net/Set/OLLCP%2028 OLLCP 28] [http://algdb.net/Set/OLLCP%2057 OLLCP 57] [http://algdb.net/Set/OLLCP%2020 OLLCP 20]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=23005 Thread discussing this method]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?21210-KCLL Some algorithms]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

=OLLCP-A cases=
There are 15 cases, three of them have corners correctly permuted ([[CLL]] skip) and may be solved in one look using [[ELL]], two has got edges oriented and may be solved in one look using [[PLL]] ([[OLL]] skip). Removing those cases it is only 10 left (2 are mirror cases) and of those 4 may be solved using [[J-PLL]] + M setup and one can be solved using [[Y-PLL]] (or [[V-PLL]]) with a M move setup.

== Corners permuted ==
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
===Adjacent flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL PA.jpg]]
|

{{Alg|M U M' U2 M U M'}}
{{Alg|(y2) M' U M U2 M' U M}}
{{Alg|Rw U R' U' M U R U' R'}}
<center>Use [[ELL]] to solve in one look.</center>

|}

|

===Opposite flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL PO.jpg]]
|

{{Alg|(x') M' U' R U M U' R' U (x)}}
{{Alg|(R U R' U') M' (U R U' r')}}
<center>Use [[ELL]] to solve in one look.</center>

|}

|}
{|border="0" width="50%" valign="top" cellpadding="3"
|-valign="top"
|

===4-flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL P4.jpg]]
|

{{Alg|M' U2 M U2 M' U M U2 M' U2 M (U')}}
{{Alg|r U R' U' M2 U R U' R' U' M' (U)}}
<center>Use [[ELL]] to solve in one look.</center>

|}
|}

== Edges oriented ==
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
===Adjacent PLL===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL AO.jpg]]
|

{{Alg|R L U2 R' U' R U2 L' U R' (U')}}
<center>Use [[PLL]] to solve in one look.</center>

|}

|

===Diagonal PLL===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL DO.jpg]]
|

{{Alg|R' U L' U2 R U' L d' L U' R U2 L' U R'}}
<center>Use [[PLL]] to solve in one look.</center>

|}

|}

== Adjacent corners ==
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
===FR-flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL AFR.jpg]]
|
{{Alg|(y) R' F R' F2 L F' L' F2 R2}}
{{Alg|(y' x') (L' U L') U2 (R U' R') U2' L2 (x)}}
{{Alg|r U R' U' r' F R2 U' R' U' R U R' F'}}
|}

|

===RB-flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL ARB.jpg]]
|
{{Alg|(y) L F' L F2 R' F R F2 L2}}
{{Alg|(y' x') (R U' R) U2' (L' U L) U2 R2 (x)}}
{{Alg|(y2) l' U' L U l F' L2 U L U L' U' L F}}
|}

|}

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|

===BL-flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL ABL.jpg]]
|
{{Alg|(x') L2 U2 R U R' U2 L U' r}}
{{Alg|(y2 x) R2 U2 L U L' U2 R U' l}}
|}

|

===LF-flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL ALF.jpg]]
|

{{Alg|(x) L2 U2 R' U' R U2 L' U r'}}
{{Alg|r U R' F' R U R' U' R' F R2 U' r'}}

|}

|}

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|

===FB-flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL AM.jpg]]
|
{{Alg|F R U' R' U R U R2 F' r U R U' r'}}
{{Alg|r U r' F' R U R' U' R' F R r U' r'}}
{{Alg|R U R' F' U' F R2 U' L' U R' U' M' (x')}}
{{Alg|(y) R U R2 U' R' F R F' U F R2 U R' U' F'}}
{{Alg|(y') R' U2 R U2 R' U R U R' F' U' F U' R}}
{{Alg|L U F' U F U L' U L F' U L F L2}}
{{Alg|(y) R U2 r U R' U' r' U F R F' U R'}}
{{Alg|(y) R2 U R2 B L F' U2 F L' B' U' R2}}

|}

|

===RL-flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL AS.jpg]]
|
{{Alg|(x') R2 U' R' U l' F' U' F R U R'}}
{{Alg|(y) R U' R' F' U F l U' R U R2 (x)}}
|}

|}
{|border="0" width="50%" valign="top" cellpadding="3"
|-valign="top"
|

===4-flip (adjacent)===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL A4.jpg]]
|
{{Alg|F R' F R2 U R' U' F2 U' r U' r' F}}
{{Alg|(y') M' U L2 B2 L U R' U2 L U' M R}}
{{Alg|(y2) R2 (y) M' U M (y') l U' R U2 L' U L U2 (x)}}
{{Alg|L2 (y') M' U' M (y) r' U L' U2 R U' R' U2 (x)}}
|}
|}

== Diagonal corners ==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|

===Adjacent flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL DFR.jpg]]
|
{{Alg|(y) R b' R2 U' R D' R2 D R' U R2 b R'}}
{{Alg|(y2) S R2 D R' U R D' R2 d' l' U' L}}
|}
|

===Opposite flip===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL DM.jpg]]
|
{{Alg|(y) R' U L' U2 R U' (x') U L' U2 R U' L U2 M'}}
{{Alg|L' U l d R2 D R' U' R D' R2 S'}}
{{Alg|(y) R' F' U2 F U' R U R2 F R F' U2 R}}
{{Alg|R U' R2' F R F' R d' R U2 R' F'}}
|}
|}

{|border="0" width="50%" valign="top" cellpadding="3"
|-valign="top"
|

===4-flip (diagonal)===
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
[[File:CPEOLL D4.jpg]]
|

{{Alg|R F' U2 R2 F' R F2 R' F R2 U2 F R'}}
{{Alg|R2 U2 M F2 U' R2 U2 F2 U R2 U2 F2 M'}}
{{Alg|x (U R' D' R2 U2' D B2) (U' R' D' R U' R' U' R2 D) x'}}
{{Alg|R' U2 R' F2 R U R U' R' U R' F' R U' F2 U2 R}}
{{Alg|R' U2 F2 U R' F R U' R U R' U' R' F2 R U2 R}}

|}
|}

[[Category:Experimental methods]]
[[Category:3x3x3 methods]]

__NOTOC__

OLLCP

2016-11-27T18:01:08Z

Logiqx:

''This page is about the OLLCP [[method substep]]. For the [[alg]]s, see [[OLLCP (few algs)]].''

{{Substep Infobox
|name=OLLCP
|image=OLLCP.png
|proposers=Various
|year=
|anames=[[CLLEO]], [[CEOLL]], [[OCPLL]]
|variants=[[CLLEF]]
|subgroup=
|algs=331
|moves=~11
|purpose=
* [[Speedsolving]]
|previous=[[F2L cube state]]
|next=[[LL:EO+CO+CP cube state]]
}}

'''Orientation of Last Layer and Corner Permutation'''
'''OLLCP''' is an [[experimental method|experimental]] [[LL]] method which both [[OLL|orients the last layer]] and [[CLL|solves the corners]]. Thus after this step only [[EPLL]] remains. The price to get there however is a high algorithm count (300+). Only a very few number of people use the full set, but a number of people use the subsets [[COLL]] and [[CLLEF]]. Several people came up with the idea, some of them after they wanted to re-learn some OLL algorithms and noticed the new algorithms had a different effect on the corners. By 'recycling' the old OLL algorithms it is sometimes very easy and fast to be able to avoid an N perm and get higher chances of PLL-skips. Because some OLLCP algorithms are really slow and because of the high number of algorithms, it is advisable to only learn the nice and fast algorithms. A slow OLLCP plus a U perm is probably slower than a fast 'normal' OLL algorithm leaving any other PLL.

== See also ==
* [[OLLCP (few algs)]]
* [[OLLCP-A]]. The subset in which all corners are already oriented.
* [[COLL]]. The subset in which all edges are already oriented.
* [[CLLEF]]. The subset in which none of the edges are already oriented.
* [[CxLL]]. Various subsets which solve the Corners of the Last Layer
* [[EPLL]]. Edge Permutation of the Last Layer which follows OLLCP

== External links ==
* [https://docs.google.com/spreadsheet/ccc?key=0Aq2MYrmu606CdFFuallJVFRDQm9FUm44ekoxbDRwQVE#gid=0 Robert Yau's OLLCP]
* [https://sites.google.com/site/piauscubingsite/3x3x3/ollcp/others Antoine Piau's OLLCP (COLL and CLLEF on another page)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=23222 SuneOLL] Proposed system to solve all cases where the corners are already permuted
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?31506-OLLCP-(hax) Kirjava's OLLCP (hax)] List of all cases.
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:Experimental methods]]
[[Category:3x3x3 last layer substeps]]

2-Look PLL

2016-10-25T19:19:13Z

Logiqx:

This PLL system is used to permute the last layer after orientation. Of the 21 cases, only 7 are needed for '''2-Look PLL''' (commonly abbreviated as '''2LPLL'''). Permutation is broken into 2 steps: corner permutation (two cases), and edge permutation (four cases).

* Step 1: '''Permutation of Corners'''. Requires 2 algorithms , to carry out:
*# adjacent corner swap (any of [[PLL#T Permutation|T-perm]], [[PLL#A Permutation : a|A-perm]], [[PLL#F Permutation|F-perm]], [[PLL#G Permutation : a|G-perm]], [[PLL#J Permutation : a|J-perm]]...)
*# diagonal corner swap (any of [[PLL#Y Permutation|Y-Perm]], [[PLL#V Permutation|V-Perm]], [[PLL#E Permutation|E-Perm]], [[PLL#N Permutation : a|N-Perm]])

* Step 2: '''Permutation of Edges'''. Uses 4 algorithms (3 excluding mirrors):
*# clockwise 3-edge cycle ([[PLL#U Permutation : a|U-perm a]])
*# anticlockwise 3-edge cycle ([[PLL#U Permutation : b|U-perm b]])
*# opposite edges swap ([[PLL#H Permutation|H-Perm]])
*# adjacent edges swap ([[PLL#Z Permutation|Z-Perm]])

== See also ==
* [[PLL]]
* [[2-Look OLL]]
* [[4LLL]]
* [[Last Layer]]

== External links ==
* [http://www.youtube.com/watch?v=S61q3FYVFis Badmephisto's 2-look PLL guide]

[[Category:3x3x3 methods]]

2-Look OLL

2016-10-25T19:15:13Z

Logiqx:

This [[OLL|OLL system]] is used to [[orient]] all the pieces on the [[last layer]] as described in the [[CFOP method]], you do not need to know all [[OLL#OLL_Algorithms|57 OLLs]] to use '''2-look OLL''' (commonly abbreviated as '''2LOLL'''), rather the system is divided up. By first orienting the edges (three cases), then orienting the corners (7 cases), orientation of all pieces on the last layer is completed.

* Step 1: [[EOLL|'''Orientation of Edges''' (EOLL-IgnoreC)]] . This requires the use of one of 3 algorithms:
*# to [[OLL#OLL 44|flip adjacent edges]]
*# to [[OLL#OLL 45|flip opposite edges]]
*# to [[OLL#No edges flipped correctly|flip all four edges]]
* Step 2: [[OCLL|'''Orientation of Corners''' (OCLL)]] . Requires the use of 7 algorithms (6 excluding mirrors), to solve the following OLL cases:
*# [[OLL#OLL 24|T]]
*# [[OLL#OLL 25|Bowtie]]
*# [[OLL#OLL 23|Headlights]]
*# [[OLL#OLL 27|Sune]]
*# [[OLL#OLL 26|Anti-Sune]]
*# [[OLL#OLL 21|H]]
*# [[OLL#OLL 22|Pi]]

If you select EO algorithms that preserve corners, it is also possible to combine the two looks into a single look (but still using two algs). This idea is known as [http://cube.garron.us/algs/compOLL/ Compound OLL].

[[CO Only|'''Orientation of Corners''' (CO Only)]] and then [[OLL#All_Corners_Oriented|'''Orientation of Edges''' (AKA OELL, OLL-E or OLL-ACO)]] is also 2LOLL, but this is less used.

== See also ==
* [[OLL]]
* [[2-Look PLL]]
* [[4LLL]]
* [[3LLL]]
* [[Last Layer]]

[[Category:3x3x3 methods]]

2-Look OLL

2016-10-25T19:12:04Z

Logiqx:

This [[OLL|OLL system]] is used to [[orient]] all the pieces on the [[last layer]] as described in the [[CFOP method]], you do not need to know all [[OLL#OLL_Algorithms|57 OLLs]] to use '''2-look OLL''' (commonly abbreviated as '''2LOLL''', rather the system is divided up. By first orienting the edges (three cases), then orienting the corners (7 cases), orientation of all pieces on the last layer is completed.

* Step 1: [[EOLL|'''Orientation of Edges''' (EOLL-IgnoreC)]] . This requires the use of one of 3 algorithms:
*# to [[OLL#OLL 44|flip adjacent edges]]
*# to [[OLL#OLL 45|flip opposite edges]]
*# to [[OLL#No edges flipped correctly|flip all four edges]]
* Step 2: [[OCLL|'''Orientation of Corners''' (OCLL)]] . Requires the use of 7 algorithms (6 excluding mirrors), to solve the following OLL cases:
*# [[OLL#OLL 24|T]]
*# [[OLL#OLL 25|Bowtie]]
*# [[OLL#OLL 23|Headlights]]
*# [[OLL#OLL 27|Sune]]
*# [[OLL#OLL 26|Anti-Sune]]
*# [[OLL#OLL 21|H]]
*# [[OLL#OLL 22|Pi]]

If you select EO algorithms that preserve corners, it is also possible to combine the two looks into a single look (but still using two algs). This idea is known as [http://cube.garron.us/algs/compOLL/ Compound OLL].

[[CO Only|'''Orientation of Corners''' (CO Only)]] and then [[OLL#All_Corners_Oriented|'''Orientation of Edges''' (AKA OELL, OLL-E or OLL-ACO)]] is also 2LOLL, but this is less used.

== See also ==
* [[OLL]]
* [[2-Look PLL]]
* [[4LLL]]
* [[3LLL]]
* [[Last Layer]]

[[Category:3x3x3 methods]]

2LPLL

2016-10-25T19:03:26Z

Logiqx: Redirected page to 2-Look PLL

#REDIRECT [[2-Look PLL]]

2LOLL

2016-10-25T18:57:01Z

Logiqx: Logiqx moved page 2L-OLL to 2LOLL

#REDIRECT [[2-Look OLL]]

OLL cube state

2016-10-25T18:54:41Z

Logiqx:

{{Cube state Infobox
|name=OLL
|image={{CubeImage
|grey|grey|grey
|blue|blue|blue
|blue|blue|blue
|grey|orange|orange|white|white|white|red|red|grey
|grey|orange|orange|white|white|white|red|red|grey
|grey|orange|orange|white|white|white|red|red|grey
|green|green|green
|green|green|green
|grey|grey|grey
|yellow|yellow|yellow
|yellow|yellow|yellow
|yellow|yellow|yellow
}}
|anames=[[OLL done]], [[LL:EO+CO cube state]], [[LL:CO+EO cube state]],
|subgroup=
|esubgroup=
|csubgroup=
|previous=
* [[OLL]] ([[CFOP]])
* [[SuneOLL]]
* [[2-Look OLL]]
* [[Compound OLL]]
* [[SVOLL]]
* [[22LL (x2)]]
* Many others
|next=
* [[PLL]] ([[CFOP]])
* Many others
|previoussteps=[[OLL cube state#Previous_Steps|Steps before the OLL cube step]] (as [[OLL|the OLL step]])
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state#Previous_Steps | Steps before the OLL cube step (as the OLL) ]]
|nextsteps=[[OLL cube state#Next_Steps|Steps after OLL]] (as [[PLL]])
|nextimage=[[Image:PLLinfo.jpg|120px|right|link=OLL cube state#Next_Steps | Steps after OLL (as PLL) ]]
}}

The '''OLL cube state''' is the [[cube state]] with an '''Oriented Last Layer'''.

==Previous Steps==

[[Image:OLLinfo.png|120px|link=OLL]] * A previous state of this one is the [[F2L cube state]]. Use the [[OLL|OLL step]] to have the '''OLL cube state''', as in the [[CFOP|CFOP method]].

[[Image:OLLinfo.png|120px|link=SuneOLL]] * A previous state of this one is the [[F2L cube state]]. Use the [[SuneOLL]] step to have the '''OLL cube state'''.

[[Image:OLLinfo.png|120px|link=2-Look OLL]] * A previous state of this one is the [[F2L cube state]]. Use the [[2-Look OLL]] step to have the '''OLL cube state'''.

[[Image:OLLinfo.png|120px|link=SVOLL]] * A previous state of this one is the [[F2L cube state]]. Use the [[SVOLL]] step to have the '''OLL cube state'''.

[[Image:OLLinfo.png|120px|link=22LL (x2)]] * A previous state of this one is the [[F2L cube state]]. Use the [[22LL (x2)]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1E + EO cube state]]. Use the [[BLE]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1E + EO cube state]]. Use the [[JJLS 22 F2L E + CO]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[EOline + EE + CO cube state]]. Use the [[F2L ZZ hta]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 + pair cube state]]. Use the [[MW]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 + pair cube state]]. Use the [[RLS]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 + pair cube state]]. Use the [[VLS]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 + pair (RU'R') cube state]]. Use the [[HLS]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 + pair (RU'R') + EO cube state]]. Use the [[Summer Variation]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 + pair + EO cube state]]. Use the [[Winter Variation]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 + pair + EO cube state]]. Use the [[ZZ-WV]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1C + EO cube state]] (or [[F2L-1 + EO (y on U) cube state]]). Use the [[CLS]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1C + EO cube state]] (or [[F2L-1 + EO (y on U) cube state]]). Use the [[ZZ-C]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1CO cube state]]. Use the [[EJF2L]] step to have the '''OLL cube state''', as in the [[EJF2L method]].

* A previous state of this one is the [[F2L-1CO cube state]]. Use the [[I, Im, OCLL]] step to have the '''OLL cube state''', as in the [[PetRock method]].

* A previous state of this one is the [[Oriented + Belt cube state]]. Use the [[1x2x3 on D to 1x3x3 on D]] step to have the '''OLL cube state''', as in the [[LCBM method]].

* A previous state of this one is the [[F2L-1 + pair + EO cube state]]. Use the [[Winter Varition]] step to have the '''OLL cube state'''.

[[Image:ZBLL.png|120px|link=CO Ignore perm]] * A previous state of this one is the [[LL:EO cube state]]. Use the [[CO Ignore perm]] step to have the '''OLL cube state'''.

[[Image:ZBLL.png|120px|link=OCLL]] * A previous state of this one is the [[LL:EO cube state]]. Use the [[OCLL]] (also called [[OLL-C]]) step to have the '''OLL cube state'''.

[[Image:ZBLL.png|120px|link=Compound OLL-E]] * A previous state of this one is the [[LL:EO cube state]]. Use the [[Compound OLL-E]] step to have the '''OLL cube state''', as in the [[XG Method]].

[[Image:ZBLL.png|120px|link=OL4C]] * A previous state of this one is the [[LL:EO cube state]]. Use the [[OL4C]] (also called [[OLC]]) step to have the '''OLL cube state'''.

[[Image:ZBLL.png|120px|link=OCLL-EPP]] * A previous state of this one is the [[LL:EO cube state]]. Use the [[OCLL-EPP]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[BarOLL cube state]]. Use the [[OCLL (BarOLL subs)]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[U/D Oriented & Separated + Belt cube state (no parity)]]. Use the [[PUL]] step to have the '''OLL cube state''', as in the [[ZZ-1]] method.

* A previous state of this one is the [[W/Y Separated + EE + DB + DF cube state]]. Use the [[+F2L Oriented]] step to have the '''OLL cube state''', as in the [[Nielsson]] Method.

* A previous state of this one is the [[Oriented no E edg on D cube state]]. Use the [[F2L from O no EE on D (ZZ like)]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[PLL w/Parity on E cube state]]. Use the [[E edg parity fix]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[Pairs No Cross + CO cube state]]. Use the [[F2L + EO from PNC+CO]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[2x2x1 Blocks + CO + 2EP + Ortega CO cube state]]. Use the [[EO BCE Kenneth]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L - Edg on D + CO cube state]]. Use the [[ESO]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L - Edg on D + CO cube state]]. Use the [[ESO]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[LL:CO cube state]]. Use the [[E flip]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[LL:CO cube state]]. Use the [[Compound OLL-E]] step to have the '''OLL cube state''', as in the [[XG Method]].

* A previous state of this one is the [[LL:CO cube state]]. Use the [[OELL]] (also called [[OLL-E]]) step to have the '''OLL cube state'''.

* A previous state of this one is the [[LL:CO cube state]]. Use the [[EOLL]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1E(D) + EO + CO cube state]]. Use the [[+RD]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1E(D) + CO cube state]]. Use the [[MZRG DougLi]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1E(D) + CO cube state]]. Use the [[Keyhole EO]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1E(D) + CO cube state]]. Use the [[L5EOP]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1E(D) + CO cube state]]. Use the [[EOLL+DF]] step to have the '''OLL cube state''', as in the [[3CFCEP]] method.

* A previous state of this one is the [[F2L-1E(E) + CO cube state]]. Use the [[ZBLBL]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-2+1E flipped cube state]]. Use the [[OLS-FE]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1+N/O Pair+2-4EO cube state]]. Use the [[SV (Skyler Variation)]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 cube state]]. Use one of the 8042 [[Full OLS]] algs, depending of the case to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 cube state]]. Use the [[OPF2L (If LL O)]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 cube state]]. Use the [[Pair SV setup + COLS]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1 cube state]]. Use the [[ZBCOLS]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[F2L-1E (D) + EO cube state]]. Use the [[ELLC]] step to have the '''OLL cube state''', as in the [[JTLE]] method.

* A previous state of this one is the [[Solvable with coupled R-R', U, Uw cube state]]. Use the [[Finish F2L(elrog OddF2L_EO)]] step to have the '''OLL cube state'''.

* A previous state of this one is the [[1x2x3 + OffBelt + Oriented D and U cube state]]. Use the [[F2L from 1x2x3 + OB + OU + OD]] step to have the '''OLL cube state'''.

==Next Steps==

[[Image:Mini_maru.jpg|120px|link=PLL]] * Use the [[PLL|PLL step]] to have the [[Solved cube state]], as in the [[CFOP|CFOP method]].

[[Image:Mini_maru.jpg|120px|link=2-lookPLL]] * Use the [[2-look PLL]] step to have the [[Solved cube state]].

[[Image:Mini_maru.jpg|120px|link=PDL]] * Use the [[PDL]] step to have the [[Solved cube state]], as in [[ZZ-1 last]] method.

* Use the [[EPLL]] step to have the [[LL:EO+EP+CO cube state]].

* Use the [[U-perm*]] step to have the [[LL:EO+EP+CO cube state]].

* Use the [[CPLL]] step to have the [[LL:EO+CO+CP cube state]].

* Use the [[CPLL XG]] step to have the [[LL:EO+CO+CP cube state]].

* Use the [[T-perm*]] step to have the [[LL:EO+CO+CP cube state]].

* Use the [[A-perm*]] step to have the [[LL:EO+CO+CP cube state]].

* Use the [[Cubois CP]] step to have the [[LL:EO+CO+CP cube state]].

[[Category:3x3x3 cube states]]

F2L cube state

2016-10-25T18:54:09Z

Logiqx:

{{Cube state Infobox
|name=F2L
|image={{CubeImage
|grey|grey|grey
|blue|blue|blue
|blue|blue|blue
|grey|orange|orange|white|white|white|red|red|grey
|grey|orange|orange|white|white|white|red|red|grey
|grey|orange|orange|white|white|white|red|red|grey
|green|green|green
|green|green|green
|grey|grey|grey
|grey|grey|grey
|grey|yellow|grey
|grey|grey|grey
}}
|anames=First 2 Layers
|subgroup=
|esubgroup=
|csubgroup=
|previous=
* [[F2L]] ([[CFOP]])
* [[Last F2L Slot]] ([[CFOP]])
* [[2GLS]]
* [[1st Layer-1C:4E keyhole]]
* [[Multislotting]]
* [[Freeslice F2L]]
* [[F2L-1E:1E]]
* [[F2L-1C:F2L keyhole alg]]
* [[F2L-1E (D):L5EOP (pcms-var2)]]
* [[1st Layer:8355 algs]]
* [[1st Layer:Edges XG]]
* [[1st Layer:Niklas w/M]]
* [[1st Layer:std LBL edges]]
* [[Pairs No Cross:D-Edg (pcms var)]]
* [[Pairs No Cross:Salvia edg]]
* [[Pairs No Cross:Ins Cross (CAP)]]
* [[Roux Blocks:DF+DB]]
* [[Roux-cfop Hybrid]]
|next=
* [[OLL]] ([[CFOP]])
* [[BLL#The_beginner_method|Beginner BLL]] (Any [[LBL|Layer By Layer method]])
* [[BLL#The_4LLL_method|4LLL BLL]] (Any [[LBL|Layer By Layer method]])
* [[BLL#The_3LLL_method|3LLL BLL]] (Any [[LBL|Layer By Layer method]])
* [[BLL#The_2LLL_method|2LLL BLL]] (Any [[LBL|Layer By Layer method]])
* [[SuneOLL]]
* [[2-Look OLL]]
* [[Compound OLL]]
* [[SVOLL]]
* [[22LL (x2)]]
* [[1LLL (full)]]
* [[2LL Tempus 18algs]]
* [[2LL Kirjava 30algs]]
* [[F2L:EO (Ignore C)]]
* [[EOLL]]
* [[OELL (OLL-E)]]
* [[ELL]]
* [[LLEF]]
* [[PLLEF]]
* [[F2L:Niklas w/M]]
* [[F2L:EP]] ([[Randelshofer]])
* [[CLLEF]]
* [[OLLCP]]
* [[CPEOLL]]
* [[F2L:CP+EO]]
* [[F2L:CO(OLL subset)]]
* [[F2L:CO(CxLL subset)]]
* [[OCLL]]
* [[F2L:CO Only]]
* [[2LCMLL 1st look (M free subs)]]
* [[COLL]]
* [[CLL (3x3x3)]]
* [[CxLL]]
* [[2-Look CLL]]
* [[CP (CxLL subset)]]
* [[Dedmore Helm]]
* [[F2L:CP only Niklas*]]
* [[Intuit COMM (by Roux)]]
|previousimage=[[Image:F2Linfo.png|120px|left|link=F2L_cube_state#Previous_Steps|Steps before a F2L cube state]]
|previoussteps=[[F2L_cube_state#Previous_Steps|Steps before a F2L cube state]]
|nextimage=[[Image:OLLinfo.png|120px|right|link=F2L_cube_state#Next_Steps|Steps after a F2L cube state]]
|nextsteps=[[F2L_cube_state#Next_Steps|Steps after a F2L cube state]] (as the [[OLL|OLL step]])
}}

==Previous Steps==

[[Image:Cross.png|120px|link=F2L]] * A previous state of this one is the [[Cross cube state]]. Use the [[F2L|F2L step]] to have the '''F2L cube state''', as in the [[CFOP|CFOP method]].

* A previous state of this one is the [[F2L-1 cube state]]. Use the [[Last F2L Slot]] step to have the '''F2L cube state''', as in the [[CFOP|CFOP method]].

* A previous state of this one is the [[F2L-1 cube state]]. Use the [[2GLS]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[1st Layer-1C cube state]]. Use the [[4E c keyhole]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[1st Layer-1C cube state]]. Use the [[Multi keyhole]] step to have the '''F2L cube state'''.

[[Image:Cross.png|120px|link=multislotting]] * A previous state of this one is the [[Cross cube state]]. Use the [[multislotting]] step to have the '''F2L cube state'''.

[[Image:Cross.png|120px|link=Freeslice F2L]] * A previous state of this one is the [[Cross cube state]]. Use the [[Freeslice F2L]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[F2L-1E(E) cube state]]. Use the [[+1E(E) from F2L-1E(E)]] step to have the '''F2L cube state''', as in the [[LBL std]] method.

* A previous state of this one is the [[F2L-1C cube state]]. Use the [[F2L keyhole alg]] to have the '''F2L cube state'''.

* A previous state of this one is the [[F2L-1E(D) cube state]]. Use the [[L5EOP]] step to have the '''F2L cube state''', as in the [[pcms-var2]] method.

[[Image:Layer by layer.gif|120px|link=8355 algs]] * A previous state of this one is the [[1st Layer cube state]]. Use the [[8355 algs]] to have the '''F2L cube state'''.

[[Image:Layer by layer.gif|120px|link=Niklas w/M]] * A previous state of this one is the [[1st Layer cube state]]. Use the [[Niklas w/M]] to have the '''F2L cube state'''.

[[Image:Layer by layer.gif|120px|link=Edges XG]] * A previous state of this one is the [[1st Layer cube state]]. Use the [[Edges XG]] step to have the '''F2L cube state'''.

[[Image:Layer by layer.gif|120px|link=std LBL edges]] * A previous state of this one is the [[1st Layer cube state]]. Use the [[std LBL edges]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[Pair No Cross cube state]]. Use the [[D-Edg]] step to have the '''F2L cube state''', as in the [[pcms var]] method.

* A previous state of this one is the [[Pair No Cross cube state]]. Use the [[Salvia edg]] step to have the '''F2L cube state''', as in the [[Salvia]] method.

* A previous state of this one is the [[Pair No Cross cube state]]. Use the [[Ins Cross]] step to have the '''F2L cube state''', as in the [[CAP]] method.

* A previous state of this one is the [[Roux Blocks cube state]]. Use the [[DF+DB]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[Roux Blocks cube state]]. Use the [[Roux-cfop Hybrid]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[Cross + D CP cube state]]. Use the [[TF2L]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[F2L-3 cube state]] (also called [[Xcross cube state]]). Use the [[3C+3EEdg from F2L-3]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[F2L-3 cube state]] (also called [[Xcross cube state]]). Use the [[3E c keyhole]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[F2L-3 cube state]] (also called [[Xcross cube state]]). Use the [[X-CELL]] step to have the '''F2L cube state'''.

[[Image:EOLine CubeState Info.gif|120px|link=ZZ -top]] * A previous state of this one is the [[EOline cube state]]. Use the [[ZZ -top]] step to have the '''F2L cube state'''.

* A previous state of this one is the [[Unoriented F2L cube state]]. Use the [[OF2L (McM)]] step to have the '''F2L cube state'''.

==Next Steps==

[[Image:OLLinfo.png|120px|link=OLL]] * Use [[OLL|the OLL step]] to have the [[OLL cube state]], as in the [[CFOP|CFOP method]].
* Use [[BLL#The_beginner_method|the BLL Beginner EO step]] to have [[LL:EO cube state]].
* Use [[BLL#The_4LLL_method|the BLL EO step]] to have [[LL:EO cube state]].
* Use [[BLL#The_3LLL_method|the BLL Edges step]] to have [[LL:EO+EP cube state]].
* Use the [[SuneOLL]] step to have the [[OLL cube state]].
* Use the [[2-Look OLL]] step to have the [[OLL cube state]].
* Use the [[Compound OLL]] step to have the [[OLL cube state]].
* Use the [[SVOLL]] step to have the [[OLL cube state]].
* Use the [[22LL (x2)]] step to have the [[OLL cube state]].
* Use the [[1LLL (full)]] step to have the [[Solved cube state]].
* Use the [[2LL Tempus 18algs]] step to have the [[Solved cube state]].
* Use the [[2LL Kirjava 30algs]] step to have the [[Solved cube state]].
* Use the [[BLL#The_beginner_method|Beginner BLL]] step to have the [[Solved cube state]].
* Use the [[BLL#The_4LLL_method|4LLL-BLL]] step to have the [[Solved cube state]].
* Use the [[BLL#The_3LLL_method|3LLL-BLL]] step to have the [[Solved cube state]].
* Use the [[BLL#The_2LLL_method|2LLL-BLL]] step to have the [[Solved cube state]].
* Use [[Last Layer methods|any LL method]] to have the [[Solved cube state]].
* Use the [[F2L:EO (Ignore C)]] step to have [[LL:EO cube state]].
* Use the [[EOLL]] step to have [[LL:EO cube state]].
* Use the [[OELL (OLL-E)]] step to have [[LL:EO cube state]].
* [[ELL]] step to have [[LL:EO+EP cube state]].
* [[LLEF]] step to have [[LL:EO+EP cube state]].
* [[PLLEF]] step to have [[LL:EO+EP cube state]].
* [[F2L:Niklas w/M]] step to have [[LL:EO+EP cube state]].
* [[F2L:EP]] ([[Randelshofer]])
* [[CLLEF]]
* [[OLLCP]]
* [[CPEOLL]]
* [[F2L:CP+EO]]
* [[F2L:CO(OLL subset)]]
* [[F2L:CO(CxLL subset)]]
* [[OCLL]]
* [[F2L:CO Only]]
* [[2LCMLL 1st look (M free subs)]]
* [[COLL]]
* [[CLL (3x3x3)]]
* [[CxLL]]
* [[2-Look CLL]]
* [[CP (CxLL subset)]]
* [[Dedmore Helm]]
* [[F2L:CP only Niklas*]]
* [[Intuit COMM (by Roux)]]

[[Category:3x3x3 cube states]]

2-Look OLL

2016-10-25T18:48:48Z

Logiqx:

This [[OLL|OLL system]] is used to [[orient]] all the pieces on the [[last layer]] as described in the [[CFOP method]], you do not need to know all [[OLL#OLL_Algorithms|57 OLLs]] to use '''2-look OLL''' (commonly abbreviated as '''2LOLL''', rather the system is divided up. By first orienting the edges (three cases), then orienting the corners (7 cases), orientation of all pieces on the last layer is completed.

* Step 1: [[EOLL|'''Orientation of Edges''' (EOLL-IgnoreC)]] . This requires the use of one of 3 algorithms:
*# to [[OLL#OLL 44|flip adjacent edges]]
*# to [[OLL#OLL 45|flip opposite edges]]
*# to [[OLL#No edges flipped correctly|flip all four edges]]
* Step 2: [[OCLL|'''Orientation of Corners''' (OCLL)]] . Requires the use of 7 algorithms (6 excluding mirrors), to solve the following OLL cases:
*# [[OLL#OLL 24|T]]
*# [[OLL#OLL 25|Bowtie]]
*# [[OLL#OLL 23|Headlights]]
*# [[OLL#OLL 27|Sune]]
*# [[OLL#OLL 26|Anti-Sune]]
*# [[OLL#OLL 21|H]]
*# [[OLL#OLL 22|Pi]]

If you select EO algorithms that preserve corners, it is also possible to combine the two looks into a single look (but still using two algs). This idea is known as [http://cube.garron.us/algs/compOLL/ Compound OLL].

[[CO Only|'''Orientation of Corners''' (CO Only)]] and then [[OLL#All_Corners_Oriented|'''Orientation of Edges''' (AKA OELL, AKAOLL-E or OLL-ACO)]] is also 2L-OLL, but this is less used.

== See also ==
* [[OLL]]
* [[2-Look PLL]]
* [[4LLL]]
* [[3LLL]]
* [[Last Layer]]

[[Category:3x3x3 methods]]

Commutators and Conjugates

2016-10-13T10:11:31Z

Logiqx: /* Nested conjugate and commutator */

'''Commutators''' and '''conjugates''' are a way of building sequences of moves. They refer to mathematical terms of group theory and have many applications in twisty puzzles, so that many puzzle solutions are heavily or fully based on commutators.

In intuitive terms, we can define them like this:
* [[conjugate]]s: do something to set up another task which does something useful, and undo the setup (A B A').
* [[commutator]]s: do something twice (the second time backwards) so that it gets almost completely canceled, allowing to modify specific portions of a cube (A B A' B').

Where A and B can by any sequence of moves.

== Short notation ==
* [A, B] is a commonly used notation to represent the [[commutator]] A B A' B'.
* [A: B] is commonly used to represent the [[conjugate]] A B A'.

== Nested conjugate and commutator ==

The sequences used in a commutator can be conjugates, thus giving commutators of conjugates. For example, [[R: U], D] = (R U R') D (R U' R') D'

Conversely, the sequence embedded in a conjugate can be commutator, thus giving a conjugate of commutators. For examples, [F: [U, R]] = F (U R U' R') F'

== See also ==
* [[Commutator]]
* [[Conjugate]]
* [[Niklas]]
* [[Fewest Moves techniques]]
* [[BH]]
* [[Intuitive solving]]

== External links ==
* [http://www.ryanheise.com/cube/commutators.html RyanHeise.com] has a page on commutators. Also notice all kinds of other useful sections on his website on the left. He has a lot of group theory related content, and other things that will really help you understand how algorithms work, and how you can create your own.
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=169 Post from Speedsolving] on Commutators

=== Videos ===
* [https://www.youtube.com/watch?v=kv9qD1sbWRE Invent Your Own Algorithms...Good News: It's Not Magic!]
* [http://www.youtube.com/watch?v=w6S6llvs-_o Build your own algorithms with commutators]
* [http://www.youtube.com/watch?v=54SGrZbLcoE Commutators and Conjugates - The Ultimate Instructional Video]
* [http://ca.youtube.com/watch?v=7yZoDi_B1lI Rubik's Cube Theory: Commutators] by badmephisto

[[Category:Puzzle theory]]

Fastest Videos for each Method

2016-10-11T23:19:03Z

Logiqx: Felix Average of 12 (5.85)

This page contains the fastest videos for each of the "big four" [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (3.85) by [[Feliks Zemdegs]]: https://youtu.be/GE8cN1Cg3ms

Average of 5 (5.51) by [[Feliks Zemdegs]]: https://youtu.be/VEgnIs5wns8

Average of 12 (5.85) by [[Feliks Zemdegs]]: https://youtu.be/nkHeTAIko5I

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by [[Alexander Lau]]: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by [[Alexander Lau]]: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (5.91) by [[Hyeon Kyo Kyoung]]: https://youtube.com/watch?v=vepKXCohxAw

Average of 5 (7.98) by [[Hyeon Kyo Kyoung]]: http://www.youtube.com/watch?v=wVfI5w_wm34

Average of 12 (8.32) by [[Hyeon Kyo Kyoung]]: http://www.youtube.com/watch?v=wVfI5w_wm34

'''[[Petrus]]'''

Single: (6.91) by [[Tao Yu]]: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (8.94) by [[Tao Yu]]: https://www.youtube.com/watch?v=5PamrwHCfzU

Average of 12 (9.79) by [[Tao Yu]]: https://www.youtube.com/watch?v=g1YlueVry4c

ZBLL

2016-10-06T12:26:09Z

Logiqx: /* External links */

{{Substep Infobox
|name=ZBLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Lars Petrus]]
|year=2002
|anames=[[ZZ-a]], Steps 5+6+7 ([[Petrus method]])
|variants=[[NMLL]]
|subgroup=
|algs=493
|moves=12.08 (Optimal [[HTM]])
|purpose=
* [[Speedsolving]], [[FMC]]
|previous=[[LL:EO cube state]]
|next=[[Solved cube state]]
}}

'''ZBLL''' (short for ''[[Zbigniew Zborowski|Zborowski]]-[[Ron van Bruchem|Bruchem]] Last Layer'') is a step of a method which involves solving the entire [[last layer]] in one step, assuming that the [[edge]]s are already oriented. This is part of the [[ZB method]], but it can be useful for any other method which leaves the edges of the last layer oriented after F2L is solved (such as the [[Petrus method]], or [[ZZ Method]]).

ZBLL indeed sounds like a very useful step to learn, but the main reason that it is not in wide use is that it involves a massive 177 algorithms (counting inverses and mirrors are the same), or a total of 493 cases (including PLL). Only a handful of people have ever learned this step in its entirety. If you wish to learn it, it is useful to start by learning either [[OCLL]]/[[PLL]] or [[COLL]]/[[EPLL]], so that you will always be able to finish the cube relatively quickly even if you do not yet know the ZBLL case.

==Learning Approach==

The ZBLL cases are divided into 7 sets: T, U, L, Pi, Sune, Anti-sune, H, and the Pll cases, in which all pieces are oriented. The sets are then divided further into 6 subsets. They are recognized by their [[COLL]] case as well as a corresponding edge cycle. Every subset contains 12 cases, which are all different edge cycles possible with the COLL case of that set. Many people recognize ZBLL by looking at the UFR corner and its neighboring stickers. Whether the stickers are adjacent, or opposite allows for a quick recognition. However, this method only works for the T, U and L subsets of ZBLL, because in the other cases the UFR corner is not correctly oriented. Another way to recognize is through blocks of colour or simply the edge cycle.

==Edge recognition==

For the T, U and L cases (there are 3*6*12=216 algorithms in this set) recognition goes as follows:

1. Recognize the orientation case.

2. Recognize the [[COLL]] case.

3. Recognize the edge cycle by looking at the UFR corner and the edge stickers around it.

4. Apply the corresponding algorithm.

Step 3 may look a little complicated, but it's actually not too bad. In total there are 12 cases, but those are recognized by 2 minor sub-cases, of which there are 3:

C: If the FU sticker is the same as the FRU sticker, and if the RU sticker is the same as the RUF sticker.

A: If the FU sticker is an adjacent color to the FRU sticker, and if the RU sticker is an adjacent color to the RUF sticker.

O: If FU and FRU are opposite, and if RU and RUF are opposite.

A case is recognized by the combination of those. First comes the FU/FRU relation, then the RU/RUF relation, divided by a slash. That means there are 9 possibilities with these cases: C/C, C/A, C/O, A/C, A/A, A/O, O/C, O/A, O/O. However, there are 12 cases. That's because the A case can mean 2 stickers. That's why the last 3 cases are known as C/OX, O/CX and OppX. This means that you don't look for the relation between FU/FRU and RU/RUF, but between FU/RUF and RU/FRU. In the C/OX case, FU and RUF are the same, and RU and FRU are opposite to each other. The same goes for the O/CX case, but vice versa. In the OppX case, both FU/RUF and RU/FRU are opposite. This looks like a Z-permutation. Note that all of these cases can be seen as A/A cases at first, but whenever you have an A/A case, you should always look if it isn't the other one.

== See also ==

* [[ZB Method]]
* [[ZBLS]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[H ZBLL]] (Algorithms)
* [[ZBLD]]
* [[OPLL]]

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/threads/bindedsas-algorithms.55518/ BindeDSA's Algorithms] - complete (2H and OH)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=18172 Happy New Year! Also, ZBLL Algorithms] - complete
* [http://www.ai.univ-paris8.fr/~bh/cube/solutions_567.html Bernhard Helmstetter's ZBLL algs] - complete, but excludes mirrors/inverses
* [http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/zb/zbll/zbll Dan Harris's ZBLL algs] - incomplete
* [http://jmbaum.110mb.com/zbll.htm Jason Baum's ZBLL algs] - incomplete
* [http://www-personal.umich.edu/~dlli/Hardwick/zbll.html Chris Hardwick's ZBLL algs] - incomplete
* [http://lar5.com/cube/270/index.html Lars Petrus's One-look 2-alg ZBLL system]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 last layer substeps]]
[[Category:Fewest Moves methods]]
[[Category:Acronyms]]

ELL

2016-10-06T11:10:19Z

Logiqx: /* External links */

{{Substep Infobox
|name=ELL
|image=ELL.png
|proposers=[[Guus Razoux Schultz]]
|year=1981
|anames=
|variants=[[EOLL]], [[EPLL]], [[L5E]]
|subgroup=
|algs=29
|moves=~11 [[STM]] (Speed-optimized) Optimal: 11.27 ([[HTM]]), 9.03 ([[STM]])
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
|previous=[[LL:CO+CP cube state]]
|next=[[Solved cube state]]
}}

:''This page is about the ELL that solves edges preserving corners, for the method that does not, see [[LLEF|LL edges first]]''
'''Edges of Last Layer''', or normally '''ELL''', is a [[method]] that solves the last layer [[edge]]s of the [[3x3x3]] in one algorithm as the last step in the solution, normally after performing [[CLL]] to solve the last layer [[corner]]s. There are 29 cases in ELL, of these are three pure flips, four are [[EPLL]] and six cases are 3-cycles (besides the two in EPLL), all useful also for other methods, like [[BLD]].

ELL is also used for a method of solving the last layer edges on larger cubes. Since there are 8 of each type of [[wing]], though, ELL for larger cubes requires more than one look due to the large number of cases, see [[KBCM Step 6|KBCM]] for a complete 3-look ELL for the [[4x4x4 cube]].

All ELL that are pure 3-cycles are used in the blindfold method [[TuRBo]].

== See also ==
* [[CFCE]]
* [[CLL]]
* [[L5E]], [[L5EOP]]
* [[LLEF]]

== External links ==
* [http://www.erikku.110mb.com/ELL.html Erik Akkersdijk's ELL algs]
* [http://sa967st.webs.com/ellalgs.htm Sa967St's ELL algs]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=22737 Kirjava's ELL algs]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=817 New ELL Algorithms!]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=3789 Why Not Teach CLL/ELL?]

{{ELL}}

== Intuitive==
If you like to find algs for ELL in the MU-group, then knowing these short "proto algs" will help a lot:

* O = M' U M ... Orient
* O' = M' U' M ... Orient inverse
* P = M' U2 M ... Permute

If you combine these and also insert U-turns you can find optimal or near optimal algs for most ELLs

Example, 4-flip: '''P U2 O U2 P U'''' ... P U2 sets up for O that flips four edges (O' works the same in this case, choose the fastets), U2 P is restoration of the setup and last U is AUF.

==2-look ELL==
Use any ELL that orients what you currently got (3 cases) from the listings below and finnish it using [[EPLL]] (4 cases). Most [[OLL]]s that preserves corner orientation will probably also do for the first look but don't count on it, some may change corner permutation while orienting the edges.

Another way to solve ELL in 2 looks is to use [[L5E]], but that is desigend for solving one more edge than this is so there will be nearly the same number of algs as full ELL (5+16).

=ELL Algorithms=
{{Algnote}}

The naming convention here is; wich edges are fliped if they where [[permute]]d and which [[EPLL]] would it be if all was correctly [[orient]]ed.
==Pure flips==

{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== 2-flip (Adjacent) ===
{{case
|image=ELL 2-flip (a).jpg
|name=Pure adjacent 2-flip
|methods=ELL, [[BLD]]
|optimal=13 [[HTM]], 12 [[STM]]
|text=
}}
{{Alg|r U R' U' r' U2 R U R U' R2 U2 R}}
{{Alg|R' U2 R2 U R' U' R' U2 r U R U' r'}}
{{Alg|M U M' U2 M U M U M U2 M' U M2}}
{{Alg|(y) M2 U M U2 M' U M' U M' U2 M U M'}}
{{Alg|(x') U2 M2 U R U' M2 U2 M' U' R' U M}}
{{Alg|(y) R U R' U M R U2 R' U' R' U' R U' M' R' U2 R U}}
{{Alg|(y') R2 d' M' U' M U2 F2 U M' U M U2}}
{{Alg|(y2) L' U' B L' B' L U L R U B' R B R' U' R'}}
|

=== 2-flip (Opposite) ===
{{case
|image=ELL 2-flip (b).jpg
|name=Pure opposite 2-flip
|methods=ELL, [[BLD]]
|optimal=14 [[HTM]], 11 [[STM]]
|text=
}}
{{Alg|M' U' M' U' M' U2 M U' M U' M U2}}
{{Alg|U M' U M' U M' U M2 U M' U M' U M' U}}
{{Alg|M' U M' U M' U M' U2 M' U M' U M' U M' }}
{{Alg|M' d' M d' M' U2 M d M' d M U2}}
{{Alg|U2 M' U2 M d M U' R2 U M' U' R2}}
{{Alg|U2 M' U' M' U' F2 U M U' M F2}}
{{Alg|R F R U R' F' R' F U' (y') R2' U2 R U' R' U' R}}
{{Alg|F M' F M' F2 U2 M F M F' U2}}
{{Alg|B' R B R' U R' U' M' U R U' R B' R' B M}}
{{Alg|(y) R' U R2 U R' U' R' U2 r U R U' r' R' U R}}
{{Alg|B L' B' U' L2 U M' U' L2 U B L B' M}}

|-valign="top"
|

=== 4-flip ===
{{case
|image=ELL 4-flip.jpg
|name=Pure 4-flip
|methods=ELL, [[BLD]]
|optimal=14 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|M' U2 M U2 M' U' M U2 M' U2 M U}}
{{Alg|U B2 M' B2 M2 U' F2 M F2 M2}}
{{Alg|M' U M' U M' U M' U' M' U M' U M' U M' U'}}
{{Alg|U R2 U2' R' F2 U2' R2' F R l F2 D2 R F2 R2' (x)}}
{{Alg|F2 M F2 M2 U' M2 F2 M' F2 U}}
{{Alg|R2 B2 R2 U2 M U M' U2 R2 B2 R2 U}}

|

|}

==EPLLs==
Please do not add algs to the EPLL section, the ones here are just examples, all EPLLs are at the [[PLL|PLL-page]], put your contributions there too, else we will end up having two separate lists and we don't want that.
----
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U-PLL a ===
{{case
|image=ELL U-PLL (a).jpg
|name=U-PLL a
|methods=[[EPLL]], [[PLL]], ELL, [[ZBLL]], [[BLD]]
|optimal=9 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|F2 U M' U2 M U F2}}
{{Alg|M2 U' M U2 M' U' M2}}
{{Alg|(y2) R2 U' R' U' R U R U R U' R}}
{{Alg|L' U L' U' L' U' L' U L U L2}}

|

=== U-PLL b ===
{{case
|image=ELL U-PLL (b).jpg
|name=U-PLL b
|methods=[[EPLL]], [[PLL]], ELL, [[ZBLL]], [[BLD]]
|optimal=9 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|F2 U' M' U2 M U' F2}}
{{Alg|M'2 U M U2 M' U M'2}}
{{Alg|R U' R U R U R U' R' U' R2}}
{{Alg|(y') M2' u' M' u2' M' u' M2'}}

|-valign="top"
|

=== Z-PLL ===
{{case
|image=ELL Z-PLL.jpg
|name=Z-PLL
|methods=[[EPLL]], [[PLL]], ELL, [[ZBLL]], [[ZZLL]]
|optimal=10 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|M2 U' M E2 M E2 U M2}}
{{Alg|U2 M2 U' M2 U' M2 (x') U2 M2 U2}}
{{Alg|L F U' R U R' F' L' F U R U' R' F'}}
{{Alg|(y') M2 u M2 D' M S2 M'}}
{{Alg|M2 U M2 U M' U2 M2 U2 M'}}
{{Alg|U' M' U' M2' U' M2' U' M' U2' M2' U2}}

|

=== H-PLL ===
{{case
|image=ELL H-PLL.jpg
|name=H-PLL
|methods=[[EPLL]], [[CPLL]], [[PLL]], ELL, [[ZBLL]], [[ZZLL]]
|optimal=10 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|R L U2 R' L' (y) R' L' U2 R L}}
{{Alg|M2 U' M2 U2 M2 U' M2}}
{{Alg|R2 U2 R U2 R2 U2 R2 U2 R U2 R2}}

|}

==B edge solved (3-cycles)==
The cases in this group, including [[U-PLL]] a and b, are used in the edge blindfold method [[TuRBo]].

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== RF-flip U-PLL a ===
{{case
|image=ELL 3LF (b).jpg
|name=Pure 3-cycle
|methods=ELL, [[BLD]]
|optimal=9 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|M U M' U2 M U M'}}
{{Alg|(y2) M' U M U2 M' U M}}
{{Alg|(y') R U2 R' F' L' B' U2 B L F}}
{{Alg|(y'x') U2 M2 U R U' M2 U R' U}}
{{Alg|(y) R' F' R2 u2 R2 F' R2 u2 R'}}
{{Alg|y B' L' B M' B2 M B L B }}

|

=== LF-flip U-PLL b ===
{{case
|image=ELL 3RF (a).jpg
|name=Pure 3-cycle
|methods=ELL, [[BLD]]
|optimal=9 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|M U' M' U2 M U' M'}}
{{Alg|(y2) M' U' M U2 M' U' M}}
{{Alg|(y) L' U2 L F R B U2 B' R' F'}}
{{Alg|(y x') U2 M2 U' L' U M2 U' L U'}}

|-valign="top"
| bgcolor="f0f4f8" |
The following four cases are mirror + inverses of the first so you only need '1 alg' for all.
| bgcolor="f0f4f8" |
Mirror to the side and inverse in diagonal.

|-valign="top"
|

=== RL-flip U-PLL a ===
{{case
|image=ELL 3RL (a).jpg
|name=Pure 3-cycle
|methods=ELL, [[BLD]]
|optimal=10 [[HTM]], 8 [[STM]]
|text=
}}
{{Alg|(y' x') U' R U M' U' R' U M}}
{{Alg|(y') r' U' R U M' U' R' U R}}

|
=== RL-flip U-PLL b ===
{{case
|image=ELL 3RL (b).jpg
|name=Pure 3-cycle
|methods=ELL, [[BLD]]
|optimal=10 [[HTM]], 8 [[STM]]
|text=
}}
{{Alg|(y x') U L' U' M' U L U' M}}
{{Alg|(y') r U R' U' M U R U' R'}}

|-valign="top"
|
=== LF-flip U-PLL a ===
{{case
|image=ELL 3LF (a).jpg
|name=Pure 3-cycle
|methods=ELL, [[BLD]]
|optimal=10 [[HTM]], 8 [[STM]]
|text=
}}
{{Alg|(y x') M' U L' U' M U L U'}}
{{Alg|(y') R U R' U' M' U R U' r'}}

|
=== RF-flip U-PLL b ===
{{case
|image=ELL 3RF (b).jpg
|name=Pure 3-cycle
|methods=ELL, [[BLD]]
|optimal=10 [[HTM]], 8 [[STM]]
|text=
}}
{{Alg|(y' x') M' U' R U M U' R' U}}
{{Alg|(y') R' U' R U M U' R' U r}}

|}

==B edge in position but flipped==
The first six cases in this group are the worst of ELL, and that counts for both recognition and solving :-/
----
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== 4-flip U-PLL a ===
{{case
|image=ELL U4 (a).jpg
|name=3-cycle 1-flip
|methods=ELL
|optimal=
|text=
}}
{{Alg|(y') U' R2 U2 (y') M U' M' d' R2 d' M' U2 M}}
{{Alg|(y) M' U M U' M' U' M U' M' U' M U2 M' U M}}
{{Alg|M' U M U M' U2 M' U M' U M U M' U M'}}
{{Alg|F U R U' R' b' R2 (z') R' U' R' F R F' U R U2}}
{{Alg|(y) M U M2 d' R U R S' R' U' R'}}
{{Alg|(y2) (f R U R' U' f') (R' U' R' F R F' U R)}}
{{Alg|(y') M' U M U2 r U R' U M U' R U' R' U}}

|

=== 4-flip U-PLL b ===
{{case
|image=ELL U4 (b).jpg
|name=3-cycle 1-flip
|methods=ELL
|optimal=
|text=
}}
{{Alg|(y) U L2 U2 (y) M U M' d L2 d M' U2 M}}
{{Alg|(y') M' U' M U M' U M U M' U M U2 M' U' M}}
{{Alg|M' U' M U' M' U2 (M' U')*2 M (U' M')*2}}
{{Alg|U R' U' R' F R F' (y') R' U2 R2 U2' R2' U' R2 U' R' U (y) R U}}
{{Alg|(y') M U' M2 d L' U' L' S L U L}}
{{Alg|(y2) (f' L' U' L U f) (L U L F' L' F U' L')}}
{{Alg|(y') M U' M' U2 r' U' R U' M' U R' U R U'}}
{{Alg|L' U' B L' B' L U L F R U R' U' F'}}

|-valign="top"
| bgcolor="f0f4f8" |
The following four cases are mirror + inverses of the first so you only need '1 alg' for all.
| bgcolor="f0f4f8" |
Mirror to the side and inverse in diagonal.

|-valign="top"
|

=== BF-flip U-PLL a ===
{{case
|image=ELL U2AF (a).jpg
|name=3-cycle 1-flip
|methods=ELL
|optimal=
|text=
}}
{{Alg|M' U' M' U2 M' U M U' M' U2 M U M2}}
{{Alg|(y2) M U' M' U M' U M' U' M' U' M U M2}}
{{Alg|M' U' F2 M2 U' M U F2 U M2}}
{{Alg|(y') r2 U2 R2 U M' U' R2 U' M' U2 M2 U r2}}
{{Alg|(x') U' R U M' U' R' (y') R2 U2 R2 U2 R2 (y) U' M (x)}}

|

=== BF-flip U-PLL b ===
{{case
|image=ELL U2AF (b).jpg
|name=3-cycle 1-flip
|methods=ELL
|optimal=
|text=
}}
{{Alg|M' U M' U2 M' U' M U M' U2 M U' M2}}
{{Alg|(y2) M U M' U' M' U' M' U M' U M U' M2}}
{{Alg|M' U F2 M2 U M U' F2 U' M2}}
{{Alg|(y') r' U' R U2 R2 U2 R r U R2 U R2 r' U r U2}}

|-valign="top"
|

=== BL-flip U-PLL a ===
{{case
|image=ELL U2OL (a).jpg
|name=3-cycle 1-flip
|methods=ELL
|optimal=
|text=
}}
{{Alg|M2 U M' U2 M U' M' U M U2 M U' M}}
{{Alg|M2 D R2 D S' D' R2 S2 D' S' M2}}
{{Alg|(y) R' U' R (x) U (x) U R2 U' R' (x') U' (x') U R2 U2 R'}}
{{Alg|(y') U' M' U M2 U' M' U F2 U M U' M' F2}}
{{Alg|(y2) M2 U M U' M' U' M' U M' U M' U' M}}
{{Alg|U' F R2 U' R' F U R2 U' R' F' U R U F' U}}
{{Alg|M2 U F2 U M' U' M2 F2 U' M}}
{{Alg|(y') r2 U M2 U2 M' U' R2 U' M' U R2 U2 r2}}

|

=== BR-flip U-PLL b ===
{{case
|image=ELL U2OR (b).jpg
|name=3-cycle 1-flip
|methods=ELL
|optimal=
|text=
}}
{{Alg|M2 U' M' U2 M U M' U' M U2 M U M}}
{{Alg|M2 D' L2 D' S D L2 S2 D S M2}}
{{Alg|(y) R U R' (x') U' (x') U' R2 U R (x) U (x) U' R2 U2 R}}
{{Alg|(y) U M' U' M2 U M' U' F2 U' M U M' F2}}
{{Alg|(y2) M2 U' M U M' U M' U' M' U' M' U M}}
{{Alg|R' F2 U F R' U' F2 U F R U' F' U' R}}
{{Alg|M2 U' F2 U' M' U M2 F2 U M}}
{{Alg|(y) r U r' R2 U R2 U R2 U2 R2 U2 r U' r' U2}}
{{Alg|(x') M' U (y') R2 U2 R2 U2 R2 (y) R U M U' R' U (x)}}

|-valign="top"
|

=== BR-flip U-PLL a ===
{{case
|image=ELL U2AR (a).jpg
|name=3-cycle 1-flip
|methods=ELL
|optimal=
|text=
}}
{{Alg|(y) M' U' M' U2 M U' M2 U' M' U}}
{{Alg|(y2) M' U' M'2 U' M U2 M' U' M'}}
{{Alg|(y) F R U R' U' F' L' U' B L' B' L U L}}

|

=== BL-flip U-PLL b ===
{{case
|image=ELL U2AL (b).jpg
|name=3-cycle 1-flip
|methods=ELL
|optimal=
|text=
}}
{{Alg|(y') M' U M' U2 M U M2 U M' U'}}
{{Alg|(y2) M' U M2 U M U2 M' U M' U'}}
|}

==No edges in position==

{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== LF-flip Z-PLL ===
{{case
|image=ELL Z2AFR.jpg
|name=Adjacent flip Z-PLL a
|methods=ELL
|optimal=
|text=
}}
{{Alg|M U' M' U2 M U' M U' M' U2 M U' M2}}
{{Alg|(y') F R U R' U' F2 L' U' L U F}}
{{Alg|(y') r U R' U' r' U' R' U R d' M' U2 M}}
{{Alg|(y') R2 U' R' U' R U R U R2 U' M' U R' U' R2 r'}}
{{Alg|(y2) f R U R' U' f2 z U' R' U R B}}
{{Alg|(y') R' F' U' F U R U F R U R' U' F' U'}}

|

=== LB-flip Z-PLL ===
{{case
|image=ELL Z2ABR.jpg
|name=Adjacent flip Z-PLL b
|methods=ELL
|optimal=
|text=
}}
{{Alg|(y2) M' U M U M' U2 M U' M' U' M}}
{{Alg|(y2) F R U R' U' F' R' U' R' F R F' U R}}

|-valign="top"
|

=== FB-flip Z-PLL ===
{{case
|image=ELL Z2ORL.jpg
|name=Opposite flip Z-PLL a
|methods=ELL
|optimal=
|text=
}}
{{Alg|M' U M U' M' U M U M' U2 M}}
{{Alg|(y') R2' U' F U R' U' R2 F' R' U R U' R2}}
{{Alg|B2 M U M' U M U' M' U' B2}}

|

===LR-flip Z-PLL ===
{{case
|image=ELL Z2OFB.jpg
|name=Opposite flip Z-PLL b
|methods=ELL
|optimal=
|text=
}}
{{Alg|(y) M' U' M U M' U' M U' M' U2 M}}
{{Alg|(y) R2' U R' U' R F R2 U R U' F' U R2}}

|}

{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|

=== 4-flip Z-PLL ===
{{case
|image=ELL Z4.jpg
|name=4-flip Z-PLL
|methods=ELL
|optimal=
|text=
}}
{{Alg|F2 M F2 U' M2 U B2 M B2}}
{{Alg|(x) U2 M U2 (x') U' M2 U (x') U2 M U2 (x)}}
{{Alg|M U' M' U2 M U' M2 U M U2 M' U M}}
{{Alg|(y) M' U M U2 M' U M'2 U' M' U2 M U' M'}}
{{Alg|(y) R2' U2 l D (x) U2' R2' U2 F2 R2 U2' R2' F R' U2' R2}}
{{Alg|(y) F' R E2 R' F U2 F' R E2 R' F U2}}
{{Alg|r' u M2 u' r U2 r' u M2 u' r U2}}
{{Alg|r' U M2 U' r U2 r' U M2 U' r U2}}
{{Alg|R L B U2 L2 U2 L2 U2 L2 B' L' R'}}

|

=== 4-flip H-PLL ===
{{case
|image=ELL H4.jpg
|name=4-flip H-PLL
|methods=ELL
|optimal=
|text=
}}
{{Alg|M' U2 M' U2 M' U' M U2 M U2 M U}}
{{Alg|r U R' U' M2 U R U' R' U' M'}}
{{Alg|M U R U R' U' M2 U R U' r'}}
{{Alg|(x) U R' U' M2 U R U' M' (x') U' M' U}}
{{Alg|R2' U2 l D2 (x) U2' R2 F R2 U2' (x') D2 (x) R' U2 R2 U}}
{{Alg|F2 M' F2 M2 U' M2 F2 M F2 U}}
{{Alg|L' U' B L' B' L U L B' R' U' R U B}}

|-valign="top"
|

=== FR-flip H-PLL ===
{{case
|image=ELL H2A.jpg
|name=Adjacent flip H-PLL
|methods=ELL
|optimal=
|text=
}}
{{Alg|M' U' M U' M' U' M U' M' U' M U}}
{{Alg|(y) M' U M U M' U M U M' U M U'}}
{{Alg|(y) R' U2 R U B L U2 L' U' B'}}
{{Alg|(y') L' U2 L U F R U2 R' U' F'}}
{{Alg|(y') B U L U' L' B' L' U' B L' B' L U L}}

|

=== FB-flip H-PLL ===
{{case
|image=ELL H2O.jpg
|name=Opposite flip H-PLL
|methods=ELL
|optimal=11 [[STM]] 15 [[HTM]]
|text=
}}
{{Alg|M' U M U2 M' U (x') U' R U M U' R' U (x)}}
{{Alg|M' U M2 U2 M' U M' U2 M' U' M U' M}}
{{Alg|R' U2 R U' R' U' R' F R2 U R' U' R' F' R2}}
{{Alg|(yz) U' r2 U2 r' R' U M' U2 M' U' r R U'}}
{{Alg|F M' F U M2 U2 M2 U F' M F'}}
{{Alg|R U R' U' M' U2 R' U' R2 U' r' U R' U R U2}}
{{Alg|(y) (z) U R' B R U2 R2 U2 R2 U2 R B' R U' (z')}}

|}

{{ELL}}

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

__NOTOC__

Tripod Method

2016-10-06T11:03:58Z

Logiqx: /* External links */

{{Method Infobox
|name=Tripod
|image=Tripod_method.gif
|proposers=[[Ryan Heise]],[[Michael Gottlieb]]
|year=2002
|anames
|variants= [[Petrus]]
|steps=4
|algs=58
|moves= ~50
|purpose= [[Speedsolving]]
}}

A blockbuilding approach to solving the 3x3x3, first proposed by Ryan Heise and developed by Michael Gottlieb and Mirek Goljan. The method is characterized by the final steps, which involve solving a 'tripod' composed of the three 1x1x2 columns connected to the URF corner piece.

== The Steps ==

1. Build a 2x2x2 block. This is an intuitive step.

2.Build 3 1x2x2 block side by side the 2x2x2 block. This is also an intuitive step.

3. Insert the last F2L slot.

4. Finish the last layer using one of 58 algorithms.

== Pros ==

Like many other blockbuilding methods, this method uses less moves than the ever popular CFOP method.
The steps are all fairly simple and easy to execute, allowing for good lookahead.
The method has a low algorithm count compared to most mainstream methods such as CFOP or ZZ.

== Cons ==

The blocks, particularly the U layer block, are quite restrictive to the construction of the final F2L slot.
Recognition for the final step is not excellent and could be compared to that of COLL.
Beginners may find blockbuilding to be difficult.

== Example solve ==

Scramble (white on top, green in front): L' F2 R U B R2 D' F2 L' B U' R2 F2 B2 U L2 U' R2 L2

x2 R U' D R' D' - 2x2x2

y' L' F U' F2 L F' - First 2x2x1 block

L2 D L' U2 L D' - Second 2x2x1 block

U F R U' R' F' L' U' L U2 - Final 2x2x1 block

U' R F' U' F' U F R' F2 U' F2 U2 - F2L slot

L' U R U' R' U R U' R' L R U R' U' R U R' U' - Last 5 pieces

== External links ==
* [http://web.mac.com/teisenmann/Tripod/main.html Web-based tutorial]
* [http://www.ws.binghamton.edu/fridrich/L1/ece.htm Mirek Goljan's tripod algorithms]
* [http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/2234 Ryan Heise's Post]
* Speedsolving.com: [http://www.speedsolving.com/forum/threads/bindedsas-algorithms.55518/ BindeDSA's Algorithms]

[[Category:3x3x3 methods]]
[[Category:3x3x3 speedsolving methods]]

ZBLL

2016-10-06T11:02:19Z

Logiqx: Added link to BindeDSA's Algorithms

{{Substep Infobox
|name=ZBLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Lars Petrus]]
|year=2002
|anames=[[ZZ-a]], Steps 5+6+7 ([[Petrus method]])
|variants=[[NMLL]]
|subgroup=
|algs=493
|moves=12.08 (Optimal [[HTM]])
|purpose=
* [[Speedsolving]], [[FMC]]
|previous=[[LL:EO cube state]]
|next=[[Solved cube state]]
}}

'''ZBLL''' (short for ''[[Zbigniew Zborowski|Zborowski]]-[[Ron van Bruchem|Bruchem]] Last Layer'') is a step of a method which involves solving the entire [[last layer]] in one step, assuming that the [[edge]]s are already oriented. This is part of the [[ZB method]], but it can be useful for any other method which leaves the edges of the last layer oriented after F2L is solved (such as the [[Petrus method]], or [[ZZ Method]]).

ZBLL indeed sounds like a very useful step to learn, but the main reason that it is not in wide use is that it involves a massive 177 algorithms (counting inverses and mirrors are the same), or a total of 493 cases (including PLL). Only a handful of people have ever learned this step in its entirety. If you wish to learn it, it is useful to start by learning either [[OCLL]]/[[PLL]] or [[COLL]]/[[EPLL]], so that you will always be able to finish the cube relatively quickly even if you do not yet know the ZBLL case.

==Learning Approach==

The ZBLL cases are divided into 7 sets: T, U, L, Pi, Sune, Anti-sune, H, and the Pll cases, in which all pieces are oriented. The sets are then divided further into 6 subsets. They are recognized by their [[COLL]] case as well as a corresponding edge cycle. Every subset contains 12 cases, which are all different edge cycles possible with the COLL case of that set. Many people recognize ZBLL by looking at the UFR corner and its neighboring stickers. Whether the stickers are adjacent, or opposite allows for a quick recognition. However, this method only works for the T, U and L subsets of ZBLL, because in the other cases the UFR corner is not correctly oriented. Another way to recognize is through blocks of colour or simply the edge cycle.

==Edge recognition==

For the T, U and L cases (there are 3*6*12=216 algorithms in this set) recognition goes as follows:

1. Recognize the orientation case.

2. Recognize the [[COLL]] case.

3. Recognize the edge cycle by looking at the UFR corner and the edge stickers around it.

4. Apply the corresponding algorithm.

Step 3 may look a little complicated, but it's actually not too bad. In total there are 12 cases, but those are recognized by 2 minor sub-cases, of which there are 3:

C: If the FU sticker is the same as the FRU sticker, and if the RU sticker is the same as the RUF sticker.

A: If the FU sticker is an adjacent color to the FRU sticker, and if the RU sticker is an adjacent color to the RUF sticker.

O: If FU and FRU are opposite, and if RU and RUF are opposite.

A case is recognized by the combination of those. First comes the FU/FRU relation, then the RU/RUF relation, divided by a slash. That means there are 9 possibilities with these cases: C/C, C/A, C/O, A/C, A/A, A/O, O/C, O/A, O/O. However, there are 12 cases. That's because the A case can mean 2 stickers. That's why the last 3 cases are known as C/OX, O/CX and OppX. This means that you don't look for the relation between FU/FRU and RU/RUF, but between FU/RUF and RU/FRU. In the C/OX case, FU and RUF are the same, and RU and FRU are opposite to each other. The same goes for the O/CX case, but vice versa. In the OppX case, both FU/RUF and RU/FRU are opposite. This looks like a Z-permutation. Note that all of these cases can be seen as A/A cases at first, but whenever you have an A/A case, you should always look if it isn't the other one.

== See also ==

* [[ZB Method]]
* [[ZBLS]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[H ZBLL]] (Algorithms)
* [[ZBLD]]
* [[OPLL]]

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/threads/bindedsas-algorithms.55518/ BindeDSA's Algorithms ] - complete (2H and OH)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=18172 Happy New Year! Also, ZBLL Algorithms] - complete
* [http://www.ai.univ-paris8.fr/~bh/cube/solutions_567.html Bernhard Helmstetter's ZBLL algs] - complete, but excludes mirrors/inverses
* [http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/zb/zbll/zbll Dan Harris's ZBLL algs] - incomplete
* [http://jmbaum.110mb.com/zbll.htm Jason Baum's ZBLL algs] - incomplete
* [http://www-personal.umich.edu/~dlli/Hardwick/zbll.html Chris Hardwick's ZBLL algs] - incomplete
* [http://lar5.com/cube/270/index.html Lars Petrus's One-look 2-alg ZBLL system]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 last layer substeps]]
[[Category:Fewest Moves methods]]
[[Category:Acronyms]]

Fastest Videos for each Method

2016-08-15T21:36:45Z

Logiqx: ZZ 5.91 single

This page contains the fastest videos for each of the "big four" [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (3.85) by [[Feliks Zemdegs]]: https://youtu.be/GE8cN1Cg3ms

Average of 5 (5.51) by [[Feliks Zemdegs]]: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by [[Feliks Zemdegs]]: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by [[Alexander Lau]]: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by [[Alexander Lau]]: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (5.91) by [[Hyeon Kyo Kyoung]]: https://youtube.com/watch?v=vepKXCohxAw

Average of 5 (7.98) by [[Hyeon Kyo Kyoung]]: http://www.youtube.com/watch?v=wVfI5w_wm34

Average of 12 (8.32) by [[Hyeon Kyo Kyoung]]: http://www.youtube.com/watch?v=wVfI5w_wm34

'''[[Petrus]]'''

Single: (6.91) by [[Tao Yu]]: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (8.94) by [[Tao Yu]]: https://www.youtube.com/watch?v=5PamrwHCfzU

Average of 12 (9.79) by [[Tao Yu]]: https://www.youtube.com/watch?v=g1YlueVry4c

Fastest Videos for each Method

2016-07-02T20:32:57Z

Logiqx:

This page contains the fastest videos for each of the "big four" [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (3.85) by [[Feliks Zemdegs]]: https://youtu.be/GE8cN1Cg3ms

Average of 5 (5.51) by [[Feliks Zemdegs]]: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by [[Feliks Zemdegs]]: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by [[Alexander Lau]]: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by [[Alexander Lau]]: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (6.81) by [[Hyeon Kyo Kyoung]]: https://youtube.com/watch?v=wVfI5w_wm34

Average of 5 (7.98) by [[Hyeon Kyo Kyoung]]: http://www.youtube.com/watch?v=wVfI5w_wm34

Average of 12 (8.32) by [[Hyeon Kyo Kyoung]]: http://www.youtube.com/watch?v=wVfI5w_wm34

'''[[Petrus]]'''

Single: (6.91) by [[Tao Yu]]: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (8.94) by [[Tao Yu]]: https://www.youtube.com/watch?v=5PamrwHCfzU

Average of 12 (9.79) by [[Tao Yu]]: https://www.youtube.com/watch?v=g1YlueVry4c

Tao Yu

2016-04-16T08:29:38Z

Logiqx:

{{Infobox
|NAME=Tao Yu
|IMAGE=
|IMAGEYEAR=
|ALIASES=
|COUNTRY=Ireland
|BIRTHDATE=
|AGE=
|JOBS=Student
|YEARSACTIVE=2011-present
|ID=2012YUTA01
|FAMOUSFOR=Sub-10 with the "Big Four"
}}

'''Tao Yu''' is famous for his sub-10 averages of 12 with the "big four" methods - [[CFOP]], [[Roux]], [[ZZ]], [[Petrus]].

== Notable Videos ==
=== Unofficial ===
* [http://www.youtube.com/watch?v=MEKUXE6cp9Q 9.13 Rubik's cube average of 5 with 5 different methods]
* [http://www.youtube.com/watch?v=g1YlueVry4c Petrus Method: 9.79 average of 12! (YTUWR)]
* [http://www.youtube.com/watch?v=7SQmHkBaO1M 9.83 average of 12 using the ZZ method]

== External links ==
* [https://www.youtube.com/user/TaoxYu Tao Yu YouTube Channel]
* [https://www.speedsolving.com/forum/members/tao-yu.13351/ Tao Yu's Speedsolving.com profile]

[[Category:Speedcubers|Yu, Tao]]
[[Category:Cubers|Yu, Tao]]

Fastest Videos for each Method

2016-04-16T08:29:03Z

Logiqx:

This page contains the fastest videos for each of the "big four" [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (4.21) by [[Feliks Zemdegs]]: http://www.youtube.com/watch?v=XE5wUeo4Rs0

Average of 5 (5.51) by [[Feliks Zemdegs]]: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by [[Feliks Zemdegs]]: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by [[Alexander Lau]]: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by [[Alexander Lau]]: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (6.96) by [[Phil Yu]]: http://www.youtube.com/watch?v=wW0em3_goTg

Average of 5 (9.03) by [[Phil Yu]]: http://www.youtube.com/watch?v=PDHZqBbqlps

Average of 12 (9.83) by [[Tao Yu]]: http://www.youtube.com/watch?v=7SQmHkBaO1M

'''[[Petrus]]'''

Single: (6.91) by [[Tao Yu]]: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (8.94) by [[Tao Yu]]: https://www.youtube.com/watch?v=5PamrwHCfzU

Average of 12 (9.79) by [[Tao Yu]]: https://www.youtube.com/watch?v=g1YlueVry4c

Fastest Videos for each Method

2016-04-16T08:24:33Z

Logiqx: Created Wiki page for Tao Yu - links for ZZ and Petrus

This page contains the fastest videos for each of the main [[3x3x3]] [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (4.21) by [[Feliks Zemdegs]]: http://www.youtube.com/watch?v=XE5wUeo4Rs0

Average of 5 (5.51) by [[Feliks Zemdegs]]: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by [[Feliks Zemdegs]]: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by [[Alexander Lau]]: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by [[Alexander Lau]]: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (6.96) by [[Phil Yu]]: http://www.youtube.com/watch?v=wW0em3_goTg

Average of 5 (9.03) by [[Phil Yu]]: http://www.youtube.com/watch?v=PDHZqBbqlps

Average of 12 (9.83) by [[Tao Yu]]: http://www.youtube.com/watch?v=7SQmHkBaO1M

'''[[Petrus]]'''

Single: (6.91) by [[Tao Yu]]: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (8.94) by [[Tao Yu]]: https://www.youtube.com/watch?v=5PamrwHCfzU

Average of 12 (9.79) by [[Tao Yu]]: https://www.youtube.com/watch?v=g1YlueVry4c

Tao Yu

2016-04-16T08:22:17Z

Logiqx:

{{Infobox
|NAME=Tao Yu
|IMAGE=
|IMAGEYEAR=
|ALIASES=
|COUNTRY=Ireland
|BIRTHDATE=
|AGE=
|JOBS=Student
|YEARSACTIVE=2011-present
|ID=2012YUTA01
|FAMOUSFOR=Sub-10 with the "Big Four"
}}

'''Tao Yu''' is famous for his sub-10 averages of 12 with the "Big Four" - [[CFOP]], [[Roux]], [[ZZ]], [[Petrus]].

== Notable Videos ==
=== Unofficial ===
* [http://www.youtube.com/watch?v=MEKUXE6cp9Q 9.13 Rubik's cube average of 5 with 5 different methods]
* [http://www.youtube.com/watch?v=g1YlueVry4c Petrus Method: 9.79 average of 12! (YTUWR)]
* [http://www.youtube.com/watch?v=7SQmHkBaO1M 9.83 average of 12 using the ZZ method]

== External links ==
* [https://www.youtube.com/user/TaoxYu Tao Yu YouTube Channel]
* [https://www.speedsolving.com/forum/members/tao-yu.13351/ Tao Yu's Speedsolving.com profile]

[[Category:Speedcubers|Yu, Tao]]
[[Category:Cubers|Yu, Tao]]

Tao Yu

2016-04-16T08:21:52Z

Logiqx: Created page with "{{Infobox |NAME=Tao Yu |IMAGE= |IMAGEYEAR= |ALIASES= |COUNTRY=Ireland |BIRTHDATE= |AGE= |JOBS=Student |YEARSACTIVE=2011-present |ID=2012YUTA01 |FAMOUSFOR=Sub-10 with the "Big..."

{{Infobox
|NAME=Tao Yu
|IMAGE=
|IMAGEYEAR=
|ALIASES=
|COUNTRY=Ireland
|BIRTHDATE=
|AGE=
|JOBS=Student
|YEARSACTIVE=2011-present
|ID=2012YUTA01
|FAMOUSFOR=Sub-10 with the "Big Four"
}}

'''Tau Yu''' is famous for his sub-10 averages of 12 with the "Big Four" - [[CFOP]], [[Roux]], [[ZZ]], [[Petrus]].

== Notable Videos ==
=== Unofficial ===
* [http://www.youtube.com/watch?v=MEKUXE6cp9Q 9.13 Rubik's cube average of 5 with 5 different methods]
* [http://www.youtube.com/watch?v=g1YlueVry4c Petrus Method: 9.79 average of 12! (YTUWR)]
* [http://www.youtube.com/watch?v=7SQmHkBaO1M 9.83 average of 12 using the ZZ method]

== External links ==
* [https://www.youtube.com/user/TaoxYu Tao Yu YouTube Channel]
* [https://www.speedsolving.com/forum/members/tao-yu.13351/ Tao Yu's Speedsolving.com profile]

[[Category:Speedcubers|Yu, Tao]]
[[Category:Cubers|Yu, Tao]]

Fastest Videos for each Method

2016-04-16T08:01:46Z

Logiqx:

This page contains the fastest videos for each of the main [[3x3x3]] [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (4.21) by [[Feliks Zemdegs]]: http://www.youtube.com/watch?v=XE5wUeo4Rs0

Average of 5 (5.51) by Feliks Zemdegs: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by Feliks Zemdegs: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by Alexander Lau: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by Alexander Lau: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (6.96) by [[Phil Yu]]: http://www.youtube.com/watch?v=wW0em3_goTg

Average of 5 (9.03) by Phil Yu: http://www.youtube.com/watch?v=PDHZqBbqlps

Average of 12 (9.83) by Tao Yu: http://www.youtube.com/watch?v=7SQmHkBaO1M

'''[[Petrus]]'''

Single: (6.91) by Tao Yu: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (8.94) by Tao Yu: https://www.youtube.com/watch?v=5PamrwHCfzU

Average of 12 (9.79) by Tao Yu: https://www.youtube.com/watch?v=g1YlueVry4c

Fastest Videos for each Method

2016-04-16T07:59:24Z

Logiqx: Removed sections without video links - unchanged since May 2011

This page contains the fastest videos for each of the main [[3x3x3]] [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (4.21) by [[Feliks Zemdegs]]: http://www.youtube.com/watch?v=XE5wUeo4Rs0

Average of 5 (5.51) by Feliks Zemdegs: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by Feliks Zemdegs: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by Alexander Lau: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by Alexander Lau: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (6.96) by [[Phil Yu]]: http://www.youtube.com/watch?v=wW0em3_goTg

Average of 5 (9.03) by [[Phil Yu]]: http://www.youtube.com/watch?v=PDHZqBbqlps

Average of 12 (9.83) by Tao Yu: http://www.youtube.com/watch?v=7SQmHkBaO1M

'''[[Petrus]]'''

Single: (6.91) by Tao Yu: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (8.94) by Tao Yu: https://www.youtube.com/watch?v=5PamrwHCfzU

Average of 12 (9.79) by Tao Yu: https://www.youtube.com/watch?v=g1YlueVry4c

Fastest Videos for each Method

2016-04-16T07:55:27Z

Logiqx: ZZ Ao12 by Tao Yu

This page contains the fastest videos for each of the main [[3x3x3]] [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (4.21) by [[Feliks Zemdegs]]: http://www.youtube.com/watch?v=XE5wUeo4Rs0

Average of 5 (5.51) by Feliks Zemdegs: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by Feliks Zemdegs: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by Alexander Lau: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by Alexander Lau: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (6.96) by [[Phil Yu]]: http://www.youtube.com/watch?v=wW0em3_goTg

Average of 5 (9.03) by [[Phil Yu]]: http://www.youtube.com/watch?v=PDHZqBbqlps

Average of 12 (9.83) by Tao Yu: http://www.youtube.com/watch?v=7SQmHkBaO1M

'''[[Petrus]]'''

Single: (6.91) by Tao Yu: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (8.94) by Tao Yu: https://www.youtube.com/watch?v=5PamrwHCfzU

Average of 12 (9.79) by Tao Yu: https://www.youtube.com/watch?v=g1YlueVry4c

'''[[Waterman]]'''

Single:

'''[[Tripod]]'''

Single:

'''[[Hahn]]'''

Single:

'''[[Heise]]'''

Single:

'''[[Snyder]]'''

Single:

Fastest Videos for each Method

2016-04-16T07:53:13Z

Logiqx: Petrus Ao5

This page contains the fastest videos for each of the main [[3x3x3]] [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (4.21) by [[Feliks Zemdegs]]: http://www.youtube.com/watch?v=XE5wUeo4Rs0

Average of 5 (5.51) by Feliks Zemdegs: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by Feliks Zemdegs: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by Alexander Lau: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by Alexander Lau: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (6.96) by [[Phil Yu]]: http://www.youtube.com/watch?v=wW0em3_goTg

Average of 5 (9.03) by [[Phil Yu]]: http://www.youtube.com/watch?v=PDHZqBbqlps

Average of 12 (9.90) by SDSMint: http://www.youtube.com/watch?v=jLHoz7VUbwA

'''[[Petrus]]'''

Single: (6.91) by Tao Yu: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (8.94) by Tao Yu: https://www.youtube.com/watch?v=5PamrwHCfzU

Average of 12 (9.79) by Tao Yu: https://www.youtube.com/watch?v=g1YlueVry4c

'''[[Waterman]]'''

Single:

'''[[Tripod]]'''

Single:

'''[[Hahn]]'''

Single:

'''[[Heise]]'''

Single:

'''[[Snyder]]'''

Single:

Fastest Videos for each Method

2016-04-16T07:51:26Z

Logiqx: Petrus by Tao Yu

This page contains the fastest videos for each of the main [[3x3x3]] [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (4.21) by [[Feliks Zemdegs]]: http://www.youtube.com/watch?v=XE5wUeo4Rs0

Average of 5 (5.51) by Feliks Zemdegs: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by Feliks Zemdegs: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by Alexander Lau: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by Alexander Lau: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (6.96) by [[Phil Yu]]: http://www.youtube.com/watch?v=wW0em3_goTg

Average of 5 (9.03) by [[Phil Yu]]: http://www.youtube.com/watch?v=PDHZqBbqlps

Average of 12 (9.90) by SDSMint: http://www.youtube.com/watch?v=jLHoz7VUbwA

'''[[Petrus]]'''

Single: (6.91) by Tao Yu: https://www.youtube.com/watch?v=fLHh6l9Yi_o

Average of 5 (9.119) by Tao Yu: https://www.youtube.com/watch?v=g1YlueVry4c (solves 7-11)

Average of 12 (9.785) by Tao Yu: https://www.youtube.com/watch?v=g1YlueVry4c

'''[[Waterman]]'''

Single:

'''[[Tripod]]'''

Single:

'''[[Hahn]]'''

Single:

'''[[Heise]]'''

Single:

'''[[Snyder]]'''

Single:

Fastest Videos for each Method

2016-04-16T07:43:49Z

Logiqx: Removed Hawaiian Kociemba - April Fools Day

This page contains the fastest videos for each of the main [[3x3x3]] [[speedcubing | speedsolving]] methods.

'''[[CFOP]] / [[Fridrich]]'''

Single (4.21) by [[Feliks Zemdegs]]: http://www.youtube.com/watch?v=XE5wUeo4Rs0

Average of 5 (5.51) by Feliks Zemdegs: https://youtu.be/VEgnIs5wns8

Average of 12 (6.12) by Feliks Zemdegs: https://youtu.be/k8HWovcaCf0

'''[[Roux]]'''

Single (5.11) by [[Alexander Lau]]: https://www.youtube.com/watch?v=wiZw8Xp4ric

Average of 5 (6.88) by Alexander Lau: https://www.youtube.com/watch?v=eLFzwRDOhRg

Average of 12 (7.26) by Alexander Lau: https://www.youtube.com/watch?v=JihDzkQnzSQ

'''[[ZZ]]'''

Single (6.96) by [[Phil Yu]]: http://www.youtube.com/watch?v=wW0em3_goTg

Average of 5 (9.03) by Phil Yu: http://www.youtube.com/watch?v=PDHZqBbqlps

Average of 12 (9.90) by SDSMint: http://www.youtube.com/watch?v=jLHoz7VUbwA

'''[[Petrus]]'''

Single: (8.14) by [[Matt DiPalma]]: https://www.youtube.com/watch?v=IkE_6YpvfIE

Average of 5 (10.57) by Matt DiPalma: https://www.youtube.com/watch?v=jQF9lBRQ84k

Average of 12 (11.37) by [[Sebastiano Toronto]]: https://www.youtube.com/watch?v=yZGiOZF7ueo

'''[[Waterman]]'''

Single:

'''[[Tripod]]'''

Single:

'''[[Hahn]]'''

Single:

'''[[Heise]]'''

Single:

'''[[Snyder]]'''

Single:

ZZLL

2016-04-13T08:52:24Z

Logiqx: Fix BOCA link

{{Substep Infobox
|name=ZZLL
|image=
|proposers=[[Zbigniew Zborowski]]
|year=2006
|anames=
|variants=
|subgroup=
|algs=167
|moves=
|purpose=
|previous=[[LL:EO+2EP cube state]]
|next=[[Solved cube state]]
}}

The '''Z'''bigniew '''Z'''borowski '''L'''ast '''L'''ayer is the subset of [[ZBLL]] in which two opposite LL edges are correctly permuted. It is used to solve the last layer in the ZZ-b variant of the [[ZZ Method]]. Compared with ZBLL's 494 cases, ZZLL has only 167 distinct cases which can be completed with a minimum of 80 algorithms assuming mirrors and inverses are used. ZZLL also serves as a useful transition between [[COLL]]/[[EPLL]] and full [[ZBLL]].

==External links==
* [http://boca.a5.pl/cat.php?l=en&cat=th&m=zz&ch=b BOCA ZZLL algs]
* [http://stubers.org/jamesstuff/cube/zzll.php James Stuber's ZZLL algorithms]
* [https://docs.google.com/document/d/1PNdfgzfJ4xefLuNOn4e9jfS9JiwjxvBLcaysU44M5Z8/edit Simon Swanson's ZZLL algorithms]

[[Category:3x3x3 last layer substeps]]
[[Category:Advanced methods]]

COLL

2016-04-12T22:12:24Z

Logiqx:

{{Substep Infobox
|name=COLL
|image=Visualcube_coll.png
|proposers=[[Lars Petrus]]
|variants=[[CLLEF]], [[OLLCP]]
|anames=Steps 5+6 ([[Petrus method]])
|year=
|subgroup=
|algs=42
|moves=9.78 (Optimal [[HTM]])
|purpose=
* [[Speedsolving]]
|previous=[[LL:EO cube state]]
|next=[[LL:EO+CO+CP cube state]]
}}

'''COLL''' (short for '''Corners of Last Layer''') is a 3x3x3 [[last layer]] [[substep]] in the [[CxLL]] group that solves (orients and permutes) the last layer corners while preserving the last layer edge orientation, leaving only edge permutation ([[EPLL]]). It is principally used as an [[add-on]] to [[Fridrich]], when the last layer edges are already oriented after F2L. COLL has 42 cases including mirrors (24 without). 2 of these are the adjacent and diagonal corner permutation.

COLL is not to be confused with [[CLL]], also short for "Corners of Last Layer." The difference is that CLL preserves the F2L but not the last layer edges orientation, so it leaves the LL edges scrambled and the next step would be full [[ELL]]. For some cases the CLL and the COLL are the same algorithm, but for other cases the CLL is much shorter. For CLL and COLL algorithms, see the page on [[CxLL Algorithms]].

One possible extension of COLL is [[ZBLL]]. This LL method solves the entire LL if the edges are already oriented, but it has 493 cases. Another one is [[OLLCP]] which solves the corner permutation and [[OLL|orients the last layer]] with a total of 331 algorithms for all last layer cases.

== See also ==
* [https://www.speedsolving.com/wiki/index.php/Special:MediawikiAlgDB?mode=view&view=default&puzzle=3&group=COLL COLL Algorithms]
* [[ZBLL]]
* [[NMLL]]
* [[CLLEF]]
* [[CLL]], [[CLL algorithms (3x3x3)]]
* [[CMLL]]
* [[OLLCP]]
* [[CxLL Algorithms]]

== External links ==
* [http://www.cubezone.be/coll.html COLL Algorithms] By Lars Vandenbergh
* [http://www.stanford.edu/~leyanlo/ COLL Algorithms] By Leyan Lo
* [http://www.cubewhiz.com/coll.html Bob Burton's COLL Page]
* [http://jmbaum.110mb.com/coll.htm Jason Baum's COLL Page]
* [http://cube.danrcohen.com/coll.html Dan Cohen's COLL Page]

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

1LLL

2016-03-15T19:06:27Z

Logiqx: Changed link from Google document to Speedsolving.com thread - retains "Provenance"

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=[[Bernard Helmstetter]]
|year=2000
|anames= OLLCP-EP
|variants=[[ZBLL]]
[[M-CELL]]
|steps=1
|algs='''3915'''
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

There is currently no known database for all 1LLL [[algorithms]]. However, there are for subsets such as [[ELL]] and [[ZBLL]], which contain of 518 algorithms in total, leaving 3397 algorithms.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 518 [[ELL]] and [[ZBLL]] cases (4 [[EPLL]] cases appear in both sets), there would be '''3397''' algorithms to learn.

It should be noted that additional subsets of 1LLL also exist such as [[L3C]] (subset of L4C, which is a subset of ZBLL) , Pure OLL (orientation without affecting permutation), [[ZZLL]] (subset of ZBLL), [[ZZ-Blah]] (subset of ZBLL), [[Tripod]] LL and more.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=51999 1LLL/OLLCP-EP algorithms]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=55518 BindeDSA's Algorithms]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]

1LLL

2016-03-14T12:46:27Z

Logiqx: Changed order of links

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=[[Bernard Helmstetter]]
|year=2000
|anames= OLLCP-EP
|variants=[[ZBLL]]
[[M-CELL]]
|steps=1
|algs='''3915'''
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

There is currently no known database for all 1LLL [[algorithms]]. However, there are for subsets such as [[ELL]] and [[ZBLL]], which contain of 518 algorithms in total, leaving 3397 algorithms.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 518 [[ELL]] and [[ZBLL]] cases (4 [[EPLL]] cases appear in both sets), there would be '''3397''' algorithms to learn.

It should be noted that additional subsets of 1LLL also exist such as [[L3C]] (subset of L4C, which is a subset of ZBLL) , Pure OLL (orientation without affecting permutation), [[ZZLL]] (subset of ZBLL), [[ZZ-Blah]] (subset of ZBLL), [[Tripod]] LL and more.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip All 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=55518 BindeDSA's Algorithms]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]

1LLL

2016-03-14T12:45:41Z

Logiqx: Added link to BindeDSA's Algorithms

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=[[Bernard Helmstetter]]
|year=2000
|anames= OLLCP-EP
|variants=[[ZBLL]]
[[M-CELL]]
|steps=1
|algs='''3915'''
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

There is currently no known database for all 1LLL [[algorithms]]. However, there are for subsets such as [[ELL]] and [[ZBLL]], which contain of 518 algorithms in total, leaving 3397 algorithms.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 518 [[ELL]] and [[ZBLL]] cases (4 [[EPLL]] cases appear in both sets), there would be '''3397''' algorithms to learn.

It should be noted that additional subsets of 1LLL also exist such as [[L3C]] (subset of L4C, which is a subset of ZBLL) , Pure OLL (orientation without affecting permutation), [[ZZLL]] (subset of ZBLL), [[ZZ-Blah]] (subset of ZBLL), [[Tripod]] LL and more.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip All 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=55518 BindeDSA's Algorithms]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]

Roux method

2016-03-09T13:18:05Z

Logiqx: Fix typo

{{Method Infobox
|name=Roux
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames
|variants
|steps=4
|algs=9-42
|moves=[[Speedsolving|Speed]]:48, [[FM]]:28-
|purpose=
* [[Speedsolving]]
* [[Fewest Moves]]
}}

The '''Roux Method''' (French pronunciation: [ʁu]) is a 3x3 speedsolving method invented by [[Gilles Roux]]. Unlike the [[Fridrich]] and [[Petrus]] methods, the inventor of this method has used it to achieve an official sub-15 average. Similarities can be drawn to the Petrus method's block building and the [[Waterman method]]'s layer-on-the-left and edges-last aspects.

==The Steps==

1. Build a 1x2x3 block anywhere on the cube.

2. Build a second 1x2x3 block opposite of the first 1x2x3 block, without disrupting the first 1x2x3 block. After this step, there should be two 1x2x3 blocks: one on the lower left side, and one lower right side, leaving the U slice and M slice free to move.

3. Simultaneously [[orient]] and [[permute]] the remaining 4 corners on the top layer (U-slice). You can use [[CMLL]],[[COLL]], or Corner OLL's (along with the T and Y permutation) to do this.

4a. [[Orient]] the 6 remaining edges using only M and U moves (UF, UB, UL, UR, DF, DB need to be oriented correctly).

4b. Solve the UL and UR edges, preserving edge orientation. After this step, both the left and right side layers should be complete.

4c. Solve the centers and edges in the M slice, ''see [[Last Six Edges]]''.

: ''See also: [[L5E]]''

==Pros==

Like the Petrus method, the Roux method uses fewer moves than the popular Fridrich method. It is also more intuitive and requires fewer algorithms. After the first block is built the rest of the cube can be solved mostly with R, r, M and U moves thus eliminating rotations.

==Cons==

*Block building can be difficult for a beginner to get used to. The reliance on r and M moves may also be difficult for some people, so much so that cubers who have trouble with M turns should probably not use this as their main method (or better, practice practice practice the M moves). Slice turns can also be slower than using a [[quarter-turn metric]].
*Since the M-slice is used often, especially in the final stages, there is a larger chance of a [[DNF]] rather than a [[+2]] if the solver misses the second flick in an M2, or if the solver misses the last M move. It is a DNF because M uses both the R and L face in one.

==Improvement==

Some Roux users have learned multiple algorithms for each CLL case, each affecting edges in a different way. This allows for manipulation of edge orientation, leading to an easier LSE.

Possibly another improvement is to expand to solving any of the four second blocks. This means that the D-layer colors of the two blocks don't have to match. One negative, if someone has already learned a recognition method for CLL, is that to easily use the full range of second block options, a switch to [[NMCLL]] recognition is necessary. Another is that LSE EO is a bit more difficult to recognize in some solves.

== Notable Users ==
* [[Gilles Roux]] [http://www.worldcubeassociation.org/results/p.php?i=2004ROUX01]
* [[Thom Barlow]] (Kirjava) [http://www.worldcubeassociation.org/results/p.php?i=2006BARL01]
* [[Austin Moore]] (BigGreen) [http://www.worldcubeassociation.org/results/p.php?i=2009MOOR01]
* [[Jules Manalang]] (Waffo) [http://www.worldcubeassociation.org/results/p.php?i=2008MANA02]
* [[Alexander Lau]] (5BLD) [http://www.worldcubeassociation.org/results/p.php?i=2011LAUA01]
* [[Mitsuki Gunji]]
* [[Artur Kristof]] (Arcio) [http://www.worldcubeassociation.org/results/p.php?i=2012KRIS12]

==Forum links==
* [https://www.speedsolving.com/forum/showthread.php?3842-Roux-Help-and-Discussion-thread.html Roux help and discussion thread]
* [https://www.speedsolving.com/forum/showthread.php?51553-One-Answer-3x3-Roux-Question.html One-question answer thread]
* [https://www.speedsolving.com/forum/showthread.php?50819-How-to-read-a-Roux-corners-table.html Reading Roux corners tables]
* [https://www.speedsolving.com/forum/showthread.php?47572-Video-Roux-as-a-Beginner-Method.html Beginner's Roux video tutorial]
* [https://www.speedsolving.com/forum/showthread.php?48028-The-Roux-quot-Example-Solve-quot-Game!.html Roux Example solves]
* [https://www.speedsolving.com/forum/showthread.php?35350-Roux-4b-to-4c-Transition.html Roux step 4b-4c transition help]

== External links ==
* [http://grrroux.free.fr/method/Intro.html Gilles Roux's tutorial]
* [http://wafflelikescubes.webs.com/ Waffle's Roux Site]
* Wikia: [http://rubiks.wikia.com/wiki/Roux_Method Roux Method]
* [http://www.speedsolving.com/forum/showthread.php?t=11506 Waffle's Roux Tutorial]
* [http://rouxtorial.webs.com/ 5BLD's and PandaCuber's Roux Tutorial]
* [http://www.speedsolving.com/forum/showthread.php?29123-The-reconstruction-thread&p=634675&viewfull=1#post634675 Reconstruction for BigGreen's unofficial Ao5 9.51]
* [http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/5923 Original Method Proposal]

[[Category:3x3x3 methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

1LLL

2016-03-06T18:48:47Z

Logiqx: ELL is not a variant. The reason ZBLL is a variant is because it can follow ZZ F2L and therefore a 1LLL. Likewise for M-CELL which is related to Roux, etc.

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=[[Bernard Helmstetter]]
|year=2000
|anames= OLLCP-EP
|variants=[[ZBLL]]
[[M-CELL]]
|steps=1
|algs='''3915'''
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

There is currently no known database for all 1LLL [[algorithms]]. However, there are for subsets such as [[ELL]] and [[ZBLL]], which contain of 518 algorithms in total, leaving 3397 algorithms.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 518 [[ELL]] and [[ZBLL]] cases (4 [[EPLL]] cases appear in both sets), there would be '''3397''' algorithms to learn.

It should be noted that additional subsets of 1LLL also exist such as [[L3C]] (subset of L4C, which is a subset of ZBLL) , Pure OLL (orientation without affecting permutation), [[ZZLL]] (subset of ZBLL), [[ZZ-Blah]] (subset of ZBLL), [[Tripod]] LL and more.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip All 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]

1LLL

2016-03-06T18:44:22Z

Logiqx:

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=[[Bernard Helmstetter]]
|year=2000
|anames= OLLCP-EP
|variants=[[ZBLL]]
[[ELL]]

[[M-CELL]]
|steps=1
|algs='''3915'''
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

There is currently no known database for all 1LLL [[algorithms]]. However, there are for subsets such as [[ELL]] and [[ZBLL]], which contain of 518 algorithms in total, leaving 3397 algorithms.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 518 [[ELL]] and [[ZBLL]] cases (4 [[EPLL]] cases appear in both sets), there would be '''3397''' algorithms to learn.

It should be noted that additional subsets of 1LLL also exist such as [[L3C]] (subset of L4C, which is a subset of ZBLL) , Pure OLL (orientation without affecting permutation), [[ZZLL]] (subset of ZBLL), [[ZZ-Blah]] (subset of ZBLL), [[Tripod]] LL and more.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip All 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]

1LLL

2016-03-06T18:43:41Z

Logiqx:

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=[[Bernard Helmstetter]]
|year=2000
|anames= OLLCP-EP
|variants=[[ZBLL]]
[[ELL]]

[[M-CELL]]
|steps=1
|algs='''3915'''
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

There is currently no known database for all 1LLL [[algorithms]]. However, there are for subsets such as [[ELL]] and [[ZBLL]], which contain of 518 algorithms in total, leaving 3397 algorithms left.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 518 [[ELL]] and [[ZBLL]] cases (4 [[EPLL]] cases appear in both sets), there would be '''3397''' algorithms to learn.

It should be noted that additional subsets of 1LLL also exist such as [[L3C]] (subset of L4C, which is a subset of ZBLL) , Pure OLL (orientation without affecting permutation), [[ZZLL]] (subset of ZBLL), [[ZZ-Blah]] (subset of ZBLL), [[Tripod]] LL and more.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip All 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]

User talk:Bryce Springfield

2016-03-06T09:11:55Z

Logiqx: Created page with "Why 815?"

Why 815?

1LLL

2016-02-28T18:45:37Z

Logiqx: Corrected figures due to EPLL appearing in ZBLL and ELL

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=Bernard Helmstetter
|year=2000
|anames=
|variants=[[ZBLL]]
[[M-CELL]]
|steps=1
|algs=3915
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 518 [[ELL]] and [[ZBLL]] cases (4 [[EPLL]] cases appear in both sets), there would be '''3397''' algorithms to learn.

It should be noted that additional subsets of 1LLL also exist such as [[L3C]] (subset of L4C, which is a subset of ZBLL) , Pure OLL (orientation without affecting permutation), [[ZZLL]] (subset of ZBLL), [[ZZ-Blah]] (subset of ZBLL), [[Tripod]] LL and more.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip All 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]

1LLL

2016-02-28T10:55:11Z

Logiqx: /* Number of 1LLL Cases */

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=Bernard Helmstetter
|year=2000
|anames=
|variants=[[ZBLL]]
[[M-CELL]]
|steps=1
|algs=3915
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.
It should be noted that additional subsets of 1LLL also exist such as [[L3C]] (subset of L3C) , Pure OLL (orientation without affecting permutation), [[ZZLL]] (subset of ZBLL), [[ZZ-Blah]] (subset of ZBLL), [[Tripod]] LL and more besides.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip All 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]

1LLL

2016-02-28T10:53:58Z

Logiqx: /* Number of 1LLL Cases */

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=Bernard Helmstetter
|year=2000
|anames=
|variants=[[ZBLL]]
[[M-CELL]]
|steps=1
|algs=3915
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.
It should be noted that additional subsets of 1LLL also exist such as [[L3C]], Pure OLL (orientation without affecting permutation), [[ZZLL]], [[ZZ-Blah]], [[Tripod]] LL and more besides.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip All 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]

1LLL

2016-02-28T10:47:44Z

Logiqx: Formatting

{{Method Infobox
|name=1LLL
|image=1LLL.jpg
|proposers=Bernard Helmstetter
|year=2000
|anames=
|variants=[[ZBLL]]
[[M-CELL]]
|steps=1
|algs=3915
|moves=12.58 [[HTM]]
|purpose=
* [[Speedsolving]], however the multitude of algorithms makes it much less useful in whole
}}

'''1''' '''L'''ook '''L'''ast '''L'''ayer means completing the [[last layer]] using only one look. On the 3x3x3, currently [[ZBLL]] is the only known practical system for achieving a 1-look last layer, but other experimental approaches such as 1-look 2-alg (such as [[M-CELL]]) may have potential.

== Number of 1LLL Cases ==

Assuming the last layer is an outer layer, the number of cases is calculated as:
: corner orientations * edge orientations * corner permutations * edge permutations / 2
With the 2 at the end because of odd-even parity.

Numerically this is:
: 3^3 * 2^3 * 4! * 4! / 2 = '''62208'''
* The 3^3 at the beginning is because there are 4 corners on the last layer while the final one depends on the remaining three.
* The 2^3 is because there are 4 edges on the last layer while the final one depends on the remaining three.

Treating cases which are the same, but rotated by 90, 180 or 270 degrees as the same case, the number of cases becomes:
: 62208/4 = '''15552'''

Although these cases may be regarded as unique, some of them can be solved by applying the same algorithm from a different angle. For cases with no rotational symmetry, there are 3 equivalent cases which may be solved with the same alg. For cases with 180 degree rotational symmetry, there is 1 equivalent case which may be solved with the same alg. Cases with 90, 180 and 270 degree rotational symmetry are unique. By solving multiple cases with the same algorithm from different angles, the number of cases becomes:
: '''3916''' cases (including the solved state / [[AUF]] states and subsets such as [[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]]) which can be solved with '''3915''' algorithms

As well as rotationally symmetrical cases, there are also reflectively symmetrical cases. These may be solved by applying a reflection of the algorithm. Finally, some cases are inversions of others. These can be solved by reversing (inverting) the algorithm solving the original case. Exactly which cases are mirrors of each other requires a case-by-case analysis. Work by Bernard Helmstetter established that the number unique 1LLL cases (excluding mirrors and inverses) is:
: '''1212''' cases (including the solved / [[AUF]] states) which can be solved with '''1211''' algorithms

Since most speed solvers regard reflective symmetry and inversions as different cases (e.g. [[PLL]] is thought of as 21 algorithms rather than 13 algorithms plus mirrors and inverses), 1LLL should be thought of as '''3915''' algorithms.

[[PLL]], [[ELL]], [[2GLL]], [[L4C]] and [[ZBLL]] are all subsets of 1LLL, albeit a small proportion of the algorithms. Knowing some of these subsets means less algorithms need to be learnt for a 1LLL:
*If the solver already knows all 21 [[PLL]] cases, which is a subset of [[ZBLL]], there would be '''3894''' algorithms to learn.
*If the solver already knows all 29 [[ELL]] cases, there would be '''3886''' algorithms to learn.
*If the solver already knows all 84 [[2GLL]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 84 [[L4C]] cases, which is a subset of [[ZBLL]], there would be '''3831''' algorithms to learn.
*If the solver already knows all 493 [[ZBLL]] cases, there would be '''3422''' algorithms to learn.

== See also ==
* [[Last Layer]]
* [[:Category:3x3x3 last layer methods]]
* [[2LLL]], [[3LLL]], [[4LLL]]
* [[ZBLL]]
* [[Orientation]]
* [[Permutation]]

== External links ==
* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's last layer algorithms]
* [http://www.speedcubing.com/docs/uppertable.zip All 1211 last layer algorithms(1MB zipped)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12815 3x3 last layer: number of positions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=440250&postcount=31 Derivation of unique PLL cases]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

[[Category:3x3x3 methods]]