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Snyder Method

2012-02-19T15:32:58Z

Irontwig: /* External Links */

{{Method Infobox
|name=Snyder
|image=Snyder.png
|proposers=[[Anthony Snyder]]
|year=1982
|anames=
|variants=[[Heise Method]]
[[Petrus]]
|steps=3-5
|moves=
|purpose=
* [[Speedsolving]] [[FMC]]
}}
The '''Snyder Method''', invented by [[Anthony Snyder]] in 1982, is both a [[fewest moves]] and a [[speedsolving]] [[method]] for the [[3x3x3 cube]]. The start is similar to [[Petrus]], forming a 2x2x2 block with optional [[XCross]]. Then a variety of methods may be used to complete the rest of the F2L except for one CE. (Anthony has since added optional starts using a 1x2x3 or a 2x2x3, also with or without the cross.) Then the final CE pair is placed while simultaneously orienting and placing a minimum of one LLE. Then all LL edges are solved together with one corner. Then the [[last three corners]] are solved.

== Claimed Advantages ==
A salient characteristic of the Snyder Method is to orient and permute each piece at each stage simultaneously. Anthony claims several advantages for this:
* Simultaneous orientation and permutation helps to visualize piece relationships, useful to intuitive solving.
* There is a mathematical advantage.
Furthermore, all such last-layer algorithms will be a subset of [[1LLL]], making the Snyder Method a possible candidate as an intermediate method for [[1LLL]].

Though there are many cases to first solving the LLE+1C, the more common cases can generally be solved in 6-10 turns, making it quite turn efficient.

Although the Snyder Method closely resembles the [[Petrus Method]] in its F2L approach, its last-layer method differs considerably. This last-layer method was independently proposed in 2005 by [[Kenneth Gustavsson]], who called it "Fish & Chips."

== A Word about Algorithms ==
Anthony found almost all of his algorithms independently and without computer aid, and claims that his method is one of the most efficient based primarily on human-generated algorithms. Anthony explained this as follows: "In the 80's there was a general stereotype that using a computer was cheating, plus [I] enjoyed thinking up [my] own algorithms." However, he plans to upgrade his method using a computer in the near future.

== Variations ==
The Snyder Method allows a number of variations to be applied wherever convenient.
* when a 2x2x3 block is not immediately apparent he will start with either a 1x2x3 or a 2x2x2, then immediately finish the 2x2x3 block with a second look, or, he puts together several CE pairs as in [[Heise]], then assembles those into a F2L minus one CE
* two or more CE may be solved simultaneously to complete the F2L faster
* the LL may be solved in 1 look rather than 2, using either a shortest-move algorithm, combination, or substitution

In the early 80's, Anthony developed a complete set of fewest-move solutions for the CE pair cases and for the [[last three corners]] cases. However, he relied more extensively on the use of combinations and exchanges to efficiently put in the LL edges + corner. He makes up for this with a large selection of approximate direct-solves on the entire LL, claiming to switch to this mode about 20% of the time.

This method requires 1-2 looks for the block+cross start, then up to 1 look each for the 1-3 CE pairs, then 1-2 looks for the last layer. Though there are a lot of looks, an attentive solver can be quite efficient, and average around 40 turns. Though a beginner will likely take a lot more than this, and a pro taking their time may get his/her average down to about 36. Many of the shorter algorithms were added throughout the 80's and 90's, and the library of LL direct solves were mostly added in the 00's.

== Publication ==
In 1981 he printed his simple solution, a 7 algorithm system that is easy to learn. It was entitled, "Tony Snyder's Simplest Solution to Solve a Rubik's Cube", and though he personally only taught a handful of people this technique, a classmate took a copy and passed it out to students in a number of schools. He has not yet put to print his advanced technique.

'''Note:''' Having complete sets of short algorithms was very unusual in the 1980's (combining 2 algs in 1-look was a common solution). [[Kenneth Gustavsson]] suggested the same LL-method ('Fish & Chips') in 2005 but with [[VHF2L]] and the rest in two clearly defined steps, [[EP]] + 1 corner (36 cases, the 'fish' step) and then [[L3C]] (22 cases, the 'chips' step), this makes a 2-look [[ZBLL]], often a little more effective than [[COLL]]/[[EPLL]].

== Example Solves ==
Here are some of Anthony's solves.
* [http://www.youtube.com/watch?v=UB2Pb9_iNBI The Snyder Method]
* [http://www.youtube.com/watch?v=fra6go0CMgI A newer demo, easier to see]
* [http://www.youtube.com/watch?v=HEKjAHDyKLo 5 solves using Snyder Method 2, showing how fast it is despite his handicaps].

== See Also ==
* [[Anthony Snyder]]
* [[Snyder Notation]]
* [[Snyder Metric]]
* [[Heise Method]]
* [[Petrus Method]]
* [[L3C]]

If you have edges oriented when starting the last layer you can often do using only Sune, double Sune (or inverse and/or mirrors), J-PLL a/b or U-PLL a/b for the first look. Here are a couple of examples that show how this is done:

'''Scramble''' '''Solution'''
F U F' L2 B' U' B U L2 F U' F' U AUF to U-PLL a on the left side, (L3C 3-twist).
L' U R U' B2 U' B2 U B2 R' L U' AUF J-PLL b, (L3C 'Anti Niklas')
B' F R2 U' R2 U R2 U F' U' B U' J-PLL b, (L3C Niklas)
R2 F2 R2 U R' F2 R U' R2 F2 R U R U left side double Antisune (L' U2 L U...)
R' F U2 F U L' U L F U' F U F R U2 left side double Antisune (again!)
B L2 F' D F' D' F2 L2 B' U' y J-PLL a (setup L' before the y for [[1LLL]])
L U2 L D' B2 D L' U2 L D' B2 D L2 U' y2 left Antisune.

Sometimes more than one of these solutions are possible. Working like this solves the step in an easy 2:5 times, maybe more. It is effective, fast and OH-friendly, but recogniton for the sune/doublesune cases is horrible without loads of practice. For the cases where two opposite edges needs to be swapped [[COLL]] is a recommended alternative and for the cases with edges correct, one or two look [[L4C]].

== External Links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?24822-Tony-Snyder-solves-the-cube Tony Snyder solves the cube]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?29123-The-reconstruction-thread&p=633439&viewfull=1#post633439 Reconstructions]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?29123-The-reconstruction-thread&p=714631#post714631 Five more reconstructions]

[[Category:Methods]]
[[Category:Advanced Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]
[[Category:Cubing Terminology]]

Snyder Method

2011-04-15T08:47:40Z

Irontwig: added fmc in infobox

{{Method Infobox
|name=Snyder
|image=Snyder.png
|proposers=[[user:Tony Snyder|Anthony Snyder]]
|year=1982
|anames=
|variants=[[Heise Method]]
[[Petrus]]
|steps=3-5
|moves=36-45
|purpose=
* [[Speedsolving]] [[FMC]]
}}
Invented by [[user:Tony Snyder|Anthony Snyder]] in 1982, the '''Snyder Method''' is both a [[fewest moves]] [[method]] and a [[speedsolving]] [[method]] for the [[3x3x3 cube]]. The start is similar to [[Petrus]], forming a 2x2x2 block with optional [[XCross]]. Then a variety of methods may be used to complete the rest of the F2L except for one CE. (Anthony has since added optional starts using a 1x2x3 or a 2x2x3, also with or without the cross.) Then the final CE pair is placed while simultaneously orienting and placing a minimum of one LLE. Then all LL edges are solved together with one corner. Then the [[last three corners]] are solved.

The main objective to the Snyder Method is to orient and permute each piece at each stage simultaneously rather than separate steps, as he claims several strategic advantages to this:

* a simultaneous orient and permute helps the person visualize piece relationships useful to intuitive cube solving
* Snyder is convinced there is a mathematical advantage to simultaneous orient and permute, though he has not proven this
* all LL algs learned that fit this philosophy will also be a subset of the LL direct solve method, thereby making more efficient use of the learning process for people who have as an ultimate goal a LL direct solve

Video of [http://www.youtube.com/watch?v=UB2Pb9_iNBI Anthony demonstrating the Snyder Method], and [http://www.youtube.com/watch?v=fra6go0CMgI a newer demo, easier to see], and here he is seen doing 5 speed solves using Snyder Method 2 [http://www.youtube.com/watch?v=HEKjAHDyKLo showing how fast it is despite his handicaps].

Though his F2L method closely resembles the F2L in [[Petrus]], his last layer method differs considerably. Though there are many cases to first solving the LLE+1C, the more common cases can generally be solved in 6-10 turns, making it quite turn efficient. In 2005 [[Kenneth Gustavsson]] came up with the same LL method as Anthony, calling it "Fish & Chips".

The Snyder Method includes a number of variations that are applied wherever convenient.

* when a 2x2x3 block is not immediately apparent he will start with either a 1x2x3 or a 2x2x2, then immediately finish the 2x2x3 block with a second look, or, he puts together several CE pairs as in [[Heise]], then assembles those into a F2L minus one CE
* two or more CE may be solved simultaneously to complete the F2L faster
* the LL may be solved in 1 look rather than 2, using either a shortest-move algorithm, combination, or substitution

In the early 80's Anthony came up with a complete set of fewest-move solutions for the CE pair cases and for the [[last three corners]] cases. However, he relied more extensively on the use of combinations and exchanges to efficiently put in the LL edges + corner. He makes up for this with a large selection of approximate direct-solves on the entire LL, claiming to switch to this mode about 20% of the time.

This method requires 1-2 looks for the block+cross start, then up to 1 look each for the 1-3 CE pairs, then 1-2 looks for the last layer. Though there are a lot of looks, an attentive solver can be quite efficient, and average around 40 turns. Though a beginner will likely take a lot more than this, and a pro taking their time may get his/her average down to about 36. Many of the shorter algorithms were added throughout the 80's and 90's, and the library of LL direct solves were mostly added in the 00's.

Anthony came up with nearly all of the algorithms without advice from others, and without using a computer, and therefore claims that his system is one of the most efficient systems based primarily on human originated algorithms. In the 80's there was a general stereotype that using a computer was cheating, plus Anthony enjoyed thinking up his own algorithms. However, he states that he will upgrade his system using computer modeling in the near future, possibly making it a serious contender.

In 1981 he printed his simple solution, a 7 algorithm system that is easy to learn. It was entitled, "Tony Snyder's Simplest Solution to Solve a Rubik's Cube", and though he personally only taught a handful of people this technique, a classmate took a copy and passed it out to students in a number of schools. He has not yet put to print his advanced technique.

'''Note:''' Having complete sets of short algorithms was very unusual in the 1980's (combining 2 algs in 1-look was a common solution). [[Kenneth Gustavsson]] suggested the same LL-method ('Fish & Chips') in 2005 but with [[VHF2L]] and the rest in two clearly defined steps, [[EP]] + 1 corner (36 cases, the 'fish' step) and then [[L3C]] (22 cases, the 'chips' step), this makes a 2-look [[ZBLL]], often a little more effective than [[COLL]]/[[EPLL]].

'''Anthony's Turn Counting Protest:''' "I have never understood why the turn counting rules/standards follow a 'range of motion metric' rather than an 'efficiency metric'. Solving for fewest turns is a challenge in efficiency to start with, so the metric should also be based on efficiency. In my opinion the most sensible way to count turns is to figure that any parallel simultaneous movement is one turn. This would also make the rules far simpler. Another point is that there are many ways to fine-tune solves by adding more anti-slices. Examples: I far prefer solving the U-Twist (headlights) with R L U2 R' U' R U' R' L' U2 L U L' U, which works out to just 12 very easy to perform turns once you define the anti-slice into the metric (using [[Snyder Notation]] the same algorithm: R+o' U2 R' U' R U' R'o+ U2 L U L' U). This requires only 12 parallel simultaneous movements, which is in my opinion more efficient than the 13 turn F U' R2 U R2 U F U' F2 D R2 D' R2. Another example is the H-PLL, which can take just 6 turns using the [[Snyder Metric]]."

== See Also ==

* [[Snyder Notation]]
* [[Snyder Metric]]
* [[Methods]]
* [[3x3x3 Speedsolving Methods]]
* [[Fewest Moves Techniques]]
* [[Heise Method]]
* [[Petrus Method]]
* [[L3C]]

'''Tony Snyder wrote:'''
"In 1983 I set the world record for unassisted play on a video game called Q*Bert at a place called Showbiz Pizza in Minneapolis. I decided to solve the cube before starting and then again after, just to see what condition my mind would get to. Before starting the game I solved the cube in 31 seconds (early am, bad time). Then I spent half the week playing Q*Bert non-stop, finishing after 57 hours of continuous play and no sleep. I was awake for 3 hours before it started. So after 60 hours of no sleep I then solved the cube in 25 seconds. They showed some of this on local TV, and they did a write-up in March 1984 Electronic Games Magazine. BTW, I unexpectedly went colorblind for about 30 minutes during play, then recovered - lost about 300 Q*Berts during that time, but I had over 800 saved up so it was no big deal."

 <hr>
If you have edges oriented when starting the last layer you can often do using only Sune, double Sune (or inverse and/or mirrors), J-PLL a/b or U-PLL a/b for the first look. Here are a couple of examples that show how this is done:

'''Scramble''' '''Solution'''
F U F' L2 B' U' B U L2 F U' F' U AUF to U-PLL a on the left side, (L3C 3-twist).
L' U R U' B2 U' B2 U B2 R' L U' AUF J-PLL b, (L3C 'Anti Niklas')
B' F R2 U' R2 U R2 U F' U' B U' J-PLL b, (L3C Niklas)
R2 F2 R2 U R' F2 R U' R2 F2 R U R U left side double Antisune (L' U2 L U...)
R' F U2 F U L' U L F U' F U F R U2 left side double Antisune (again!)
B L2 F' D F' D' F2 L2 B' U' y J-PLL a (setup L' before the y for [[1LLL]])
L U2 L D' B2 D L' U2 L D' B2 D L2 U' y2 left Antisune.

Sometimes more than one of these solutions are possible. Working like this solves the step in an easy 2:5 times, maybe more. It is effective, fast and OH-friendly, but recogniton for the sune/doublesune cases is horrible without loads of practice. For the cases where two opposite edges needs to be swapped [[COLL]] is a recommended alternative and for the cases with edges correct, one or two look [[L4C]].

[[Category:Methods]]
[[Category:Advanced Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]
[[Category:Cubing Terminology]]

PLL

2011-01-12T14:07:53Z

Irontwig: /* F Permutation */

{{Method Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|steps=1
|algs=21
|moves=12.3 [[HTM]]
|purpose=
* [[Speedsolving]]
}}
'''PLL''' is the Permutation of the [[Last Layer]], the last step of many speedsolving methods. In this step, the pieces on the top layer have already been oriented ([[OLL]]) so that the top face has all the same color, and they can now be moved into their solved positions. There are 21 PLLs (13 if you count mirrors and inverses as being the same) and each one is named after a letter. The following page gives a list of all of the PLLs, along with a picture and a list of common [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|T Permutation]] (or 'T perm') swaps the UL and UR edges, as well as the UFR and UBR corners. Make sure to try out all of the available algorithms for a case to see which one feels the fastest to you - the same algorithm may not be the fastest for everyone, and shorter algorithms are not always faster than longer ones. PLL is a subgroup of [[ZBLL]].

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

== External Links ==

* [http://rishidoshi.blogspot.com/2010/11/test-option-2.html PLL Patterns and Algs] (Recognize PLLs by patterns. Printable and customizable Excel sheet by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]

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

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

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

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

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=[[PLL]], [[ZBLL]], [[ZZLL]]
|optimal=
|text=
}}
{{Alg|(y2) R U' R' U R2 y R U R' U' x U' R' U R U2|PLL}}
{{Alg|yz R U R' U' R U2 z' y' R U R' U' y x L' U' L U L2 x'|PLL}}
{{Alg|R' U R U' R2 F' U' F U x R U R' U' R2 B'|PLL}}
{{Alg|R' U R U' R2' F' U' F U R U' x' R2 U' R' U|PLL}}
{{Alg|R' U R U' R2 y' R' U' R U y x R U R' U' R2 x'|PLL}}
{{Alg|y R U R' U R U2 R2 U' R U' R' U2 R U r U R' U' L' U R U'|PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
{{Alg|(y) U' R' U R U' R'2 F' U' F U R x U R' U' R2|PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2|PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|PLL}}
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|PLL}}
{{Alg|(r U R' U') z U' (l' U2 r' U') (r U2 l' U l2) |PLL}}
{{Alg| y M2 U M2 y' T permutation/(R U R' U' R' F R2 U' R' U' R U R' F') y M2 U' M2 |PLL}}
{{Alg|(y) F x R2 F R2 U' R' U l' U2 L F' L' U x' R2 U' |PLL}}

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=[[PLL]], [[ZBLL]]
|optimal=
|text=
}}
{{Alg|(y) R2' u R' U R' U' R u' R2 y' R' U R|PLL}}
{{Alg|(y) R2 D B' U B' U' B D' R2 F' U F|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' y' R' U L' U2 R U' L|PLL}}
{{Alg|(y) d' L U' R' U L' U' L U L' U L U2 L' U R U' R' U R U' R' U2 R|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=[[PLL]], [[ZBLL]]
|optimal=
|text=
}}
{{Alg|R' U' R y R2 u R' U R U' R u' R2|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L y' R2' u R' U R U' R u' R2 |PLL}}
{{Alg|(y') R' U L' U2 R U' L y R L U2 L' R' U2|PLL}}
{{Alg|(y2) d R' U2 R U R' U' R U R' U' L U2 L' U' L U' L' U L U' R U L'|PLL}}

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

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=[[PLL]], [[ZBLL]]
|optimal=
|text=
}}
{{Alg|(y2) R U R' y' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y2) R U R' F2 D' L U' L' U L' D F2|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l x|PLL}}
{{Alg|(y) L U' R U2 L' U R' y R' L' U2 R L|PLL}}
{{Alg|(y) L U' R U2 L' U R' y' L' R' U2 L R|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y2) d' L U2 L' U' L U L' U' L U R' U2 R U R' U RU' R' U L' U' R|PLL}}
{{Alg| U' x R' U R' D2 R U' R' D2 x' U R' U' R U R U R U' R|PLL}} (This one seems long, but it's just a combination of A(a) and U(a))

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a
|methods=[[PLL]], [[ZBLL]], [[BLD]]
|optimal=
|text=
}}
{{Alg|(y2) R' U2 R U R' z R2' U R' D R U'|PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R U|PLL}}
{{Alg|(y2) F2 L' U' r U2 l' U R' U' R2|PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|PLL}}
{{Alg|(y2) x U2 r' U' r U2 l' U R' U' R2|PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 L R U'|PLL}}
{{Alg|U' L' U R' z R2 U R' U' R2 U D|PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|PLL}}
{{Alg|R L d2 R' U' R d2 R' U L'|PLL}}
{{Alg|(L' U R' U2 L U' R) U (L' U R' U2 L U' R)|PLL}}
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|PLL}}
{{Alg|L' U2 L U L' U2 R U' L U R'|PLL}}
{{Alg|L' U' L F L' U' L U L F' L2 U L U|PLL}}
{{Alg|y R2 (U D') R2' U R2 U' R2' D R2 U' R2' U|PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=[[PLL]], [[ZBLL]], [[BLD]]
|optimal=
|text=
}}
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|PLL}}
{{Alg|R U2 R' U' R d2' R' U L' U' R|PLL}}
{{Alg|y2 R L U2 L' U' L U2 R' U L' U'|PLL}}
{{Alg|(R U R' F') (R U R' U' R') F (R2 U' R' U')|PLL}}
{{Alg|y' L U' Rw U2 Lw' U R' U' Lw2 F2 L2|PLL}}
{{Alg|y' L' U' R U2 L' U L U2 L' R U|PLL}}
{{Alg|y2 F2' R U R' y r2 y' R U' R U R2'|PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|PLL}}
{{Alg|y2 r2 U' L' U r' U2 R B' R' U2|PLL}}
{{Alg|(R U' L U2 R' U L) U' (R U' L U2 R' U L)|PLL}}
{{Alg|L' U R' U2 L U' L' U2 R L|PLL}}
{{Alg|y2 (F2) R U R' (F2) L D' L D L2|PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=[[PLL]], [[ZBLL]], [[ZZLL]]
|optimal=
|text=
}}
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R|PLL}}
{{Alg|z D R' U R2 D' R (U' D) R' U R2 D' R U' R|PLL}}
{{Alg|z U R' D R2 U' R (D' U) R' D R2 U' R D' R z'|PLL}}
{{Alg|y' L U' R U2 L' U R' L U' R U2 L' U R'|PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|PLL}}
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l' U' y2|PLL}}
{{Alg|L U' R U2 L' U R' L U' R U2 L' U R' U'|PLL}}
{{Alg|y z R' U R' D R2' U' R U D' R' D R2' U' R D'|PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 L' U R' U'|PLL}}
{{Alg|F' R U R' U' R' F R2 F U' R' U' R U F' R'|PLL}}
{{Alg|z U2 R2 U' R2 y' R2 U2 R2 U R2 y R2 U2 R2 d R2 x y |PLL}}
{{Alg|z U R' U' R U F R F' U' R' U F' U F U' R U' |PLL}}
{{Alg|(R U R' U) (R U R') F' (R U R' U') (R' F R2 U' R' U2) (R U' R')|PLL}}
{{Alg| L U L' y J Perm/( R U' F' R U R' U' R' F R2 U' R' U') y R U' R'|PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=[[PLL]], [[ZBLL]], [[ZZLL]]
|optimal=
|text=
}}
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R'|PLL}}
{{Alg|z U' R D' R2' U R' (U' D) R D' R2 U R' D |PLL}}
{{Alg|z (D' R U' R2' D R3 U) 2|PLL}}
{{Alg|L' U R' U2' L U' L' R U R' U2' L U' R U'|PLL}}
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|PLL}}
{{Alg|z U' R D' R2 U R' U' z' R U R' z R2 U R' z' R U'|PLL}}
{{Alg|L' U R' z R2 U R' U z' R U R' z R2 U R' z' R U'|PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|PLL}}
{{Alg|L U' R U2 L' U R' L U' R U2 L' U R' U'|PLL}}
{{Alg|(R' U R U' R') F' (U' F R U R' U' R d') (R U R')|PLL}}
{{Alg|R' U L' U2 R U' L R' U L' U2 R U' L|PLL}}
{{PLL|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2}}
{{PLL|L' U R' U2' L U' R L' U R' U2' L U' R}}

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=[[PLL]], [[ZBLL]]
|optimal=
|text=
}}{{Alg|y2 z U R2 U' R2 U F' U' R' U R U F U2 R|PLL}}
{{Alg|y' R U R' F' R U2 R' U2 R' F R U R U2 R' U'|PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|PLL}}
{{Alg|y' R2 B' R' U' R' U R B R' U2 R U2 R'|PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2' U|PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 F|PLL}}
{{Alg|y2 R' U' R U2 R U2 L' R2 U R U' R L U2 R'|PLL}}
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|PLL}}
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|PLL}}
{{Alg|y2 L U2 L' U2 L F' L' U' L U L F L2 U|PLL}}
{{Alg|R l U' l' U' R' U l U l' U2 R U2' R'|PLL}}
{{Alg|y x' R' U' F' U R' U' x U R' U' R' U R B R2|PLL}}
{{Alg|y2 U' L2 F' L' U' L' U L F L' U2 L U2 L'|PLL}}
===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=[[PLL]], [[ZBLL]]
|optimal=
|text=
}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2' U'|PLL}}
{{Alg|y R2 B2 U' R' U' R U R U B2 R U' R U|PLL}}
{{Alg|R' U2 R U' y' R' F R B' R' F' R z x' R' U R'|PLL}}
{{Alg|y2 R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|PLL}}
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|PLL}}
{{Alg|r' L' U r U L U' r' U' r U2 L' U2 L|PLL}}
{{Alg|U R2 F R U R U' R' F' R U2 R' U2 R|PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=[[PLL]], [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|PLL}}
{{Alg|y2 L' U' L U L F' L2 U L U L' U' L F|PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|PLL}}
{{Alg|y2 B L U' L' U L U L2 B' L U L U' L'|PLL}}
{{Alg|L2 U' L2 D F2 R2 U R2 D' F2|PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|PLL}}
{{Alg|R2' u' R2 U R2' y R2 u R2' U' R2|PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|PLL}}
{{Alg|(z x2) U2 r' U2 r U2 x U2 r U2 r' U2|PLL}}

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=[[PLL]], [[ZBLL]]
|optimal=
|text=
}}
{{Alg|R' U R' U' y x R' F R' F' R2 U' R' U R U|PLL}}
{{Alg|R' U R' U' y x R' U' R2 B' R' B R' U R U|PLL}}
{{Alg|R' U R' U' y x R' U' R2 x' U' R' U R' F R F|PLL}}
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|PLL}}
{{Alg|R' U R' U' x2 y' R' U R' U' l R U' R' U R U|PLL}}
{{Alg|R' U R' U' y z' U' R U' R' U2 y' R' U' R U R|PLL}}
{{Alg|R' U R' U' y R' F' R2 U' R' U R' F R F|PLL}}
{{Alg|R' U R' U' y R' D R' D' R2 F' R' F R F|PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|PLL}}
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U r'|PLL}}
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|PLL}}
{{Alg|y' R' U L U' R U R' U L' U' R U2 L U2 L'|PLL}}
{{Alg|y2 R U' L' U R' U' R U' L U R' U2 L' U2 L|PLL}}
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|PLL}}
{{Alg|y L' U R U' L U L' U R' U' L U2 R U2 R'|PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=[[PLL]], [[ZBLL]], [[BLD]]
|optimal=
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
{{Alg|R2 u R2' U R2 D' R' U' R F2' R' U R|PLL}}
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|PLL}}
{{Alg|R2 U' R' U R U' z' y' L' U' R U' R' U' L U y z|PLL}}
{{Alg|y F' L' U L U L' U' L F L' U' L U L' F' L F|PLL}}
{{Alg|F R U' R' F D R' y x R' U' R z R2 y L' d2|PLL}}
{{Alg|z' U2 L' U' L U L' y' L' U' R U' R' U' L U|PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U|PLL}}
{{Alg|z U2 R U R' U' R y R U L' U L U R' U'|PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|PLL}}
{{Alg|R' F R F' y' U' R' U R2 U R' U' R' F R F' U'|PLL}}
{{Alg|y2 z U2 R' U2 R' U2 R B R B ' U2 B R' B'|PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|PLL}}

 {{PLL}}

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Algorithms]]
[[Category:Sub Steps]]

__NOTOC__

Hahn Method

2011-01-12T09:15:34Z

Irontwig: /* steps */ l4c

{{Method Infobox
|name=Hahn Method
|image=keyhole.jpg‎
|proposers=[[Eric Hahn]]
|year=2010
|anames
|variants
|steps=4
|moves
|purpose
}}

The '''Hahn Method''' is a [[blockbuilding]] and intuitive [[keyhole]] based method. First build a 2x3x2 block then add one edge at the bottom and one edge at the left side. Next use the keyhole for placing every edge and two corners into position. The last step is to solve the remaining corners with [[CLL]].

== Steps ==

1. Build a 2x2x3 block leaving the F and U faces free

2. Add the FD and FL edge pieces

3. Use keyhole advanced to solve the remaining 5 edges and the UFL and UFR corners

4. Use an x rotation and solve the 4 remaining corners using [[L4C]].

[[Category:3x3x3 Methods]]
[[Category:Experimental Methods]]
{{Stub}}

Category:Fewest Moves techniques

2010-12-28T19:05:24Z

Irontwig: /* Inserted Algorithms/Commutators */

This page introduces some tips and techniques to help you solve the cube in as [[Fewest Moves|few moves]] as possible.

The best results can be obtained when all techniques are controlled. It is strongly advised not to follow a strict pattern, for example a [[3x3x3 Speedsolving Methods|speedsolving method]]. However some algorithms learned from a speedsolving method will give some advantages in some cases. The most useful [[Fewest Moves Methods|methods]] are [[Heise]], [[Petrus]], [[Fridrich]], [[Roux]] and [[ZBLL]].

== Block Building ==
Best start for an FMC is block building technique. Try to build a [[2x2x2 block]] then a [[2x2x3 block]]. After the 2x2x2 block you have 3 sides to extend it to a 2x2x3. Explore all of them. After the 2x2x3 block

== Pair Insertion ==
when inserting Fridrich-pairs in F2L don't get stuck with you speedcubing methods but try some alternatives and check each of them for

== Pseudoblocks or Pre-scramble-moves==
Like [[Heise Method]] you can build pseudo blocks, which are adjacent 1x2x2 blocks or c/e pairs that are not adjacent but need an extra turn to get those blocks at the right color-centre. Solving with pseudo blocks needs can be very difficult and needs a lot of experience. As an alternative you can replace a pseudo block by a pre-scramble-move to give more oversight over your solve.

A pre-scramble move is a move you apply before the scramble and which allows you to find more possible solutions. Of course you must not forget to add the premove at the end of your solution.

== Inserted Moves (single) ==
Sometimes after a promising start you can't find a good continuation. Say you have solved a 2x2x2 block, but after that there's nothing good. By stepping through the solution you might see that at one place there's no 2x2x2-pieces on U, at that place you can try to insert U, U' or U2 and see if a better continuation is possible.

== Inserted Algorithms/Commutators ==
A very powerful technique in FMC is to solve everything except 3-5 corners and then insert 8 move [[commutators]] that cycle three corners earlier in the solution. Since there many corner configurations that can be solved in 8 moves often one will cancel moves, and thus one corner cycle will add less than 8 moves to the total solution length. Edge cycles are not used as oftenas FMC is judged in [[HTM]] and edge cycles often involve slice moves that are counted as two moves. Some people use stickers to more easily track the unsolved pieces through the solution.

== Freestyle Solving ==
If you see some opportunity to solve a lot of blocks without any (known) pattern you could try to solve it. When leaving a maximum of 4 edges and 4 corners try to conjugate them to 1 face during a solve. Then use pre-scramble-moves or a second cube to solve that face / LL

== LL-algorithms ==
sometimes you solve a lot of LL blocks using a very short LL algorithm, 8 or 9 moves maximum. Try to learn short LL algorithms in such a way that you know what it does to corners and edges. Start with the length-6 LL-alg, then the three 7-move LL-algs, the five 8-move LL-algs, and so on. You are really an expert when learning all LL-algs up to 10 moves.

== Other Tips ==

* Do not use moves that turn the cube!

* Use fixed colors for up & front to enhance recognition!

* Better still, look at the centre of the face you are turning, it tells wich side it is ("White" = U and so on), then orientation does not matter anymore.

* Write down promising moves, do not wait till the very end!

* Create a backup solve!

* Learn to scramble fast, it can save a lot of time during a 1-hour solve.

* Bring stickers (for insertions) and extra cubes during a competition.

== See Also ==

* [[Fewest Moves]]
* [[Commutators]]
* [[Niklas]]
* [[God's Algorithm]]
* [[Fewest Moves Methods]]
* [[Puzzle Theory]]

== External Links ==

* [http://www.ryanheise.com/cube/fundamental_techniques.html Ryan Heise's page on intuitive solving techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=1566 Fewest Moves: Tips and Techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?p=221756 The FMC thread]

[[Category:Fewest Moves Methods]]

{{Stub}}

__NOTOC__

Corners First

2010-12-21T15:21:25Z

Irontwig: ortega added in info box

{{Method Infobox
|name=Corners First
|image=Corners_first.gif
|proposers=[[Erno Rubik]]
|year=1974
|anames=CF
|variants=[[Waterman]], [[Roux]], [[Ortega]]
|steps=3
|algs=4 min
|moves
|purpose=
* [[Speedsolving]]
* [[Beginner Method]]
* [[Blindsolving]]
}}

'''Corners First''' methods, abbreviated as '''CF''', are [[speedcubing]] methods that solve all of the corners (relative to each other) before anything else. There are not very many serious CF solvers for [[3x3x3]] these days, because it is very difficult to get under 20 seconds with a pure CF method, but CF methods are relatively easy to invent and were very popular in the [[1980s]]. At least in theory, CF methods exist for all puzzles with corners, although for many puzzles (such as [[big cube]]s) they are impractical for speedsolving. For the [[2x2x2]], on the other hand, there are only corners, so any method is in effect a CF method, and ideas from 2x2 solving can be applied to CF methods on any larger [[cube]] puzzle. The most popular methods for solving the corners are [[Guimond]], [[Ortega]], and [[CLL]]; there are many ways to do the edges, perhaps the most efficient of which is the [[Waterman]] method.

===See also:===
* [[Columns first]]
* [[Waterman]]
* [[Roux]]

== Beginner CF Methods ==
There are no specifically named methods in this group, but a typical beginner CF method may look like this:

'''Corners:'''
* Solve the corners of the first layer using intuition.
* Orient the [[LL]] corners using R U R' U' R' F R F' or a similar algorithm.
* Permute the [[LL]] corners using a 3 cycle of corners (A Permutation)
'''Centres:'''
* Move centres into position using slice turns (trivial).
'''Edges:'''
* Place the edges of the E layer using moves like ([[AUF]]) + M' R U' M U R'.
* Place the edges of first layer using M' U M or M' U2 M.
* Orient the last layer edges using [[EOLL#EOLL preserving corners|EOLL]].
* Permute the last layer edges with [[EPLL]] (for the most basic methods this can be done with only the [[PLL#U Permutation : a|U-perm]]).

== External Links ==
* [http://rubikscube.info/beginner.php Marc Waterman's Beginner Tutorial]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Beginner Methods]]
[[Category:Cubing Terminology]]

LSE

2010-12-21T15:20:44Z

Irontwig: cf-style approaches

{{Method Infobox
|name=Last Six Edges
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames=LSE
|variants=[[ELL]], [[L5E]]
|steps=1
|moves=
|purpose=
* [[Speedsolving]]
}}

'''Last Six Edges''', abbrevaited '''LSE''' or '''L6E''', is the last [[step]] of the [[Roux Method]] and the [[Ortega method]].

The original Roux method have three sub steps for LSE:
* Orientation of centres and edges.
* Permutation of UR and UL edges.
* Permutation of the M slice.

Other styles are also in use, for example you can solve the last of F2L, centres, BD and FD and do [[ELL]] or just centres and BD and end in [[L5E]]. Two ways more common in [[Corners first]] methods is first to solve UL or UR and then insert UL/UR while orienting the M-slice or solving both UL and UR and then solving the M-slices in one look.

{{stub}}

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Sub Steps]]

Tripod Method

2010-12-13T20:12:05Z

Irontwig:

{{Method Infobox
|name=Tripod
|image=Tripod_method.gif
|proposers=[[Mirek Goljan]],[[Michael Gottlieb]]
|year
|anames
|variants
|steps=6
|moves
|purpose=
* [[Speedsolving]]
* [[Fewest Moves]]
}}

A blockbuilding approach to solving the 3x3x3, invented by Michael Gottlieb. The final step involves solving a 'tripod' composed of the three 1x1x2 columns connected to the URF corner piece.

== 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]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Speedsolving Methods]]

{{Stub}}

LLEF

2010-12-04T14:08:04Z

Irontwig: /* Opposite swap (T-PLL) */

{{Method Infobox
|name=LLEF
|image=LLEF.png
|variants=[[ELL]], [[EOLL]], [[EPLL]]
|steps=1
|algs=15
|moves=7.87 (Optimal [[HTM]])
|purpose=
* [[Speedsolving]], [[FMC]]
}}

:'''Last Layer Edges First'''
The '''ELL''' (Edges of the Last Layer) that ignores corners is easier to solve, it uses both lesser moves and has lesser cases than what is the '[[ELL|normal ELL]]'. This variation is useful for a 2-look method that solves corners last (see [[L4C]]). But L4C is not in use for speed solving, this because of two reasons, it has twice the number of cases of [[CLL]] and the [[algorithm]]s that solves them are mostly long (the worst LL case of them all is in this group, it needs 16 turns optimally ([[HTM]])). Another backdraw is that recognition for solving the edges before the corners is not so easy. If you don't have a system for colour recognition you have to [[AUF]] to have a chance, sometimes even repeated AUFs.

It can however be useful for [[FMC]]. LLEF has a low average optimal solution length of 7.87, while for the last four corners it is 11.73 (a half move more than optimal [[PLL]]). Both of these can however be lowered. One can quite often choose a inversion/mirror version of an alg to solve the same LLEF situation thus increasing one's chances of cancelling moves and/or getting a better corner case. [[Partial Edge Control|Partial edge control]] can also be used to avoid the cases with four flipped edges. The corners can in turn be solved more efficiently with inserted corner 3-cycles rather than at the very end of the solution.

Solving ELL first is 15 cases from a group of totally 48, i.e. a skip of this step occures 1:48 times, skip to [[EP]] only occures 1:8 times and skip to pure [[EO]] occures 1:6 times.

===See also:===
* [[ELL]]
* [[FMC]]
== External Links ==

* [http://www.ai.univ-paris8.fr/~bh/cube/ Bernard Helmstetter's LL algorithms]
* [http://emsee.110mb.com/Speedcubing/ZZLL/No%20parity.html Michal Hordecki's algorithms for the last 4 corners]

=Algorithms=
{{Algnote}}

The images have corners solved in darker colours, this works as a guide for those who don't know the colour sheme or is using something diffrent from this. For all other reasons you can ignore the corners.

The first alg given for each case is the optimal solution in [[HTM|Half Turn Metric]].

==All edges oriented (EP) ==
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== Adjacent swap (Sune) ===
[[File:LLE OA.jpg]]

{{Alg|(y') R' U2 R U R' U R}}

|

=== Opposite swap (T-PLL) ===
[[File:LLE OO.jpg]]

{{Alg|R' F R' u2 R F' R' u2 R2 F'}}
{{Alg|R2 u R2 u' R2 y' R2 u' R2 u R2}}

|}

==Pure flips (EO) ==

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

|-valign="top"
|
=== 2-flip (Adjacent) ===
[[File:LLE 2AP.jpg]]

{{Alg|R' U' R2 B' R' B2 U' B'}}

|

=== 2-flip (Opposite) ===
[[File:LLE 2OP.jpg]]

{{Alg|(y) R B L' B L U B' U' R'}}

|-valign="top"
|

=== 4-flip ===
[[File:LLE 4P.jpg]]

{{Alg|R2 L' B R' B L U2 L' B R' L}}

|
|}

==Adjacent swap==

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

|-valign="top"
|
=== Adjacent RF ===
[[File:LLE ASFR.jpg]]

{{Alg|(y2) R2 L' B R' B R B2 R' B R' L}}

|

=== Adjacent FL ===
[[File:LLE ASLF.jpg]]

{{Alg|F U R U' R' F'}}

|-valign="top"
|

=== Adjacent LB ===
[[File:LLE ASBL.jpg]]

{{Alg|(y) L' B' R B' R' B2 L}}
{{Alg|r U R' U R U2 r' U'}}
{{Alg|y r U2 R' U' R U' r' U}}
{{Alg|M U M' U2 M U M' U'}}

|

=== Adjacent BR ===
[[File:LLE ASRB.jpg]]

{{Alg|(y') B' U' R' U R B}}

|-valign="top"
|

=== Opposite RF ===
[[File:LLE ASOF.jpg]]

{{Alg|(y2) F R U R' U' F'}}
{{Alg|r U L' U' r' U L U' (x) U}}

|

=== Opposite BR ===
[[File:LLE ASOB.jpg]]

{{Alg|F' L' U' L U F}}

|-valign="top"
|

=== 4-flip (A4) ===
[[File:LLE AS4.jpg]]

{{Alg|(y') B L U L' B' U2 B' R B R'}}

|
|}

==Opposite swap==

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

|-valign="top"
|
=== Adjacent (OA) ===
[[File:LLE OSA.jpg]]

{{Alg|(y2) B' R' U R B L U' L'}}

|

=== Opposite (OO) ===
[[File:LLE OSO.jpg]]

{{Alg|B' R' U R B L' B L B2 U B}}

|-valign="top"
|

=== 4-flip (O4) ===
[[File:LLE OS4.jpg]]

{{Alg|R B' R' B U B2 L' B' L U' B'}}

|
|}

[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Algorithms]]
[[Category:Sub Steps]]

__NOTOC__

Waterman method

2010-11-23T00:50:40Z

Irontwig: minus 50 on step3 #algs according to http://www.speedsolving.com/forum/showthread.php?4877-Marc-Waterman&p=62511&viewfull=1#post62511

{{Method Infobox
|name=Waterman
|image=Waterman_method.gif
|proposers=[[Marc Waterman]]
|year=1982
|algs=117 Total 42 (Step 2) 75 (Step 3)
|anames
|variants
|steps=3
|moves=40 to 45 [[STM]], over 50 [[HTM]]
|purpose=
* [[Speedsolving]]
}}
The '''Waterman Method''' is a method for solving the [[3x3x3 Cube]] which was invented by [[Marc Waterman]] in the 1980s. The method is based on [[Corners First]] methods but is efficient enough to be used for advanced speedsolving (average times of under 20 seconds). The steps are as follows:
* Step 1: Solve one layer of the cube. The original way to do this is by first putting together the corners and then solving the center and edges together. This can also be done with [[block building]] (start with a 1x2x3 block as with [[Roux]] and then fill in the last three pieces).
* Step 2: Solve the corners of the opposite layer. This is done in one step in the style of [[CxLL]]. After this step, turn the cube so that the solved layer is on L.
* Step 3a: Solve two of the edges on R, while at the same time placing a third somewhere in the R layer.
* Step 3b: Finish the R edges while orienting the M edges, all in one algorithm. This step is difficult to learn and has around 80 algorithms, but the algorithms mostly use only M, R, r, and U moves, so this is a fast step.
* Step 3c: Solve the M edges. This is trivial and there are only a few possible cases, all very fast.

If you are truly interested in learning this method you should check out [http://rubikscube.info/waterman/index.php Josef Jelinek's webpage] which has very thorough descriptions as well as a complete list of algorithms for the last four steps. He also has a copy of the original booklet containing the method.

== See Also ==
* [[Corners First]]
* [[Roux Method]]

== External Links ==

* [http://rubikscube.info/waterman/index.php rubikscube.info Waterman Tutorial]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:2x2x2 Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:2x2x2 Speedsolving Methods]]

ELL

2010-11-22T12:46:09Z

Irontwig: /* FB-flip H-PLL */

{{Method Infobox
|name=ELL
|image=ELL.png
|proposers=[[Guus Razoux Schultz]]
|year=1981
|anames=
|variants=[[EOLL]], [[EPLL]], [[L5E]]
|steps=1
|algs=29
|moves=~11 [[STM]] (Speed-optimized) Optimal: 11.27 ([[HTM]]), 9.03 ([[STM]])
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
}}

:''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 compleate 3-look ELL for the [[4x4x4 cube]].

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

== External Links ==
* [http://www.erikku.110mb.com/ELL.html Erik Akkersdijk's ELL algs]
* [http://www.speedsolving.com/forum/showthread.php?t=22737 Kirjava's ELL algs]
* [http://sa967st.webs.com/ell.htm Sa967St'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|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}}

|
=== 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|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}}

|-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' U2 M' U M' U M' U M'}}
{{Alg|U R2 U2' R' F2 U2' R2' F R l F2 D2 R F2 R2' (x)}}

|
Smile =)
|}

==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 to 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|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|M2 U M U2 M' U M2}}
{{Alg|R U' R U R U R U' R' U' R2}}

|-valign="top"
|
=== Z-PLL ===
{{case
|image=ELL Z-PLL.jpg
|name=Z-PLL
|methods=[[EPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=12 [[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'}}

|

=== 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)==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== RF-flip U-PLL a ===
{{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') 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'}}

|

=== LF-flip U-PLL b ===
{{case
|image=ELL 3RF (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) 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}}

|
=== 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}}

|-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|M U' M' U M' U M' U' M' U' M U M2}}
{{Alg|M' U' F2 M2 U' M U F2 U M2}}

|
=== 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|M U M' U' M' U' M' U M' U M U' M2}}
{{Alg|M' U F2 M2 U M U' F2 U' M2}}

|-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}}

|
=== 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}}

|-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'}}

|
=== 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'}}
|}

==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}}

|
=== 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}}

|-valign="top"
|
=== RL-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}}

|
=== FB-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}}

|
=== 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}}

|-valign="top"
|

=== LB-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'}}
|

=== FB-flip H-PLL ===
{{case
|image=ELL H2O.jpg
|name=Opposite flip H-PLL
|methods=[[ELL]]
|optimal=
|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'}}

|}

{{ELL}}

[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Algorithms]]
[[Category:Sub Steps]]

__NOTOC__

ELL

2010-11-22T12:44:48Z

Irontwig: /* FB-flip H-PLL */ LEU aka z RMU group alg

{{Method Infobox
|name=ELL
|image=ELL.png
|proposers=[[Guus Razoux Schultz]]
|year=1981
|anames=
|variants=[[EOLL]], [[EPLL]], [[L5E]]
|steps=1
|algs=29
|moves=~11 [[STM]] (Speed-optimized) Optimal: 11.27 ([[HTM]]), 9.03 ([[STM]])
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
}}

:''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 compleate 3-look ELL for the [[4x4x4 cube]].

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

== External Links ==
* [http://www.erikku.110mb.com/ELL.html Erik Akkersdijk's ELL algs]
* [http://www.speedsolving.com/forum/showthread.php?t=22737 Kirjava's ELL algs]
* [http://sa967st.webs.com/ell.htm Sa967St'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|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}}

|
=== 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|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}}

|-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' U2 M' U M' U M' U M'}}
{{Alg|U R2 U2' R' F2 U2' R2' F R l F2 D2 R F2 R2' (x)}}

|
Smile =)
|}

==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 to 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|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|M2 U M U2 M' U M2}}
{{Alg|R U' R U R U R U' R' U' R2}}

|-valign="top"
|
=== Z-PLL ===
{{case
|image=ELL Z-PLL.jpg
|name=Z-PLL
|methods=[[EPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=12 [[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'}}

|

=== 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)==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== RF-flip U-PLL a ===
{{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') 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'}}

|

=== LF-flip U-PLL b ===
{{case
|image=ELL 3RF (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) 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}}

|
=== 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}}

|-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|M U' M' U M' U M' U' M' U' M U M2}}
{{Alg|M' U' F2 M2 U' M U F2 U M2}}

|
=== 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|M U M' U' M' U' M' U M' U M U' M2}}
{{Alg|M' U F2 M2 U M U' F2 U' M2}}

|-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}}

|
=== 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}}

|-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'}}

|
=== 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'}}
|}

==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}}

|
=== 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}}

|-valign="top"
|
=== RL-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}}

|
=== FB-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}}

|
=== 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}}

|-valign="top"
|

=== LB-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'}}
|

=== FB-flip H-PLL ===
{{case
|image=ELL H2O.jpg
|name=Opposite flip H-PLL
|methods=[[ELL]]
|optimal=
|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}}
{{Alf|(yz) U' r2 U2 r' R' U M' U2 M' U' r R U'}}

|}

{{ELL}}

[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Algorithms]]
[[Category:Sub Steps]]

__NOTOC__

ELL

2010-11-17T21:26:56Z

Irontwig: /* RF-flip U-PLL a */

{{Method Infobox
|name=ELL
|image=ELL.png
|proposers=[[Guus Razoux Schultz]]
|year=1981
|anames=
|variants=[[EOLL]], [[EPLL]], [[L5E]]
|steps=1
|algs=29
|moves=~11 [[STM]] (Speed-optimized) Optimal: 11.27 ([[HTM]]), 9.03 ([[STM]])
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
}}

:''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 compleate 3-look ELL for the [[4x4x4 cube]].

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

== External Links ==
* [http://www.erikku.110mb.com/ELL.html Erik Akkersdijk's ELL algs]
* [http://www.speedsolving.com/forum/showthread.php?t=22737 Kirjava's ELL algs]
* [http://sa967st.webs.com/ell.htm Sa967St'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|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}}

|
=== 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|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}}

|-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' U2 M' U M' U M' U M'}}
{{Alg|U R2 U2' R' F2 U2' R2' F R l F2 D2 R F2 R2' (x)}}

|
Smile =)
|}

==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 to 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|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|M2 U M U2 M' U M2}}
{{Alg|R U' R U R U R U' R' U' R2}}

|-valign="top"
|
=== Z-PLL ===
{{case
|image=ELL Z-PLL.jpg
|name=Z-PLL
|methods=[[EPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=12 [[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'}}

|

=== 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)==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== RF-flip U-PLL a ===
{{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') 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'}}

|

=== LF-flip U-PLL b ===
{{case
|image=ELL 3RF (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) 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}}

|
=== 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}}

|-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|M U' M' U M' U M' U' M' U' M U M2}}
{{Alg|M' U' F2 M2 U' M U F2 U M2}}

|
=== 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|M U M' U' M' U' M' U M' U M U' M2}}
{{Alg|M' U F2 M2 U M U' F2 U' M2}}

|-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}}

|
=== 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}}

|-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'}}

|
=== 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'}}
|}

==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}}

|
=== 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}}

|-valign="top"
|
=== RL-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}}

|
=== FB-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}}

|
=== 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}}

|-valign="top"
|

=== LB-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'}}
|

=== FB-flip H-PLL ===
{{case
|image=ELL H2O.jpg
|name=Opposite flip H-PLL
|methods=[[ELL]]
|optimal=
|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}}

|}

{{ELL}}

[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Algorithms]]
[[Category:Sub Steps]]

__NOTOC__

ELL

2010-11-17T21:23:31Z

Irontwig: /* LB-flip H-PLL */

{{Method Infobox
|name=ELL
|image=ELL.png
|proposers=[[Guus Razoux Schultz]]
|year=1981
|anames=
|variants=[[EOLL]], [[EPLL]], [[L5E]]
|steps=1
|algs=29
|moves=~11 [[STM]] (Speed-optimized) Optimal: 11.27 ([[HTM]]), 9.03 ([[STM]])
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
}}

:''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 compleate 3-look ELL for the [[4x4x4 cube]].

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

== External Links ==
* [http://www.erikku.110mb.com/ELL.html Erik Akkersdijk's ELL algs]
* [http://www.speedsolving.com/forum/showthread.php?t=22737 Kirjava's ELL algs]
* [http://sa967st.webs.com/ell.htm Sa967St'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|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}}

|
=== 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|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}}

|-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' U2 M' U M' U M' U M'}}
{{Alg|U R2 U2' R' F2 U2' R2' F R l F2 D2 R F2 R2' (x)}}

|
Smile =)
|}

==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 to 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|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|M2 U M U2 M' U M2}}
{{Alg|R U' R U R U R U' R' U' R2}}

|-valign="top"
|
=== Z-PLL ===
{{case
|image=ELL Z-PLL.jpg
|name=Z-PLL
|methods=[[EPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=12 [[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'}}

|

=== 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)==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== RF-flip U-PLL a ===
{{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') R U2 R' F' L' B' U2 B L F}}
{{Alg|(y'x') U2 M2 U R U' M2 U R' U}}

|
=== LF-flip U-PLL b ===
{{case
|image=ELL 3RF (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) 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}}

|
=== 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}}

|-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|M U' M' U M' U M' U' M' U' M U M2}}
{{Alg|M' U' F2 M2 U' M U F2 U M2}}

|
=== 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|M U M' U' M' U' M' U M' U M U' M2}}
{{Alg|M' U F2 M2 U M U' F2 U' M2}}

|-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}}

|
=== 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}}

|-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'}}

|
=== 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'}}
|}

==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}}

|
=== 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}}

|-valign="top"
|
=== RL-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}}

|
=== FB-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}}

|
=== 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}}

|-valign="top"
|

=== LB-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'}}
|

=== FB-flip H-PLL ===
{{case
|image=ELL H2O.jpg
|name=Opposite flip H-PLL
|methods=[[ELL]]
|optimal=
|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}}

|}

{{ELL}}

[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Algorithms]]
[[Category:Sub Steps]]

__NOTOC__

COALL

2010-11-16T14:51:34Z

Irontwig: just made it nicer looking

{{Method Infobox
|name=Coall
|image=Winter variation.gif
|proposers=
|year=
|anames=KLL, WW
|variants=[[ZB]], [[Fridrich]], [[VH]]
|steps=4
|algs=63(unique)+21(pll)+27(f2ll w/o mirrors)= 111(all)
|moves=est. 35-50
|purpose=
* [[Speedsolving]]
}}
COALL(Corner Orientation And Last Layer) is an experimental 3x3 method that is a variation of the [[ZB]] method that orients the corners when inserting the last F2L pair (Winter variation). Then solves edge orientation and PLL in one step. Orienting the corners first rather than orienting edges(like in ZB) has the advantage of using less algorithms(using only 111 total compared to zb's 300). It is unknown if and very doudtful if it has ever been used before.

To solve using COALL first solve cross and 3 F2L slots like in fridrich(or any way one wishes). Next make the last F2L pair and use the Winter variation to insert it to orient last layer corners. Finally solve EOLL and PLL in one algorithm.

==Pros==
Uses a fairly large amount of algorithms(21 of which are pll algs).Almost as fast as zb using much less algorithms. Fair reconization.

==Cons==
Has some bad algorithms and having to do another look when enserting F2l for Co in [[Winter variation]].

== See Also ==
* [[ZBLL]]
* [[Winter Variation]]
* [[CPEOLL]]

== External Links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19320 KLL]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?24146-WW-New-speedcubing-method-Zb-variant WW New Speedcubing Method ZB Variant]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Experimental Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

Petrus Method

2010-11-16T09:35:46Z

Irontwig: /* The Steps */ 2gll

{{Method Infobox
|name=Petrus
|image=Petrus_method.gif
|proposers=[[Lars Petrus]]
|year=1981
|anames
|algs=2 to 493 (for the last layer)
|variants
|steps=7
|moves=45 to 60
|purpose=
* [[Fewest Moves]]
* [[Speedsolving]]
}}
The '''Petrus Method''', invented by [[Lars Petrus]], is a block-building [[method]] where the [[F2L]] is solved intuitively with no [[algorithm]]s. Behind [[Fridrich]], it is currently the second most popular speed cubing method in use.

== The Steps ==
The following steps describe a approach suited for beginners, more advanced users might combine steps 1 and 2 and/or 5 and 6 ([[COLL]]) or use a [[Fridrich]] type last layer and do [[OLL]] and then [[PLL]]. If the fifth step is skipped the last layer can be solved with a [[2GLL]] algorithm.

1. First, build a [[2x2x2 block]] anywhere on the cube.

2. Next, you expand the 2x2x2 block to a [[2x2x3 block]], three ways is possible.

3. After that, you fix the "bad edges" or orient the remaining seven edges on the cube that have not been solved.

4. Then, you finish the First Two Layers (F2L). The pure Petrus approach is to create a 1x2x2 block and expand it to a 1x2x3 block to finish off the F2L, not to solve the cross piece and two corner/edge pairs, two ways is possible.

5. Next, you permute the last layer corners, or put them in their proper places (they do not have to be oriented.)

6. Now, you orient the last layer corners, making the whole last layer a solid color.

7. Finally, you permute the last layer edges, without disturbing anything else, to solve the cube.

== Pros ==

The Petrus Method uses fewer moves than the [[Fridrich]] method and most other non-block-building methods. It is more intuitive than the Fridrich method, and it requires far less algorithms. The last layer can even be solved in one look with [[ZBLL]] or [[ZZLL]], however this drastically increases the number of algorithms one must learn.

== Cons ==

It can be sometimes hard (especially for a beginner) to optimize block building, and it's difficult to keep consistently turning throughout the solve.

== Petrus variations ==

There are several other [[sub step|substeps]] that can be used [[EJLS]], [[WV]], [[COLL]], [[JSLS]], and [[ZBLL]], which completes the entire last layer in a single algorithm.

== Petrus as a Beginner Method ==
Used as a beginner method, Petrus requires much more intuition, but also involves learning fewer algorithms. For a tutorial, see the external links below.

== External Links ==

* [http://lar5.com/cube/ Lars Petrus's tutorial]
* [http://petrus-speed.netne.net/ Petrus Speed Website]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=14014 YouTube Beginner Petrus Tutorial]
* YouTube: [http://www.youtube.com/watch?v=EQ9OrFVQw0o Petrus Tutorial] by fallofshadows
* YouTube: [http://www.youtube.com/watch?v=WqXdO2H2FTs Petrus Tutorial] by CuberChris

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Beginner Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Roux method

2010-11-16T08:23:40Z

Irontwig: /* Pros */ RrMU rather than LRMU

{{Method Infobox
|name=Roux
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames
|variants
|steps=4
|moves=[[Speedsolving|Speed]]:48, [[FM]]:28-
|purpose=
* [[Speedsolving]]
* [[Fewest Moves]]
}}

The '''Roux Method''' was invented by [[Gilles Roux]]. Unlike [[Fridrich]] and [[Petrus]], the inventor of this [[method]] has done a sub-15 second average (of 5) with it in competition. This method is influenced by the block building of the Petrus method and the layer on the left and edges last aspects of the [[Waterman method]].

==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 T and Y permutation) to do this.

4. [[Orient]] the 6 remaining edges (UF, UB, UF, UR, DF, DB need to be oriented correctly).

5. Solve the left and right layer edges. After this step, both the left and right side layers should be complete.

6. 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 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. Slice turns can also be slower than using a [[quarter-turn metric]].

== External Links ==

* [http://grrroux.free.fr/method/Intro.html Gilles Roux's tutorial]
* [http://wafflelikescubes.webs.com/ Waffle's Roux Site]
* [http://rouxcentral.forummotion.com/forum.htm Roux Central Forums]
* Wikia: [http://rubiks.wikia.com/wiki/Roux_Method Roux Method]
* [http://www.speedsolving.com/forum/showthread.php?t=11506 Waffle's Roux Tutorial]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Roux method

2010-11-16T08:21:59Z

Irontwig:

{{Method Infobox
|name=Roux
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames
|variants
|steps=4
|moves=[[Speedsolving|Speed]]:48, [[FM]]:28-
|purpose=
* [[Speedsolving]]
* [[Fewest Moves]]
}}

The '''Roux Method''' was invented by [[Gilles Roux]]. Unlike [[Fridrich]] and [[Petrus]], the inventor of this [[method]] has done a sub-15 second average (of 5) with it in competition. This method is influenced by the block building of the Petrus method and the layer on the left and edges last aspects of the [[Waterman method]].

==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 T and Y permutation) to do this.

4. [[Orient]] the 6 remaining edges (UF, UB, UF, UR, DF, DB need to be oriented correctly).

5. Solve the left and right layer edges. After this step, both the left and right side layers should be complete.

6. 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 with L, 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. Slice turns can also be slower than using a [[quarter-turn metric]].

== External Links ==

* [http://grrroux.free.fr/method/Intro.html Gilles Roux's tutorial]
* [http://wafflelikescubes.webs.com/ Waffle's Roux Site]
* [http://rouxcentral.forummotion.com/forum.htm Roux Central Forums]
* Wikia: [http://rubiks.wikia.com/wiki/Roux_Method Roux Method]
* [http://www.speedsolving.com/forum/showthread.php?t=11506 Waffle's Roux Tutorial]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Roux method

2010-11-16T08:21:11Z

Irontwig:

{{Method Infobox
|name=Roux
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames
|variants
|steps=4
|moves=[[Speedsolving|Speed]]:48, [[FM]]:28-
|purpose=
* [[Speedsolving]]
* [[Fewest Moves]]
}}

The '''Roux Method''' was invented by [[Gilles Roux]]. Unlike [[Fridrich]] and [[Petrus]], the inventor of this [[method]] has done a sub-15 second average (of 5) with it in competition. This method is influenced by the block building of the Petrus method and the layer on the left aspect and edges last aspects of the [[Waterman method]].

==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 T and Y permutation) to do this.

4. [[Orient]] the 6 remaining edges (UF, UB, UF, UR, DF, DB need to be oriented correctly).

5. Solve the left and right layer edges. After this step, both the left and right side layers should be complete.

6. 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 with L, 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. Slice turns can also be slower than using a [[quarter-turn metric]].

== External Links ==

* [http://grrroux.free.fr/method/Intro.html Gilles Roux's tutorial]
* [http://wafflelikescubes.webs.com/ Waffle's Roux Site]
* [http://rouxcentral.forummotion.com/forum.htm Roux Central Forums]
* Wikia: [http://rubiks.wikia.com/wiki/Roux_Method Roux Method]
* [http://www.speedsolving.com/forum/showthread.php?t=11506 Waffle's Roux Tutorial]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Waterman method

2010-11-16T08:18:23Z

Irontwig: #algs and made steps 345 into 3abc to make it 3 steps like in the infobox and on jelinek's site

{{Method Infobox
|name=Waterman
|image=Waterman_method.gif
|proposers=[[Marc Waterman]]
|year=1982
|algs=167 Total 42 (Step 2) 125 (Step 3)
|anames
|variants
|steps=3
|moves=40 to 45 [[STM]], over 50 [[HTM]]
|purpose=
* [[Speedsolving]]
}}
The '''Waterman Method''' is a method for solving the [[3x3x3 Cube]] which was invented by [[Marc Waterman]] in the 1980s. The method is based on [[Corners First]] methods but is efficient enough to be used for advanced speedsolving (average times of under 20 seconds). The steps are as follows:
* Step 1: Solve one layer of the cube. The original way to do this is by first putting together the corners and then solving the center and edges together. This can also be done with [[block building]] (start with a 1x2x3 block as with [[Roux]] and then fill in the last three pieces).
* Step 2: Solve the corners of the opposite layer. This is done in one step in the style of [[CxLL]]. After this step, turn the cube so that the solved layer is on L.
* Step 3a: Solve two of the edges on R, while at the same time placing a third somewhere in the R layer.
* Step 3b: Finish the R edges while orienting the M edges, all in one algorithm. This step is difficult to learn and has around 80 algorithms, but the algorithms mostly use only M, R, r, and U moves, so this is a fast step.
* Step 3c: Solve the M edges. This is trivial and there are only a few possible cases, all very fast.

If you are truly interested in learning this method you should check out [http://rubikscube.info/waterman/index.php Josef Jelinek's webpage] which has very thorough descriptions as well as a complete list of algorithms for the last four steps. He also has a copy of the original booklet containing the method.

== See Also ==
* [[Corners First]]
* [[Roux Method]]

== External Links ==

* [http://rubikscube.info/waterman/index.php rubikscube.info Waterman Tutorial]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:2x2x2 Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:2x2x2 Speedsolving Methods]]

Petrus Method

2010-11-16T08:08:23Z

Irontwig: #algs

{{Method Infobox
|name=Petrus
|image=Petrus_method.gif
|proposers=[[Lars Petrus]]
|year=1981
|anames
|algs=2 to 493 (for the last layer)
|variants
|steps=7
|moves=45 to 60
|purpose=
* [[Fewest Moves]]
* [[Speedsolving]]
}}
The '''Petrus Method''', invented by [[Lars Petrus]], is a block-building [[method]] where the [[F2L]] is solved intuitively with no [[algorithm]]s. Behind [[Fridrich]], it is currently the second most popular speed cubing method in use.

== The Steps ==
The following steps describe a approach suited for beginners, more advanced users might combine steps 1 and 2 and/or 5 and 6 ([[COLL]]) or use a [[Fridrich]] type last layer and do [[OLL]] and then [[PLL]].

1. First, build a [[2x2x2 block]] anywhere on the cube.

2. Next, you expand the 2x2x2 block to a [[2x2x3 block]], three ways is possible.

3. After that, you fix the "bad edges" or orient the remaining seven edges on the cube that have not been solved.

4. Then, you finish the First Two Layers (F2L). The pure Petrus approach is to create a 1x2x2 block and expand it to a 1x2x3 block to finish off the F2L, not to solve the cross piece and two corner/edge pairs, two ways is possible.

5. Next, you permute the last layer corners, or put them in their proper places (they do not have to be oriented.)

6. Now, you orient the last layer corners, making the whole last layer a solid color.

7. Finally, you permute the last layer edges, without disturbing anything else, to solve the cube.

== Pros ==

The Petrus Method uses fewer moves than the [[Fridrich]] method and most other non-block-building methods. It is more intuitive than the Fridrich method, and it requires far less algorithms. The last layer can even be solved in one look with [[ZBLL]] or [[ZZLL]], however this drastically increases the number of algorithms one must learn.

== Cons ==

It can be sometimes hard (especially for a beginner) to optimize block building, and it's difficult to keep consistently turning throughout the solve.

== Petrus variations ==

There are several other [[sub step|substeps]] that can be used [[EJLS]], [[WV]], [[COLL]], [[JSLS]], and [[ZBLL]], which completes the entire last layer in a single algorithm.

== Petrus as a Beginner Method ==
Used as a beginner method, Petrus requires much more intuition, but also involves learning fewer algorithms. For a tutorial, see the external links below.

== External Links ==

* [http://lar5.com/cube/ Lars Petrus's tutorial]
* [http://petrus-speed.netne.net/ Petrus Speed Website]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=14014 YouTube Beginner Petrus Tutorial]
* YouTube: [http://www.youtube.com/watch?v=EQ9OrFVQw0o Petrus Tutorial] by fallofshadows
* YouTube: [http://www.youtube.com/watch?v=WqXdO2H2FTs Petrus Tutorial] by CuberChris

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Beginner Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Category:Fewest Moves techniques

2010-11-15T20:13:58Z

Irontwig: removed the empty conj and comm sections

This page introduces some tips and techniques to help you solve the cube in as [[Fewest Moves|few moves]] as possible.

The best results can be obtained when all techniques are controlled. It is strongly advised not to follow a strict pattern, for example a [[3x3x3 Speedsolving Methods|speedsolving method]]. However some algorithms learned from a speedsolving method will give some advantages in some cases. The most useful [[Fewest Moves Methods|methods]] are [[Heise]], [[Petrus]], [[Fridrich]], [[Roux]] and [[ZBLL]].

== Block Building ==
Best start for an FMC is block building technique. Try to build a [[2x2x2 block]] then a [[2x2x3 block]]. After the 2x2x2 block you have 3 sides to extend it to a 2x2x3. Explore all of them. After the 2x2x3 block

== Pair Insertion ==
when inserting Fridrich-pairs in F2L don't get stuck with you speedcubing methods but try some alternatives and check each of them for

== Pseudoblocks or Pre-scramble-moves==
Like [[Heise Method]] you can build pseudo blocks, which are adjacent 1x2x2 blocks or c/e pairs that are not adjacent but need an extra turn to get those blocks at the right color-centre. Solving with pseudo blocks needs can be very difficult and needs a lot of experience. As an alternative you can replace a pseudo block by a pre-scramble-move to give more oversight over your solve.

A pre-scramble move is a move you apply before the scramble and which allows you to find more possible solutions. Of course you must not forget to add the premove at the end of your solution.

== Inserted Moves (single) ==
Sometimes after a promising start you can't find a good continuation. Say you have solved a 2x2x2 block, but after that there's nothing good. By stepping through the solution you might see that at one place there's no 2x2x2-pieces on U, at that place you can try to insert U, U' or U2 and see if a better continuation is possible.

== Inserted Algorithms/Commutators ==
A very powerful technique in FMC is to solve everything except 3-5 corners and then insert 8 move [[commutators]] that cycle three corners earlier in the solution. Since there many corner configurations that can be solved in 8 moves often one will cancel moves, and thus one corner cycle will add less than 8 moves to the total solution length. Edge cycles are not used as often FMC is judged in [[HTM]] and edge cycles often involve slice moves that are counted as two moves. Some people use stickers to more easily track the unsolved pieces through the solution.

== Freestyle Solving ==
If you see some opportunity to solve a lot of blocks without any (known) pattern you could try to solve it. When leaving a maximum of 4 edges and 4 corners try to conjugate them to 1 face during a solve. Then use pre-scramble-moves or a second cube to solve that face / LL

== LL-algorithms ==
sometimes you solve a lot of LL blocks using a very short LL algorithm, 8 or 9 moves maximum. Try to learn short LL algorithms in such a way that you know what it does to corners and edges. Start with the length-6 LL-alg, then the three 7-move LL-algs, the five 8-move LL-algs, and so on. You are really an expert when learning all LL-algs up to 10 moves.

== Other Tips ==

* Do not use moves that turn the cube!

* Use fixed colors for up & front to enhance recognition!

* Better still, look at the centre of the face you are turning, it tells wich side it is ("White" = U and so on), then orientation does not matter anymore.

* Write down promising moves, do not wait till the very end!

* Create a backup solve!

* Learn to scramble fast, it can save a lot of time during a 1-hour solve.

* Bring stickers (for insertions) and extra cubes during a competition.

== See Also ==

* [[Fewest Moves]]
* [[Commutators]]
* [[Niklas]]
* [[God's Algorithm]]
* [[Fewest Moves Methods]]
* [[Puzzle Theory]]

== External Links ==

* [http://www.ryanheise.com/cube/fundamental_techniques.html Ryan Heise's page on intuitive solving techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=1566 Fewest Moves: Tips and Techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?p=221756 The FMC thread]

[[Category:Fewest Moves Methods]]

{{Stub}}

__NOTOC__

Category:Fewest Moves techniques

2010-11-15T20:12:14Z

Irontwig: /* Inserted Moves (single) */ added description

This page introduces some tips and techniques to help you solve the cube in as [[Fewest Moves|few moves]] as possible.

The best results can be obtained when all techniques are controlled. It is strongly advised not to follow a strict pattern, for example a [[3x3x3 Speedsolving Methods|speedsolving method]]. However some algorithms learned from a speedsolving method will give some advantages in some cases. The most useful [[Fewest Moves Methods|methods]] are [[Heise]], [[Petrus]], [[Fridrich]], [[Roux]] and [[ZBLL]].

== Block Building ==
Best start for an FMC is block building technique. Try to build a [[2x2x2 block]] then a [[2x2x3 block]]. After the 2x2x2 block you have 3 sides to extend it to a 2x2x3. Explore all of them. After the 2x2x3 block

== Pair Insertion ==
when inserting Fridrich-pairs in F2L don't get stuck with you speedcubing methods but try some alternatives and check each of them for

== Commutators ==

== Conjugates ==

== Pseudoblocks or Pre-scramble-moves==
Like [[Heise Method]] you can build pseudo blocks, which are adjacent 1x2x2 blocks or c/e pairs that are not adjacent but need an extra turn to get those blocks at the right color-centre. Solving with pseudo blocks needs can be very difficult and needs a lot of experience. As an alternative you can replace a pseudo block by a pre-scramble-move to give more oversight over your solve.

A pre-scramble move is a move you apply before the scramble and which allows you to find more possible solutions. Of course you must not forget to add the premove at the end of your solution.

== Inserted Moves (single) ==
Sometimes after a promising start you can't find a good continuation. Say you have solved a 2x2x2 block, but after that there's nothing good. By stepping through the solution you might see that at one place there's no 2x2x2-pieces on U, at that place you can try to insert U, U' or U2 and see if a better continuation is possible.

== Inserted Algorithms/Commutators ==
A very powerful technique in FMC is to solve everything except 3-5 corners and then insert 8 move [[commutators]] that cycle three corners earlier in the solution. Since there many corner configurations that can be solved in 8 moves often one will cancel moves, and thus one corner cycle will add less than 8 moves to the total solution length. Edge cycles are not used as often FMC is judged in [[HTM]] and edge cycles often involve slice moves that are counted as two moves. Some people use stickers to more easily track the unsolved pieces through the solution.

== Freestyle Solving ==
If you see some opportunity to solve a lot of blocks without any (known) pattern you could try to solve it. When leaving a maximum of 4 edges and 4 corners try to conjugate them to 1 face during a solve. Then use pre-scramble-moves or a second cube to solve that face / LL

== LL-algorithms ==
sometimes you solve a lot of LL blocks using a very short LL algorithm, 8 or 9 moves maximum. Try to learn short LL algorithms in such a way that you know what it does to corners and edges. Start with the length-6 LL-alg, then the three 7-move LL-algs, the five 8-move LL-algs, and so on. You are really an expert when learning all LL-algs up to 10 moves.

== Other Tips ==

* Do not use moves that turn the cube!

* Use fixed colors for up & front to enhance recognition!

* Better still, look at the centre of the face you are turning, it tells wich side it is ("White" = U and so on), then orientation does not matter anymore.

* Write down promising moves, do not wait till the very end!

* Create a backup solve!

* Learn to scramble fast, it can save a lot of time during a 1-hour solve.

* Bring stickers (for insertions) and extra cubes during a competition.

== See Also ==

* [[Fewest Moves]]
* [[Commutators]]
* [[Niklas]]
* [[God's Algorithm]]
* [[Fewest Moves Methods]]
* [[Puzzle Theory]]

== External Links ==

* [http://www.ryanheise.com/cube/fundamental_techniques.html Ryan Heise's page on intuitive solving techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=1566 Fewest Moves: Tips and Techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?p=221756 The FMC thread]

[[Category:Fewest Moves Methods]]

{{Stub}}

__NOTOC__

Category:Fewest Moves techniques

2010-11-15T20:07:30Z

Irontwig: /* Inserted Algorithms/Commutators */ added description

This page introduces some tips and techniques to help you solve the cube in as [[Fewest Moves|few moves]] as possible.

The best results can be obtained when all techniques are controlled. It is strongly advised not to follow a strict pattern, for example a [[3x3x3 Speedsolving Methods|speedsolving method]]. However some algorithms learned from a speedsolving method will give some advantages in some cases. The most useful [[Fewest Moves Methods|methods]] are [[Heise]], [[Petrus]], [[Fridrich]], [[Roux]] and [[ZBLL]].

== Block Building ==
Best start for an FMC is block building technique. Try to build a [[2x2x2 block]] then a [[2x2x3 block]]. After the 2x2x2 block you have 3 sides to extend it to a 2x2x3. Explore all of them. After the 2x2x3 block

== Pair Insertion ==
when inserting Fridrich-pairs in F2L don't get stuck with you speedcubing methods but try some alternatives and check each of them for

== Commutators ==

== Conjugates ==

== Pseudoblocks or Pre-scramble-moves==
Like [[Heise Method]] you can build pseudo blocks, which are adjacent 1x2x2 blocks or c/e pairs that are not adjacent but need an extra turn to get those blocks at the right color-centre. Solving with pseudo blocks needs can be very difficult and needs a lot of experience. As an alternative you can replace a pseudo block by a pre-scramble-move to give more oversight over your solve.

A pre-scramble move is a move you apply before the scramble and which allows you to find more possible solutions. Of course you must not forget to add the premove at the end of your solution.

== Inserted Moves (single) ==

== Inserted Algorithms/Commutators ==
A very powerful technique in FMC is to solve everything except 3-5 corners and then insert 8 move [[commutators]] that cycle three corners earlier in the solution. Since there many corner configurations that can be solved in 8 moves often one will cancel moves, and thus one corner cycle will add less than 8 moves to the total solution length. Edge cycles are not used as often FMC is judged in [[HTM]] and edge cycles often involve slice moves that are counted as two moves. Some people use stickers to more easily track the unsolved pieces through the solution.

== Freestyle Solving ==
If you see some opportunity to solve a lot of blocks without any (known) pattern you could try to solve it. When leaving a maximum of 4 edges and 4 corners try to conjugate them to 1 face during a solve. Then use pre-scramble-moves or a second cube to solve that face / LL

== LL-algorithms ==
sometimes you solve a lot of LL blocks using a very short LL algorithm, 8 or 9 moves maximum. Try to learn short LL algorithms in such a way that you know what it does to corners and edges. Start with the length-6 LL-alg, then the three 7-move LL-algs, the five 8-move LL-algs, and so on. You are really an expert when learning all LL-algs up to 10 moves.

== Other Tips ==

* Do not use moves that turn the cube!

* Use fixed colors for up & front to enhance recognition!

* Better still, look at the centre of the face you are turning, it tells wich side it is ("White" = U and so on), then orientation does not matter anymore.

* Write down promising moves, do not wait till the very end!

* Create a backup solve!

* Learn to scramble fast, it can save a lot of time during a 1-hour solve.

* Bring stickers (for insertions) and extra cubes during a competition.

== See Also ==

* [[Fewest Moves]]
* [[Commutators]]
* [[Niklas]]
* [[God's Algorithm]]
* [[Fewest Moves Methods]]
* [[Puzzle Theory]]

== External Links ==

* [http://www.ryanheise.com/cube/fundamental_techniques.html Ryan Heise's page on intuitive solving techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=1566 Fewest Moves: Tips and Techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?p=221756 The FMC thread]

[[Category:Fewest Moves Methods]]

{{Stub}}

__NOTOC__

Petrus Method

2010-11-15T19:49:06Z

Irontwig: /* The Steps */

{{Method Infobox
|name=Petrus
|image=Petrus_method.gif
|proposers=[[Lars Petrus]]
|year=1981
|anames
|variants
|steps=7
|moves=45 to 60
|purpose=
* [[Fewest Moves]]
* [[Speedsolving]]
}}
The '''Petrus Method''', invented by [[Lars Petrus]], is a block-building [[method]] where the [[F2L]] is solved intuitively with no [[algorithm]]s. Behind [[Fridrich]], it is currently the second most popular speed cubing method in use.

== The Steps ==
The following steps describe a approach suited for beginners, more advanced users might combine steps 1 and 2 and/or 5 and 6 ([[COLL]]) or use a [[Fridrich]] type last layer and do [[OLL]] and then [[PLL]].

1. First, build a [[2x2x2 block]] anywhere on the cube.

2. Next, you expand the 2x2x2 block to a [[2x2x3 block]], three ways is possible.

3. After that, you fix the "bad edges" or orient the remaining seven edges on the cube that have not been solved.

4. Then, you finish the First Two Layers (F2L). The pure Petrus approach is to create a 1x2x2 block and expand it to a 1x2x3 block to finish off the F2L, not to solve the cross piece and two corner/edge pairs, two ways is possible.

5. Next, you permute the last layer corners, or put them in their proper places (they do not have to be oriented.)

6. Now, you orient the last layer corners, making the whole last layer a solid color.

7. Finally, you permute the last layer edges, without disturbing anything else, to solve the cube.

== Pros ==

The Petrus Method uses fewer moves than the [[Fridrich]] method and most other non-block-building methods. It is more intuitive than the Fridrich method, and it requires far less algorithms. The last layer can even be solved in one look with [[ZBLL]] or [[ZZLL]], however this drastically increases the number of algorithms one must learn.

== Cons ==

It can be sometimes hard (especially for a beginner) to optimize block building, and it's difficult to keep consistently turning throughout the solve.

== Petrus variations ==

There are several other [[sub step|substeps]] that can be used [[EJLS]], [[WV]], [[COLL]], [[JSLS]], and [[ZBLL]], which completes the entire last layer in a single algorithm.

== Petrus as a Beginner Method ==
Used as a beginner method, Petrus requires much more intuition, but also involves learning fewer algorithms. For a tutorial, see the external links below.

== External Links ==

* [http://lar5.com/cube/ Lars Petrus's tutorial]
* [http://petrus-speed.netne.net/ Petrus Speed Website]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=14014 YouTube Beginner Petrus Tutorial]
* YouTube: [http://www.youtube.com/watch?v=EQ9OrFVQw0o Petrus Tutorial] by fallofshadows
* YouTube: [http://www.youtube.com/watch?v=WqXdO2H2FTs Petrus Tutorial] by CuberChris

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Beginner Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Petrus Method

2010-11-15T19:47:53Z

Irontwig: /* The Steps */

{{Method Infobox
|name=Petrus
|image=Petrus_method.gif
|proposers=[[Lars Petrus]]
|year=1981
|anames
|variants
|steps=7
|moves=45 to 60
|purpose=
* [[Fewest Moves]]
* [[Speedsolving]]
}}
The '''Petrus Method''', invented by [[Lars Petrus]], is a block-building [[method]] where the [[F2L]] is solved intuitively with no [[algorithm]]s. Behind [[Fridrich]], it is currently the second most popular speed cubing method in use.

== The Steps ==
The following steps describe a approach suited for beginners, more advanced users might combine steps 1 and 2, 5 and 6 ([[COLL]]) or use a [[Fridrich]] type last layer and do [[OLL]] and then [[PLL]].

1. First, build a [[2x2x2 block]] anywhere on the cube.

2. Next, you expand the 2x2x2 block to a [[2x2x3 block]], three ways is possible.

3. After that, you fix the "bad edges" or orient the remaining seven edges on the cube that have not been solved.

4. Then, you finish the First Two Layers (F2L). The pure Petrus approach is to create a 1x2x2 block and expand it to a 1x2x3 block to finish off the F2L, not to solve the cross piece and two corner/edge pairs, two ways is possible.

5. Next, you permute the last layer corners, or put them in their proper places (they do not have to be oriented.)

6. Now, you orient the last layer corners, making the whole last layer a solid color.

7. Finally, you permute the last layer edges, without disturbing anything else, to solve the cube.

== Pros ==

The Petrus Method uses fewer moves than the [[Fridrich]] method and most other non-block-building methods. It is more intuitive than the Fridrich method, and it requires far less algorithms. The last layer can even be solved in one look with [[ZBLL]] or [[ZZLL]], however this drastically increases the number of algorithms one must learn.

== Cons ==

It can be sometimes hard (especially for a beginner) to optimize block building, and it's difficult to keep consistently turning throughout the solve.

== Petrus variations ==

There are several other [[sub step|substeps]] that can be used [[EJLS]], [[WV]], [[COLL]], [[JSLS]], and [[ZBLL]], which completes the entire last layer in a single algorithm.

== Petrus as a Beginner Method ==
Used as a beginner method, Petrus requires much more intuition, but also involves learning fewer algorithms. For a tutorial, see the external links below.

== External Links ==

* [http://lar5.com/cube/ Lars Petrus's tutorial]
* [http://petrus-speed.netne.net/ Petrus Speed Website]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=14014 YouTube Beginner Petrus Tutorial]
* YouTube: [http://www.youtube.com/watch?v=EQ9OrFVQw0o Petrus Tutorial] by fallofshadows
* YouTube: [http://www.youtube.com/watch?v=WqXdO2H2FTs Petrus Tutorial] by CuberChris

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Beginner Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Petrus Method

2010-11-15T19:47:27Z

Irontwig: /* The Steps */ added coll and oll

{{Method Infobox
|name=Petrus
|image=Petrus_method.gif
|proposers=[[Lars Petrus]]
|year=1981
|anames
|variants
|steps=7
|moves=45 to 60
|purpose=
* [[Fewest Moves]]
* [[Speedsolving]]
}}
The '''Petrus Method''', invented by [[Lars Petrus]], is a block-building [[method]] where the [[F2L]] is solved intuitively with no [[algorithm]]s. Behind [[Fridrich]], it is currently the second most popular speed cubing method in use.

== The Steps ==
The following steps describe a approach suited for beginners, more advanced users might combine steps 1 and 2, 5 and 6 ([[COLL]]) or use a [[Fridrich]] type last layer and do [[OLL]] and then [[PLL]]

1. First, build a [[2x2x2 block]] anywhere on the cube.

2. Next, you expand the 2x2x2 block to a [[2x2x3 block]], three ways is possible.

3. After that, you fix the "bad edges" or orient the remaining seven edges on the cube that have not been solved.

4. Then, you finish the First Two Layers (F2L). The pure Petrus approach is to create a 1x2x2 block and expand it to a 1x2x3 block to finish off the F2L, not to solve the cross piece and two corner/edge pairs, two ways is possible.

5. Next, you permute the last layer corners, or put them in their proper places (they do not have to be oriented.)

6. Now, you orient the last layer corners, making the whole last layer a solid color.

7. Finally, you permute the last layer edges, without disturbing anything else, to solve the cube.

== Pros ==

The Petrus Method uses fewer moves than the [[Fridrich]] method and most other non-block-building methods. It is more intuitive than the Fridrich method, and it requires far less algorithms. The last layer can even be solved in one look with [[ZBLL]] or [[ZZLL]], however this drastically increases the number of algorithms one must learn.

== Cons ==

It can be sometimes hard (especially for a beginner) to optimize block building, and it's difficult to keep consistently turning throughout the solve.

== Petrus variations ==

There are several other [[sub step|substeps]] that can be used [[EJLS]], [[WV]], [[COLL]], [[JSLS]], and [[ZBLL]], which completes the entire last layer in a single algorithm.

== Petrus as a Beginner Method ==
Used as a beginner method, Petrus requires much more intuition, but also involves learning fewer algorithms. For a tutorial, see the external links below.

== External Links ==

* [http://lar5.com/cube/ Lars Petrus's tutorial]
* [http://petrus-speed.netne.net/ Petrus Speed Website]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=14014 YouTube Beginner Petrus Tutorial]
* YouTube: [http://www.youtube.com/watch?v=EQ9OrFVQw0o Petrus Tutorial] by fallofshadows
* YouTube: [http://www.youtube.com/watch?v=WqXdO2H2FTs Petrus Tutorial] by CuberChris

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Beginner Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

2GLL

2010-11-13T09:41:54Z

Irontwig: Petrus6+7 alt name

{{Method Infobox
|name=2GLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Timothy Sun]], [[Lars Petrus]]
|year=2005?
|anames=Step 6+7 ([[Petrus method]])
|steps=1
|algs=85
|moves=~13?
|purpose=
* [[Speedsolving]]
}}

'''2GLL''' (short for ''2-Generator Last Layer'') is a subset of [[ZBLL]]. ZBLL is meant to orient and permute corners of the last layer while permuting the edges, and comes up to hefty 493 cases. Taking the subset of this that does not permute the corners, and instead only orients the corners and permutes the edges, these cases can be reduced to 85, while also having each case be able to be solved by a "2-generator" algorithm (one that uses only 2 algorithms, in this case usually the R and U faces.

2GLL is very useful when one has a system for permuting the [[LL]] corners and orienting the LL edges prior to getting to the last layer. One system that achieves rooting off of [[CFOP]] would be to do the [[cross]], three [[F2L]] pairs, [[ELS]], and lastly [[CPLS]]. While this could be a good system to branch off of [[CFOP]], most would agree that the system would work better on methods which naturally orient the edges before getting to the final slot of [[F2L]] such as [[ZZ]] or [[Petrus]]. Another method to use during [[CFOP]] to accomplish 2GLL would be to orient edges while doing 'normal' [[F2L]], perhaps having two or more algs for each [[F2L]] case, influencing different edge orientations.

===Learning Approach===

Much like in [[ZBLL]] and [[COLL]], the cases of 2GLL can be divided into seven individual sets to learn and recognize by. These sets are typically called Sune, Anti-Sune, H (or Double-Sune), Pi, U, T, L, and [[EPLL]]. Each 2GLL is typically recognized by the [[COLL]] of the case, followed by the edge cycle that is present (see [[EPLL]]. Typically, there are 12 cases per [[COLL[[, but some can be eliminated due to mirrors and the like.

===Recognition===

For every subset, one can recognize their case by the means of the following system:

1. Recognize the corner orientation case. (one of 7)

1.5? - Some people prefer to AUF right now in order to have their corners not only in their relatively correct spot, but also in their *actual* correct spot. As in, rather than having the corners a U2 away from being correctly permuted, they would do a d2, then recognize from there, or something along those lines.
Because a good percentage of the 'good' algs have AUFs and/or initial rotations anyway, it doesn't make all that much of a difference, so if it helps you to recognize this way, do so.

2. Recognize the edge cycle by looking only at the FU and RU stickers in relation to the UFR piece.

3. Apply the corresponding algorithm.

Step 1 should be fairly easy to recognize, as there are only seven possible cases, and if you have used another [[LL]] technique, then you have most likely had to recognize corner orientation before. When you see the case, simply adjust the upper-most face in order to get the case into the angle you typically recognize from, and continue to the next step.

Step 2 is a tiny bit more complicated to recognize, but once it is gotten used to, it can really be quite easy.
Since there are a possible of 12 edge permutations (assuming that the puzzle is solvable and the corners are permuted) one has to be prepared for all 12.

Here is one system to recognize these in:
- If you see that both the FU and RU edges are correctly positioned between corners that have been pre-permuted, then this is a "good" case, meaning that all of the edges are correctly positioned.

- If you see that both the FU and RU edges are opposite colors of what they should be (red/orange or blue/green on the standard color scheme) then this is an "H perm" case.

- If you see that the FU piece and RU piece should be switched with each other (a visible 2-cycle) then you have "Z1," one of two possible Z perms.
- If you see that FU needs to go to LU while RU needs to go to BU, then you have the other Z perm, "Z2."

If the case does not follow into any of the above, then
- For the remaining 8 cases, the U perms, without rotating the cube, the solver should ask themselves the following:
--"Is this cycle going clockwise or anti-clockwise?"
--"Where is the edge that is correct?"

Both of these questions can be answered by figuring out the following:
--"Where does the FU sticker need to be in respect to the corner permutation?"
--"Where does the RU sticker need to be in respect to the corner permutation?"

Simply put, try to trace a 3-cycle of edges in the last layer. The piece that does not belong combined with the direction of the cycle is a great way to recognize and notate the cycle.

As a quick example, scramble a standard 3x3x3 Rubik's Cube with the following:
R' U2 R U R' U R U' R' U' R U' R' U2 R

Firstly, look at the corner orientation. You should be able to find this as a [[Headlights]] case. Put these headlights in the back - if you ever decide to learn COLL or ZBLL, this is how you will probably recognize headlights cases, so it's a good idea to start that way now!
Next note that this is not a "good", H, or Z case, and therefore must be a Uperm of sorts.
Next, note that this is a clockwise U perm - one that does not cycle RU.
That's it.
Right then, you should be able to apply your alg, AUF, and slam your cube down, stopping the timer.

For this case, y R' U2 R U R' U R U R' U' R U' R' U2 R is a nice alg. Success.

Before looking too far into 2GLL, it would probably be best to check out [[CPLS]] first.

== See Also ==

* [[ZB Method]]
* [[ZBF2L]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[ZBLL]]

== External Links ==
* [http://www.speedsolving.com/forum/showpost.php?p=445774&postcount=207 Stachu's 2GLL list] - complete
* [http://www.speedsolving.com/forum/showthread.php?p=454801#post454801 SpeedSolving.com thread]
* [http://lar5.com/cube/xMain.html Lars Petrus' 2GLL algorithms]
* [http://boca.bee.pl/cat.php?l=pl&cat=th&m=zz&ch=d BOCA 2GLL algs]

[[Category:Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

CxLL

2010-09-13T15:25:30Z

Irontwig: /* See Also */ ollcp

'''Corners Last Layer''' is a group of methods collectively known as '''C*LL''' or '''CxLL''' that solve the last layer corners in one algorithm. Each method has certain restrictions that apply, and each can affect other pieces in different ways. For example, [[CMLL]] allows movement of the M layer and allows destruction of the UL and UR edges. Two other common sets of algorithms include [[CLL]] and [[COLL]]. These differ from the fact that the latter preserves last layer's edges orientation while the former does not necessarily. In some cases, CLL will give shorter algorithms due to lack of restrictions.

C*LL is useful for the [[2x2x2]], which has no edges, and also for [[CF|corners first]], which solves edges after the corners. C*LL is also used in [[Roux Method|Roux's method]], and is specifically known as CMLL. It is of course also useful after a normal F2L is compleated, COLL often together with the [[Petrus method]] or in the Fridrich variation, with a preceeding VH or ZB F2L. CLL for 3x3 solves the LL corners before anything is done to the edges, that then are solved using [[ELL]] (the Guus method), probably the most effective way (that is used) to solve a compleatly scrambled LL in two steps.

== The lists ==
=== Browse ===

At bottom of each page there is a [[CxLL Algorithms#Navigator|navigator]] that you use to browse from page to page by clicking the names under the thumbnail images.

=== Case Descriptions ===
There are 2 tables for case descriptions. The first is the positional recognition system and the second is the hyperorientation recognition system.

'''Positional System:'''
{|
| valign="top"| [[image:CxLL Stickers.jpg|96px|]]
| valign="top"| All colour patterns showed in the decriptions assumes white on top and green in front (official colour sheme). The description images divided into four quadrants makes one corner each as showed in the image to the left. The stickers showed in the images at the pages are whites for the four belonging to the U face and four more, the important recognition stickers, the rest of the stickers of the corners you can ignore in recognition, that's why those are not displayed in the images.
|}

'''Hyperorientation System:'''
{|
| valign="top"| [[image:Hyper CxLL T U.jpg|96px|]]
| valign="top"| All color patterns show the orientation case in white. The blue and green stickers show the position of opposite color stickers (red/orange, blue/green, white/yellow on the standard scheme).
|}
In case descriptions there are sometimes links to the "inverse case", that is the case you get if you do N-PLL on the case you got (or faster R2 F2 R2).

=== The Algorithms ===
In each page there is a list of algorithms for different CxLL based methods: topmost is COLL, followed by CLL, CMLL etc. An algorithm suitable for COLL preserves the edge orientation. If not, it is a CLL algorithm. If the algorithm changes the M slice then it is a CMLL. If it changes F2L edges it is a Corners First/2x2x2 algorithm and if it changes FL corner permutation it is a EG 0/1 alg (all levels are also useful for [[Ortega]]).
CLLEF acts in the same way as COLL, except that it flips 4 edges (to be used with OLLs 1, 2, 3, 4, 17, 18 & 19).

== Beginners ==
For a beginner who likes a stepping stone it is possible to do CxLL in two steps; first orientation and then permutation. In the navigator these algs are the grey cases having single letter names, orientations are in the leftmost row and permutations in the topmost line.

== See Also ==
* [[CLL]]
* [[COLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=COLL COLL Algorithm Database]
* [[CMLL]]
* [[CLLEF]]
* [[OLLCP]]
* [[CxLL algorithms]]
* [[Last Three Corners]]
* [[Last Four Corners]]

== External Links ==
* [http://www.speedsolving.com/forum/showthread.php?t=6365 Thread discussing this CxLL page]
* [http://www.speedsolving.com/forum/showthread.php?t=6497 Thread discussing 2x2x2 algorithms]
* [http://home.comcast.net/~quadricode/hyperorientations/ Hyperorientations]: A proposed method for recognizing C*LL cases easily.
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12864 CxLL Recognition]

== Navigator ==
{{CxLLnav}}

[[Category:Methods]]
[[Category:2x2x2 Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Algorithms]]
[[Category:Sub Steps]]

COLL

2010-09-13T15:24:17Z

Irontwig: /* See Also */ ollcp

{{Method Infobox
|name=COLL
|image=OLLCP.png
|proposers=[[Lars Petrus]]
|variants=[[CLLEF]],[[OLLCP]]
|anames=Steps 5+6 ([[Petrus method]])
|year=
|steps=1
|algs=42
|moves=9.78 (Optimal [[HTM]])
|purpose=
* [[Speedsolving]]
}}

'''COLL''' (an abbreviation for '''Corners of Last Layer''') is a method in the [[CxLL]] group that solves the [[Last Layer]] [[corner]]s in one [[algorithm]], while preserving the [[F2L]] and the orientation of the LL [[edge]]s. So, after the COLL step, only edge permutation (EPLL) is left. COLL requires learning 40 algorithms (42 if you include T-Perm and Y-Perm and 24 if you exclude mirrors).

COLL is not to be confused with [[CLL]], which is an abbreviation for exactly the same name. 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 almost 500 cases. Another one is [[OLLCP]] which solves the corner permutation and [[OLL|orients the last layer]] with a total of over 300 algorithms for all last layer cases.

==See Also==
* [[CxLL Algorithms]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=COLL&moves=FU2B%27UF%27U%27BU%27FU%27F%27 COLL Algorithms]
* [[CLLEF]]
* [[CLL]]
* [[CMLL]]
* [[ZBLL]]
* [[OLLCP]]

== 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://www.cubestation.co.uk/cs2/index.php?page=3x3x3/vh/coll/coll Dan Harris's COLL Page]
* [http://cube.danrcohen.com/coll.html Dan Cohen's COLL Page]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

CLLEF

2010-09-13T15:23:44Z

Irontwig: infobox and minor changes

{{Method Infobox
|name=OLLCP
|image=OLLCP.png
|proposers=Lars Vennike Nielsson
|year=
|anames=
|variants=[[COLL]],[[OLLCP]]
|steps=1
|algs=43
|moves=~12
|purpose=
* [[Speedsolving]]
}}

'''C'''orners '''L'''ast '''L'''ayer [and] '''E'''dge '''F'''lip is a subset of [[OLLCP]]. CLLEF is similar to [[COLL]] in that it orients and permutes last layer corners simultaneously. However, instead of preserving LL edge orientation the algorithms flip all last-layer edges. This would be used as an alternative to [[OLL]]/[[PLL]] in a regular [[Fridrich]] solve, where the OLL case has no oriented edges.

== See Also ==
* [[CxLL]]
* [[CxLL algorithms]]
* [[CLL]]
* [[COLL]]
* [[OLLCP]]

== External Links ==

* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=7809 CLLEF, the evil twin of COLL]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Sub Steps]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]

2GLL

2010-09-13T12:03:43Z

Irontwig: "subset" instead of "fraction" to keep it consistent with other pages (L4C e.g.).

{{Method Infobox
|name=2GLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Timothy Sun]], [[Lars Petrus]]
|year=2005?
|steps=1
|algs=85
|moves=~13?
|purpose=
* [[Speedsolving]]
}}

'''2GLL''' (short for ''2-Generator Last Layer'') is a subset of [[ZBLL]]. ZBLL is meant to orient and permute corners of the last layer while permuting the edges, and comes up to hefty 493 cases. Taking the subset of this that does not permute the corners, and instead only orients the corners and permutes the edges, these cases can be reduced to 85, while also having each case be able to be solved by a "2-generator" algorithm (one that uses only 2 algorithms, in this case usually the R and U faces.

2GLL is very useful when one has a system for permuting the [[LL]] corners and orienting the LL edges prior to getting to the last layer. One system that achieves rooting off of [[CFOP]] would be to do the [[cross]], three [[F2L]] pairs, [[ELS]], and lastly [[CPLS]]. While this could be a good system to branch off of [[CFOP]], most would agree that the system would work better on methods which naturally orient the edges before getting to the final slot of [[F2L]] such as [[ZZ]] or [[Petrus]]. Another method to use during [[CFOP]] to accomplish 2GLL would be to orient edges while doing 'normal' [[F2L]], perhaps having two or more algs for each [[F2L]] case, influencing different edge orientations.

===Learning Approach===

Much like in [[ZBLL]] and [[COLL]], the cases of 2GLL can be divided into seven individual sets to learn and recognize by. These sets are typically called Sune, Anti-Sune, H (or Double-Sune), Pi, U, T, L, and [[EPLL]]. Each 2GLL is typically recognized by the [[COLL]] of the case, followed by the edge cycle that is present (see [[EPLL]]. Typically, there are 12 cases per [[COLL[[, but some can be eliminated due to mirrors and the like.

===Recognition===

For every subset, one can recognize their case by the means of the following system:

1. Recognize the corner orientation case. (one of 7)

1.5? - Some people prefer to AUF right now in order to have their corners not only in their relatively correct spot, but also in their *actual* correct spot. As in, rather than having the corners a U2 away from being correctly permuted, they would do a d2, then recognize from there, or something along those lines.
Because a good percentage of the 'good' algs have AUFs and/or initial rotations anyway, it doesn't make all that much of a difference, so if it helps you to recognize this way, do so.

2. Recognize the edge cycle by looking only at the FU and RU stickers in relation to the UFR piece.

3. Apply the corresponding algorithm.

Step 1 should be fairly easy to recognize, as there are only seven possible cases, and if you have used another [[LL]] technique, then you have most likely had to recognize corner orientation before. When you see the case, simply adjust the upper-most face in order to get the case into the angle you typically recognize from, and continue to the next step.

Step 2 is a tiny bit more complicated to recognize, but once it is gotten used to, it can really be quite easy.
Since there are a possible of 12 edge permutations (assuming that the puzzle is solvable and the corners are permuted) one has to be prepared for all 12.

Here is one system to recognize these in:
- If you see that both the FU and RU edges are correctly positioned between corners that have been pre-permuted, then this is a "good" case, meaning that all of the edges are correctly positioned.

- If you see that both the FU and RU edges are opposite colors of what they should be (red/orange or blue/green on the standard color scheme) then this is an "H perm" case.

- If you see that the FU piece and RU piece should be switched with each other (a visible 2-cycle) then you have "Z1," one of two possible Z perms.
- If you see that FU needs to go to LU while RU needs to go to BU, then you have the other Z perm, "Z2."

If the case does not follow into any of the above, then
- For the remaining 8 cases, the U perms, without rotating the cube, the solver should ask themselves the following:
--"Is this cycle going clockwise or anti-clockwise?"
--"Where is the edge that is correct?"

Both of these questions can be answered by figuring out the following:
--"Where does the FU sticker need to be in respect to the corner permutation?"
--"Where does the RU sticker need to be in respect to the corner permutation?"

Simply put, try to trace a 3-cycle of edges in the last layer. The piece that does not belong combined with the direction of the cycle is a great way to recognize and notate the cycle.

As a quick example, scramble a standard 3x3x3 Rubik's Cube with the following:
R' U2 R U R' U R U' R' U' R U' R' U2 R

Firstly, look at the corner orientation. You should be able to find this as a Headlights case. Put these headlights in the back - if you ever decide to learn COLL or ZBLL, this is how you will probably recognize headlights cases, so it's a good idea to start that way now!
Next note that this is not a "good", H, or Z case, and therefore must be a Uperm of sorts.
Next, note that this is a clockwise U perm - one that does not cycle RU.
That's it.
Right then, you should be able to apply your alg, AUF, and slam your cube down, stopping the timer.

For this case, y R' U2 R U R' U R U R' U' R U' R' U2 R is a nice alg. Success.

== See Also ==

* [[ZB Method]]
* [[ZBF2L]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[ZBLL]]

== External Links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=445774&postcount=207 Stachu's 2GLL list] - complete
* [http://lar5.com/cube/xMain.html Lars Petrus' 2GLL algorithms]
* [http://boca.bee.pl/cat.php?l=pl&cat=th&m=zz&ch=d BOCA 2GLL algs]

[[Category:Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

2GLL

2010-09-13T12:02:33Z

Irontwig: /* External Links */ boca

{{Method Infobox
|name=2GLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Timothy Sun]], [[Lars Petrus]]
|year=2005?
|steps=1
|algs=85
|moves=~13?
|purpose=
* [[Speedsolving]]
}}

'''2GLL''' (short for ''2-Generator Last Layer'') is a fraction of [[ZBLL]]. ZBLL is meant to orient and permute corners of the last layer while permuting the edges, and comes up to hefty 493 cases. Taking the subset of this that does not permute the corners, and instead only orients the corners and permutes the edges, these cases can be reduced to 85, while also having each case be able to be solved by a "2-generator" algorithm (one that uses only 2 algorithms, in this case usually the R and U faces.

2GLL is very useful when one has a system for permuting the [[LL]] corners and orienting the LL edges prior to getting to the last layer. One system that achieves rooting off of [[CFOP]] would be to do the [[cross]], three [[F2L]] pairs, [[ELS]], and lastly [[CPLS]]. While this could be a good system to branch off of [[CFOP]], most would agree that the system would work better on methods which naturally orient the edges before getting to the final slot of [[F2L]] such as [[ZZ]] or [[Petrus]]. Another method to use during [[CFOP]] to accomplish 2GLL would be to orient edges while doing 'normal' [[F2L]], perhaps having two or more algs for each [[F2L]] case, influencing different edge orientations.

===Learning Approach===

Much like in [[ZBLL]] and [[COLL]], the cases of 2GLL can be divided into seven individual sets to learn and recognize by. These sets are typically called Sune, Anti-Sune, H (or Double-Sune), Pi, U, T, L, and [[EPLL]]. Each 2GLL is typically recognized by the [[COLL]] of the case, followed by the edge cycle that is present (see [[EPLL]]. Typically, there are 12 cases per [[COLL[[, but some can be eliminated due to mirrors and the like.

===Recognition===

For every subset, one can recognize their case by the means of the following system:

1. Recognize the corner orientation case. (one of 7)

1.5? - Some people prefer to AUF right now in order to have their corners not only in their relatively correct spot, but also in their *actual* correct spot. As in, rather than having the corners a U2 away from being correctly permuted, they would do a d2, then recognize from there, or something along those lines.
Because a good percentage of the 'good' algs have AUFs and/or initial rotations anyway, it doesn't make all that much of a difference, so if it helps you to recognize this way, do so.

2. Recognize the edge cycle by looking only at the FU and RU stickers in relation to the UFR piece.

3. Apply the corresponding algorithm.

Step 1 should be fairly easy to recognize, as there are only seven possible cases, and if you have used another [[LL]] technique, then you have most likely had to recognize corner orientation before. When you see the case, simply adjust the upper-most face in order to get the case into the angle you typically recognize from, and continue to the next step.

Step 2 is a tiny bit more complicated to recognize, but once it is gotten used to, it can really be quite easy.
Since there are a possible of 12 edge permutations (assuming that the puzzle is solvable and the corners are permuted) one has to be prepared for all 12.

Here is one system to recognize these in:
- If you see that both the FU and RU edges are correctly positioned between corners that have been pre-permuted, then this is a "good" case, meaning that all of the edges are correctly positioned.

- If you see that both the FU and RU edges are opposite colors of what they should be (red/orange or blue/green on the standard color scheme) then this is an "H perm" case.

- If you see that the FU piece and RU piece should be switched with each other (a visible 2-cycle) then you have "Z1," one of two possible Z perms.
- If you see that FU needs to go to LU while RU needs to go to BU, then you have the other Z perm, "Z2."

If the case does not follow into any of the above, then
- For the remaining 8 cases, the U perms, without rotating the cube, the solver should ask themselves the following:
--"Is this cycle going clockwise or anti-clockwise?"
--"Where is the edge that is correct?"

Both of these questions can be answered by figuring out the following:
--"Where does the FU sticker need to be in respect to the corner permutation?"
--"Where does the RU sticker need to be in respect to the corner permutation?"

Simply put, try to trace a 3-cycle of edges in the last layer. The piece that does not belong combined with the direction of the cycle is a great way to recognize and notate the cycle.

As a quick example, scramble a standard 3x3x3 Rubik's Cube with the following:
R' U2 R U R' U R U' R' U' R U' R' U2 R

Firstly, look at the corner orientation. You should be able to find this as a Headlights case. Put these headlights in the back - if you ever decide to learn COLL or ZBLL, this is how you will probably recognize headlights cases, so it's a good idea to start that way now!
Next note that this is not a "good", H, or Z case, and therefore must be a Uperm of sorts.
Next, note that this is a clockwise U perm - one that does not cycle RU.
That's it.
Right then, you should be able to apply your alg, AUF, and slam your cube down, stopping the timer.

For this case, y R' U2 R U R' U R U R' U' R U' R' U2 R is a nice alg. Success.

== See Also ==

* [[ZB Method]]
* [[ZBF2L]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[ZBLL]]

== External Links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=445774&postcount=207 Stachu's 2GLL list] - complete
* [http://lar5.com/cube/xMain.html Lars Petrus' 2GLL algorithms]
* [http://boca.bee.pl/cat.php?l=pl&cat=th&m=zz&ch=d BOCA 2GLL algs]

[[Category:Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

ZZLL

2010-09-13T12:01:04Z

Irontwig: /* External Links */ boca

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://emsee.110mb.com/Speedcubing/ZZLL/ Michal Hordecki's ZZLL algorithms]
* [http://boca.bee.pl/cat.php?l=pl&cat=th&m=zz&ch=b&o=1 BOCA ZZLL algs]

[[Category:Methods]]
[[Category:Last Layer Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Advanced Methods]]
[[Category:Sub Steps]]

ZBLL

2010-09-13T11:59:23Z

Irontwig: /* External Links */ boca

{{Method Infobox
|name=ZBLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Lars Petrus]]
|year=2002
|anames=Steps 5+6+7 ([[Petrus method]])
|variants=
|steps=1
|algs=493
|moves=12.08 (Optimal [[HTM]])
|purpose=
* [[Speedsolving]], [[FMC]]
}}

'''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]]).

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 40 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]]
* [[ZBF2L]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[H ZBLL]] (Algorithms)
* [[ZBLD]]

== External Links ==
* 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]
* [http://boca.bee.pl/cat.php?l=pl&cat=th&m=zb&ch=zbll BOCA ZBLL algs]

[[Category:Methods]]
[[Category:Last Layer Methods]]
[[Category:Fewest Moves Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

COLL

2010-09-10T07:15:53Z

Irontwig: info box

{{Method Infobox
|name=COLL
|image=OLLCP.png
|proposers=[[Lars Petrus]]
|variants=[[CLLEF]],[[OLLCP]]
|anames=Steps 5+6 ([[Petrus method]])
|year=
|steps=1
|algs=42
|moves=9.78 (Optimal [[HTM]])
|purpose=
* [[Speedsolving]]
}}

'''COLL''' (an abbreviation for '''Corners of Last Layer''') is a method in the [[CxLL]] group that solves the [[Last Layer]] [[corner]]s in one [[algorithm]], while preserving the [[F2L]] and the orientation of the LL [[edge]]s. So, after the COLL step, only edge permutation (EPLL) is left. COLL requires learning 40 algorithms (42 if you include T-Perm and Y-Perm and 24 if you exclude mirrors).

COLL is not to be confused with [[CLL]], which is an abbreviation for exactly the same name. 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 almost 500 cases. Another one is [[OLLCP]] which solves the corner permutation and [[OLL|orients the last layer]] with a total of over 300 algorithms for all last layer cases.

==See Also==
* [[CxLL Algorithms]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=COLL&moves=FU2B%27UF%27U%27BU%27FU%27F%27 COLL Algorithms]
* [[CLLEF]]
* [[CLL]]
* [[CMLL]]
* [[ZBLL]]

== 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://www.cubestation.co.uk/cs2/index.php?page=3x3x3/vh/coll/coll Dan Harris's COLL Page]
* [http://cube.danrcohen.com/coll.html Dan Cohen's COLL Page]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

ZBLL

2010-09-10T07:15:03Z

Irontwig:

{{Method Infobox
|name=ZBLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Lars Petrus]]
|year=2002
|anames=Steps 5+6+7 ([[Petrus method]])
|variants=
|steps=1
|algs=493
|moves=12.08 (Optimal [[HTM]])
|purpose=
* [[Speedsolving]], [[FMC]]
}}

'''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]]).

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 40 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]]
* [[ZBF2L]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[H ZBLL]] (Algorithms)
* [[ZBLD]]

== External Links ==
* 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]

[[Category:Methods]]
[[Category:Last Layer Methods]]
[[Category:Fewest Moves Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

2GLL

2010-09-10T07:06:02Z

Irontwig: /* External Links */

{{Method Infobox
|name=2GLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Timothy Sun]], [[Lars Petrus]]
|year=2005?
|steps=1
|algs=85
|moves=~13?
|purpose=
* [[Speedsolving]]
}}

'''2GLL''' (short for ''2-Generator Last Layer'') is a fraction of [[ZBLL]]. ZBLL is meant to orient and permute corners of the last layer while permuting the edges, and comes up to hefty 493 cases. Taking the subset of this that does not permute the corners, and instead only orients the corners and permutes the edges, these cases can be reduced to 85, while also having each case be able to be solved by a "2-generator" algorithm (one that uses only 2 algorithms, in this case usually the R and U faces.

2GLL is very useful when one has a system for permuting the [[LL]] corners and orienting the LL edges prior to getting to the last layer. One system that achieves rooting off of [[CFOP]] would be to do the [[cross]], three [[F2L]] pairs, [[ELS]], and lastly [[CPLS]]. While this could be a good system to branch off of [[CFOP]], most would agree that the system would work better on methods which naturally orient the edges before getting to the final slot of [[F2L]] such as [[ZZ]] or [[Petrus]]. Another method to use during [[CFOP]] to accomplish 2GLL would be to orient edges while doing 'normal' [[F2L]], perhaps having two or more algs for each [[F2L]] case, influencing different edge orientations.

===Learning Approach===

Much like in [[ZBLL]] and [[COLL]], the cases of 2GLL can be divided into seven individual sets to learn and recognize by. These sets are typically called Sune, Anti-Sune, H (or Double-Sune), Pi, U, T, L, and [[EPLL]]. Each 2GLL is typically recognized by the [[COLL]] of the case, followed by the edge cycle that is present (see [[EPLL]]. Typically, there are 12 cases per [[COLL[[, but some can be eliminated due to mirrors and the like.

===Recognition===

For every subset, one can recognize their case by the means of the following system:

1. Recognize the corner orientation case. (one of 7)

1.5? - Some people prefer to AUF right now in order to have their corners not only in their relatively correct spot, but also in their *actual* correct spot. As in, rather than having the corners a U2 away from being correctly permuted, they would do a d2, then recognize from there, or something along those lines.
Because a good percentage of the 'good' algs have AUFs and/or initial rotations anyway, it doesn't make all that much of a difference, so if it helps you to recognize this way, do so.

2. Recognize the edge cycle by looking only at the FU and RU stickers in relation to the UFR piece.

3. Apply the corresponding algorithm.

Step 1 should be fairly easy to recognize, as there are only seven possible cases, and if you have used another [[LL]] technique, then you have most likely had to recognize corner orientation before. When you see the case, simply adjust the upper-most face in order to get the case into the angle you typically recognize from, and continue to the next step.

Step 2 is a tiny bit more complicated to recognize, but once it is gotten used to, it can really be quite easy.
Since there are a possible of 12 edge permutations (assuming that the puzzle is solvable and the corners are permuted) one has to be prepared for all 12.

Here is one system to recognize these in:
- If you see that both the FU and RU edges are correctly positioned between corners that have been pre-permuted, then this is a "good" case, meaning that all of the edges are correctly positioned.

- If you see that both the FU and RU edges are opposite colors of what they should be (red/orange or blue/green on the standard color scheme) then this is an "H perm" case.

- If you see that the FU piece and RU piece should be switched with each other (a visible 2-cycle) then you have "Z1," one of two possible Z perms.
- If you see that FU needs to go to LU while RU needs to go to BU, then you have the other Z perm, "Z2."

If the case does not follow into any of the above, then
- For the remaining 8 cases, the U perms, without rotating the cube, the solver should ask themselves the following:
--"Is this cycle going clockwise or anti-clockwise?"
--"Where is the edge that is correct?"

Both of these questions can be answered by figuring out the following:
--"Where does the FU sticker need to be in respect to the corner permutation?"
--"Where does the RU sticker need to be in respect to the corner permutation?"

Simply put, try to trace a 3-cycle of edges in the last layer. The piece that does not belong combined with the direction of the cycle is a great way to recognize and notate the cycle.

As a quick example, scramble a standard 3x3x3 Rubik's Cube with the following:
R' U2 R U R' U R U' R' U' R U' R' U2 R

Firstly, look at the corner orientation. You should be able to find this as a Headlights case. Put these headlights in the back - if you ever decide to learn COLL or ZBLL, this is how you will probably recognize headlights cases, so it's a good idea to start that way now!
Next note that this is not a "good", H, or Z case, and therefore must be a Uperm of sorts.
Next, note that this is a clockwise U perm - one that does not cycle RU.
That's it.
Right then, you should be able to apply your alg, AUF, and slam your cube down, stopping the timer.

For this case, y R' U2 R U R' U R U R' U' R U' R' U2 R is a nice alg. Success.

== See Also ==

* [[ZB Method]]
* [[ZBF2L]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[ZBLL]]

== External Links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=445774&postcount=207 Stachu's 2GLL list] - complete
* [http://lar5.com/cube/xMain.html Lars Petrus' 2GLL algorithms]

[[Category:Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

2GLL

2010-09-05T14:48:40Z

Irontwig:

{{Method Infobox
|name=2GLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Timothy Sun]], [[Lars Petrus]]
|year=2005?
|steps=1
|algs=85
|moves=~13?
|purpose=
* [[Speedsolving]]
}}

'''2GLL''' (short for ''2-Generator Last Layer'') is a fraction of [[ZBLL]]. ZBLL is meant to orient and permute corners of the last layer while permuting the edges, and comes up to hefty 493 cases. Taking the subset of this that does not permute the corners, and instead only orients the corners and permutes the edges, these cases can be reduced to 85, while also having each case be able to be solved by a "2-generator" algorithm (one that uses only 2 algorithms, in this case usually the R and U faces.

2GLL is very useful when one has a system for permuting the [[LL]] corners and orienting the LL edges prior to getting to the last layer. One system that achieves rooting off of [[CFOP]] would be to do the [[cross]], three [[F2L]] pairs, [[ELS]], and lastly [[CPLS]]. While this could be a good system to branch off of [[CFOP]], most would agree that the system would work better on methods which naturally orient the edges before getting to the final slot of [[F2L]] such as [[ZZ]] or [[Petrus]]. Another method to use during [[CFOP]] to accomplish 2GLL would be to orient edges while doing 'normal' [[F2L]], perhaps having two or more algs for each [[F2L]] case, influencing different edge orientations.

===Learning Approach===

Much like in [[ZBLL]] and [[COLL]], the cases of 2GLL can be divided into seven individual sets to learn and recognize by. These sets are typically called Sune, Anti-Sune, H (or Double-Sune), Pi, U, T, L, and [[EPLL]]. Each 2GLL is typically recognized by the [[COLL]] of the case, followed by the edge cycle that is present (see [[EPLL]]. Typically, there are 12 cases per [[COLL[[, but some can be eliminated due to mirrors and the like.

===Recognition===

For every subset, one can recognize their case by the means of the following system:

1. Recognize the corner orientation case. (one of 7)

1.5? - Some people prefer to AUF right now in order to have their corners not only in their relatively correct spot, but also in their *actual* correct spot. As in, rather than having the corners a U2 away from being correctly permuted, they would do a d2, then recognize from there, or something along those lines.
Because a good percentage of the 'good' algs have AUFs and/or initial rotations anyway, it doesn't make all that much of a difference, so if it helps you to recognize this way, do so.

2. Recognize the edge cycle by looking only at the FU and RU stickers in relation to the UFR piece.

3. Apply the corresponding algorithm.

Step 1 should be fairly easy to recognize, as there are only seven possible cases, and if you have used another [[LL]] technique, then you have most likely had to recognize corner orientation before. When you see the case, simply adjust the upper-most face in order to get the case into the angle you typically recognize from, and continue to the next step.

Step 2 is a tiny bit more complicated to recognize, but once it is gotten used to, it can really be quite easy.
Since there are a possible of 12 edge permutations (assuming that the puzzle is solvable and the corners are permuted) one has to be prepared for all 12.

Here is one system to recognize these in:
- If you see that both the FU and RU edges are correctly positioned between corners that have been pre-permuted, then this is a "good" case, meaning that all of the edges are correctly positioned.

- If you see that both the FU and RU edges are opposite colors of what they should be (red/orange or blue/green on the standard color scheme) then this is an "H perm" case.

- If you see that the FU piece and RU piece should be switched with each other (a visible 2-cycle) then you have "Z1," one of two possible Z perms.
- If you see that FU needs to go to LU while RU needs to go to BU, then you have the other Z perm, "Z2."

If the case does not follow into any of the above, then
- For the remaining 8 cases, the U perms, without rotating the cube, the solver should ask themselves the following:
--"Is this cycle going clockwise or anti-clockwise?"
--"Where is the edge that is correct?"

Both of these questions can be answered by figuring out the following:
--"Where does the FU sticker need to be in respect to the corner permutation?"
--"Where does the RU sticker need to be in respect to the corner permutation?"

Simply put, try to trace a 3-cycle of edges in the last layer. The piece that does not belong combined with the direction of the cycle is a great way to recognize and notate the cycle.

As a quick example, scramble a standard 3x3x3 Rubik's Cube with the following:
R' U2 R U R' U R U' R' U' R U' R' U2 R

Firstly, look at the corner orientation. You should be able to find this as a Headlights case. Put these headlights in the back - if you ever decide to learn COLL or ZBLL, this is how you will probably recognize headlights cases, so it's a good idea to start that way now!
Next note that this is not a "good", H, or Z case, and therefore must be a Uperm of sorts.
Next, note that this is a clockwise U perm - one that does not cycle RU.
That's it.
Right then, you should be able to apply your alg, AUF, and slam your cube down, stopping the timer.

For this case, y R' U2 R U R' U R U R' U' R U' R' U2 R is a nice alg. Success.

== See Also ==

* [[ZB Method]]
* [[ZBF2L]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[ZBLL]]

== External Links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showpost.php?p=445774&postcount=207 Stachu's 2GLL list] - complete

[[Category:Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

OLLCP

2010-08-26T07:30:46Z

Irontwig: added Guus and Kenneth in infobox

{{Method Infobox
|name=OLLCP
|image=OLLCP.png
|proposers=Guus Razoux Schultz, Kenneth Gustavsson
|year=
|anames=
|variants
|steps=1
|algs=~330
|moves=~11
|purpose=
* [[Speedsolving]]
}}

'''Orientation of Last Layer and Corner Permutation'''
'''OLLCP''' is a [[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+). Though full OLLCP is not known to be used, a number of people use the subsets [[COLL]] and [[CLLEF]].

== See also ==
* [[CxLL]]
* [[EPLL]]
* [[CPEOLL]] The subset were all corners are already oriented

== External links ==
* [http://www.speedsolving.com/forum/showthread.php?t=23222 SuneOLL] Proposed system to solve all cases where the corners are already permuted

[[Category:Methods]]
[[Category:Experimental Methods]]
[[Category:Last Layer Methods]]
[[Category:3x3x3 Methods]]
[[Category:Cubing Terminology]]

Last Three Corners

2010-08-22T19:54:40Z

Irontwig: link to heise's site added

{{Method Infobox
|name=Last Three Corners
|image=L3C.png
|proposers=Ryan Heise
|anames=L3C
|variants=[[L4C]], [[CxLL]]
|steps=1
|algs=22
|moves=~10 [[HTM]]
|purpose=
* [[Speedsolving]], [[FMC]], [[BLD]]
}}

'''Last three corners''', abbrevaited '''L3C''' (or 3LC), is a [[method]] that solves three of the [[last layer]] corners preserving all the rest, a sub group of [[L4C]], [[ZBLL]] and [[ZZLL]].

'''Usage:''' besides L4C, [[CxLL]], ZBLL and ZZLL it is useful for [[FMC]] and the 3-cycles are nice for [[Freestyle BLD]].

'''See also:'''
* [[Last Four Corners]]
* [[Beyer-Hardwick Method]]

=L3C Cases=
The group have 27 cases including solved, 3*3 orientations and 3 permutations. Most of the cases (18) are pure [[3-cycle]]s, the rest are pure twists U, T, L, S and -S. Some of the twist occures 2 times (U, T and L) and the T-twist is the same as the U-twist if the puzzle is reoriented. Subtracting the duplicates and solved it will be 22 cases left. 16 of them are pure L3C cases and listed at this page, the rest are in one of two sub groups.

===Sub groups:===
*'''Pure twists''' you can find at the [[Corner orientation|Corner orientation page]].
*'''Only permutation''', look at [[A-PLL]] a and b at the PLL page for those.''

The '''naming system''' used here is adapted to BLD, the ULB corner is always the solved one and URF is the 'buffer' with U as the buffer sticker. The piece in the buffer will go to two places, either URB or UFL and the sticker in U will go to any of the three stickers on each goal position and that sticker is in uppercase, the other two letters will be in lowercase. The second half of the name is the same but from the goal position of the first. The last piece will always go to the first buffer position so that will not be in the name.

Example: CW A-PLL is Ufl-Urb and CCW A-PLL is Urb-Ufl.

==Algorithms==

Note that all of these algorithms are written in the Western [[notation]], where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z.

Click on an algorithm (not the camera icon) to watch an animation of it.
----

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

|-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"
|
=== uFl-Urb ===
[[File:L3C case1(a).jpg]]

{{Alg|R2 D R' U2 R D' R' U2 R'}}

|

=== uRb-Ufl ===
[[File:L3C case1(b).jpg]]

{{Alg|(y) L2 D' L U2 L' D L U2 L}}

|-valign="top"
|

=== Ufl-uRb ===
[[File:L3C case1(c).jpg]]

{{Alg|(y) L' U2 L' D' L U2 L' D L2}}

|

=== Urb-uFl ===
[[File:L3C case1(d).jpg]]

{{Alg|R U2 R D R' U2 R D' R2}}

|-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"
|

=== ufL-uRb ===
[[File:L3C case2(a).jpg]]

{{Alg|(y x') R2 D2 R U2 R' D2 R U2 l}}

|

=== urB-uFl ===
[[File:L3C case2(b).jpg]]

{{Alg|(x') L2 D2 L' U2 L D2 L' U2 r'}}

|-valign="top"
|

=== uFl-urB ===
[[File:L3C case2(c).jpg]]

{{Alg|r U2 L D2 L' U2 L D2 L2 (x')}}

|

=== uRb-ufL ===
[[File:L3C case2(d).jpg]]

{{Alg|(y) l' U2 R' D2 R U2 R' D2 R2 (x')}}

|-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"
|

=== ufL-Urb ===
[[File:L3C case3(a).jpg]]

{{Alg|(y) r' U' R U L U' R' U (x)}}

|

=== urB-Ufl ===
[[File:L3C case3(b).jpg]]

{{Alg|(y2) l U L' U' R' U L U' (x)}}

|-valign="top"
|

=== Ufl-urB ===
[[File:L3C case3(c).jpg]]

{{Alg|(x') U L' U' R U L U' l'}}

|

=== Urb-ufL ===
[[File:L3C case3(d).jpg]]

{{Alg|(y x') U' R U L' U' R' U r}}

|-valign="top"
| bgcolor="f0f4f8" |
This is the classic [[Niklas]].
| bgcolor="f0f4f8" |
Mirror of Niklas.

|-valign="top"
|

=== ufL-urB ===
[[File:L3C case4(a).jpg]]

{{Alg|R' U L U' R U L' U'}}

|

=== urB-ufL ===
[[File:L3C case4(b).jpg]]

{{Alg|U L U' R' U L' U' R}}

|-valign="top"
| bgcolor="f0f4f8" |
Anti Niklas.
| bgcolor="f0f4f8" |
Mirror of Anti Niklas.
|-valign="top"
|

=== uFl-uRb ===
[[File:L3C case5(a).jpg]]

{{Alg|B L' U2 L B' L' B U2 B' L}}

|

=== uRb-uFl ===
[[File:L3C case5(b).jpg]]

{{Alg|L' B U2 B' L B L' U2 L B'}}

|}

=== External links ===
[http://www.ryanheise.com/cube/corner_3_cycles.html] Ryan Heise explains a intuitive approach to solve the last three corners.

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Sub Steps]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]

__NOTOC__

Last Three Corners

2010-08-22T19:51:34Z

Irontwig: Heise added in infobox

{{Method Infobox
|name=Last Three Corners
|image=L3C.png
|proposers=Ryan Heise
|anames=L3C
|variants=[[L4C]], [[CxLL]]
|steps=1
|algs=22
|moves=~10 [[HTM]]
|purpose=
* [[Speedsolving]], [[FMC]], [[BLD]]
}}

'''Last three corners''', abbrevaited '''L3C''' (or 3LC), is a [[method]] that solves three of the [[last layer]] corners preserving all the rest, a sub group of [[L4C]], [[ZBLL]] and [[ZZLL]].

'''Usage:''' besides L4C, [[CxLL]], ZBLL and ZZLL it is useful for [[FMC]] and the 3-cycles are nice for [[Freestyle BLD]].

'''See also:'''
* [[Last Four Corners]]
* [[Beyer-Hardwick Method]]

=L3C Cases=
The group have 27 cases including solved, 3*3 orientations and 3 permutations. Most of the cases (18) are pure [[3-cycle]]s, the rest are pure twists U, T, L, S and -S. Some of the twist occures 2 times (U, T and L) and the T-twist is the same as the U-twist if the puzzle is reoriented. Subtracting the duplicates and solved it will be 22 cases left. 16 of them are pure L3C cases and listed at this page, the rest are in one of two sub groups.

===Sub groups:===
*'''Pure twists''' you can find at the [[Corner orientation|Corner orientation page]].
*'''Only permutation''', look at [[A-PLL]] a and b at the PLL page for those.''

The '''naming system''' used here is adapted to BLD, the ULB corner is always the solved one and URF is the 'buffer' with U as the buffer sticker. The piece in the buffer will go to two places, either URB or UFL and the sticker in U will go to any of the three stickers on each goal position and that sticker is in uppercase, the other two letters will be in lowercase. The second half of the name is the same but from the goal position of the first. The last piece will always go to the first buffer position so that will not be in the name.

Example: CW A-PLL is Ufl-Urb and CCW A-PLL is Urb-Ufl.

==Algorithms==

Note that all of these algorithms are written in the Western [[notation]], where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z.

Click on an algorithm (not the camera icon) to watch an animation of it.
----

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

|-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"
|
=== uFl-Urb ===
[[File:L3C case1(a).jpg]]

{{Alg|R2 D R' U2 R D' R' U2 R'}}

|

=== uRb-Ufl ===
[[File:L3C case1(b).jpg]]

{{Alg|(y) L2 D' L U2 L' D L U2 L}}

|-valign="top"
|

=== Ufl-uRb ===
[[File:L3C case1(c).jpg]]

{{Alg|(y) L' U2 L' D' L U2 L' D L2}}

|

=== Urb-uFl ===
[[File:L3C case1(d).jpg]]

{{Alg|R U2 R D R' U2 R D' R2}}

|-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"
|

=== ufL-uRb ===
[[File:L3C case2(a).jpg]]

{{Alg|(y x') R2 D2 R U2 R' D2 R U2 l}}

|

=== urB-uFl ===
[[File:L3C case2(b).jpg]]

{{Alg|(x') L2 D2 L' U2 L D2 L' U2 r'}}

|-valign="top"
|

=== uFl-urB ===
[[File:L3C case2(c).jpg]]

{{Alg|r U2 L D2 L' U2 L D2 L2 (x')}}

|

=== uRb-ufL ===
[[File:L3C case2(d).jpg]]

{{Alg|(y) l' U2 R' D2 R U2 R' D2 R2 (x')}}

|-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"
|

=== ufL-Urb ===
[[File:L3C case3(a).jpg]]

{{Alg|(y) r' U' R U L U' R' U (x)}}

|

=== urB-Ufl ===
[[File:L3C case3(b).jpg]]

{{Alg|(y2) l U L' U' R' U L U' (x)}}

|-valign="top"
|

=== Ufl-urB ===
[[File:L3C case3(c).jpg]]

{{Alg|(x') U L' U' R U L U' l'}}

|

=== Urb-ufL ===
[[File:L3C case3(d).jpg]]

{{Alg|(y x') U' R U L' U' R' U r}}

|-valign="top"
| bgcolor="f0f4f8" |
This is the classic [[Niklas]].
| bgcolor="f0f4f8" |
Mirror of Niklas.

|-valign="top"
|

=== ufL-urB ===
[[File:L3C case4(a).jpg]]

{{Alg|R' U L U' R U L' U'}}

|

=== urB-ufL ===
[[File:L3C case4(b).jpg]]

{{Alg|U L U' R' U L' U' R}}

|-valign="top"
| bgcolor="f0f4f8" |
Anti Niklas.
| bgcolor="f0f4f8" |
Mirror of Anti Niklas.
|-valign="top"
|

=== uFl-uRb ===
[[File:L3C case5(a).jpg]]

{{Alg|B L' U2 L B' L' B U2 B' L}}

|

=== uRb-uFl ===
[[File:L3C case5(b).jpg]]

{{Alg|L' B U2 B' L B L' U2 L B'}}

|}

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Sub Steps]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]

__NOTOC__

Last Four Corners

2010-08-16T06:13:08Z

Irontwig: /* H E (a) */

{{Method Infobox
|name=L4C
|image=LLEF.png
|algs=84
|moves=11.73 (Optimal [[HTM]]))
|purpose=
* [[Speedsolving]], [[FMC]]
}}

'''Last four corners''', abbrevaited '''L4C''' (or 4LC), is a [[method]] that solves the [[last layer]] corners preserving all the rest, a sub group of [[ZBLL]] and [[ZZLL]]. For a 2-look last layer this is preceeded with [[LLEF]] (ELL first).

'''See also:'''
* [[Last Three Corners]]

=L4C Cases=
Because edges are solved at this point you cannot AUF as in [[CxLL]] so the number of cases is quadrupled, but because you cannot have parity that is reduced again by factor 2. The orientations are the usual seven [[CO]]s plus the solved case ([[CPLL]]). The permutations (with fix position orientations) that occure are permutation solved, A-PLL a and b from all four angles, the two possible ways of E-PLL and finally X-PLL (that is H-PLL + U2) giving a total of twelve possible permutations. This gives a total of 8 * 12 = 96 cases, but it is possible to reduce that a bit because of duplicates. The whole group is larger, corner orientations are for real 27 so you will have 27 * 12 = 324, so the chance of a skip is 1:324.
==2-look L4C==
It is possible to solve most L4C in two looks using 3-cycle [[commutator]]s. The method is to use the first 3-cycle to solve one piece and at the same time move any placed but twisted corner out from position (to avoid the pure twists that uses long algs) and then follow it up with a second 3-cycle. This will solve all cases but the pure twists with 4 corners wrong, that you can solve in two looks using only the U-twist and puzzle orientations, the other pure cases, T and U use the U-twist, L and S; cycle the twisted corners using any 3-cycle and then the appropiate cycle to move them back.

Another way is to use COs that preserves edges but not corner permutation and then end the solve using [[CPLL]]. This will use lesser algs but more turns than the first approach.

=Algorithms=
Note that all of these algorithms are written in the Western [[notation]], where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z.

Click on an algorithm (not the camera icon) to watch an animation of it.

==Pure COs==
See [[Corner Orientation]] for the seven cases and algorithms to solve them.

==All corners oriented==
Use the [[CPLL]]s for this, cases are [[A-PLL]] a and b, [[E-PLL]] and [[H-PLL]] (X-PLL).

''Mabye list the optimal algs for the cases here but with no images, for FMC usage (I'm trying to save a little on the size of the page ... and work creating images =)''

==L3C==
Another sub group of L4C is L3C. Two of the cases are the [[A-PLL]]s listed in the previous group, leaving 16 that have both orientation and permutation and these you can find at the [[L3C|L3C page]], the rest of the cases are the pure twists U, T, L, S and -S.

==L3C 1-twist +==
27 in the group, 9 are pure twists U, T, L, 3xS, H and 2xpi, 18 cases are having both orientation and permutation.

==L3C 1-twist -==
The 18 mirror cases of the previous group.

==Four corners wrong (E)==
16 cases, two are [[E-PLL]], leaving 14.

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

|-valign="top"
|
=== U E (a) ===
[[File:L4C UE (a).jpg]]

{{Alg|!}}

|

=== U E (b) ===
[[File:L4C UE (b).jpg]]

{{Alg|!}}

|-valign="top"
|
=== T E (a) ===
[[File:L4C TE (a).jpg]]

{{Alg|!}}

|

=== T E (b) ===
[[File:L4C TE (b).jpg]]

{{Alg|!}}

|-valign="top"
|
=== L E (a) ===
[[File:L4C LE (a).jpg]]

{{Alg|!}}

|

=== L E (b) ===
[[File:L4C LE (b).jpg]]

{{Alg|!}}

|-valign="top"
|
=== S E (a) ===
[[File:L4C SE (a).jpg]]

{{Alg|!}}

|

=== S E (b) ===
[[File:L4C SE (b).jpg]]

{{Alg|!}}

|-valign="top"
|
=== -S E (a) ===
[[File:L4C aSE (a).jpg]]

{{Alg|!}}

|

=== -S E (b) ===
[[File:L4C aSE (b).jpg]]

{{Alg|!}}

|-valign="top"
|
=== H E (a) ===
This case can be solved optimally by simply doing [[OLL#.22T.22_shapes|OLL 45]] three times.

[[File:L4C HE (a).jpg]]

{{Alg|F(RUR'U')3F'}}

|

=== H E (b) ===
[[File:L4C HE (b).jpg]]

{{Alg|!}}

|-valign="top"
|
=== pi E (a) ===
[[File:L4C piE (a).jpg]]

{{Alg|!}}

|

=== pi E (b) ===
[[File:L4C piE (b).jpg]]

{{Alg|!}}

|}

==Four corners wrong (X)==
8 to solve and one of these is [[X-PLL]], leaving 7, all solveable using only RU ([[2-gen]]).
----
U X and its inverse T X can be solved with optimal movecount with 2 [[conjugate]]s.
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U X ===
[[File:L4C UX.jpg]]

{{Alg|U2 R2 U' R2 U2 R U R' U R' U R' U R2 U2 R}}
{{Alg|F R B' R' F' R2 F2 R' B R F2 R2}}

|

=== T X ===
[[File:L4C TX.jpg]]
{{Alg|U2 R' U2 R2 U' R U' R U' R U' R' U2 R2 U R2}}
{{Alg|R2 B2 R F R' B2 R2 B' R' F' R B }}

|-valign="top"
|

=== L X ===
[[File:L4C LX.jpg]]

{{Alg|(y') R U R' U R U' R' U R U' R' U R U2 R' }}
{{Alg|L' U L2 F' L D' B L B' L2 D L' F U'}}

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

|-valign="top"
|

=== S X ===
[[File:L4C SX.jpg]]

{{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}}

|

=== -S X ===
[[File:L4C aSX.jpg]]

{{Alg|(y') R U R' U R' U' R2 U' R2 U2 R U2}}

|-valign="top"
|

=== H X ===
[[File:L4C HX.jpg]]

{{Alg|R U2 R2 U2 R' U R' U' R U2 R U R U' R' U}}
{{Alg|(y) L2 R D' R' U B2 U B2 U' R D L2 R' U'}}

|

=== Pi X ===
[[File:L4C piX.jpg]]

{{Alg|(y) R U2 R2 U' R' U R2 U' R' U' R' U2 R' U2 R}}
{{Alg|L U' R' U L' U' R2 U' L' U R' U' L U2}}
{{Alg|F' R D2 R' F U' F' R D2 R' F U}}

|
|}

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Sub Steps]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]

__NOTOC__

COLL

2010-08-14T18:32:00Z

Irontwig:

'''COLL''' (an abbreviation for '''Corners of Last Layer''') is a method in the [[CxLL]] group that solves the [[Last Layer]] [[corner]]s in one [[algorithm]], while preserving the [[F2L]] and the orientation of the LL [[edge]]s. So, after the COLL step, only edge permutation (EPLL) is left. COLL requires learning 40 algorithms (42 if you include T-Perm and Y-Perm and 24 if you exclude mirrors).

COLL is not to be confused with [[CLL]], which is an abbreviation for exactly the same name. 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 almost 500 cases. Another one is [[OLLCP]] which solves the corner permutation and [[OLL|orients the last layer]] with a total of over 300 algorithms for all last layer cases.

==See Also==
* [[CxLL Algorithms]]
* [http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=COLL&moves=FU2B%27UF%27U%27BU%27FU%27F%27 COLL Algorithms]
* [[CLLEF]]
* [[CLL]]
* [[CMLL]]
* [[ZBLL]]

== 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://www.cubestation.co.uk/cs2/index.php?page=3x3x3/vh/coll/coll Dan Harris's COLL Page]
* [http://cube.danrcohen.com/coll.html Dan Cohen's COLL Page]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Sub Steps]]

OLLCP-A

2010-08-14T13:34:23Z

Irontwig: mispelling, link to ollcp

'''CPEOLL''', ''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]]. This is the second last step and the goal is to reach [[EPLL]]. Normally it would be used as a add on to the [[Fridrich method]] the times [[CO]] skips (occures 1:27 times) but it may be used as a second step in a 3-look last layer where the first step is to orient the corners.

CPEOLL is a sub group of CEOLL or CLLEO (CLL + EO), the same as OCPLL or [[OLLCP]] (OLL + CP), a very advanced method with more than 300 cases that solves all last layer but EPLL in one look.

===See also:===
* [[OLL]], [[PLL]], [[CLL]], [[ELL]]
* [[OLLCP]]
* [[Fridrich Method]]
* [http://www.speedsolving.com/forum/showthread.php?t=23005 Thread discussing this method]

=CPEOLL 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'}}
<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)}}
<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'}}
<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' x') (L' U L') U2 (R U' R') U2' L2 (x)}}

|}

|

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

{{Alg|(y' x') (R U' R) U2' (L' U L) U2 R2 (x)}}

|}

|}

{|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|(y2 x) R2 U2 L U L' U2 R U' l U}}

|}

|

===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'}}

|}

|}

{|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|(y) R2 U R2 B L F' U2 F L' B' U' R2 U}}

|}

|

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

{{Alg|(y) R U' R' F' U F l U' R U R2 (x) U}}

|}

|}
{|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|(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|(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|L' U l d R2 D R' U' R D' R2 S'}}

|}
|}

{|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'}}

|}
|}

[[Category:Methods]]
[[Category:Experimental Methods]]
[[Category:3x3x3 Methods]]
[[Category:Cubing Terminology]]

__NOTOC__

Reduction Method

2010-08-13T20:19:21Z

Irontwig: infobox

{{Method Infobox
|name=Reduction
|image=reduction.png
|proposers=
|year=
|anames=Centers first
|variants=Yau
|steps=3
|algs=2 (min)
|moves=
|purpose=
* [[Speedsolving]]
}}

Reduction is a prevalent [[method]] for solving [[big cube]]s, which involves solving [[Center|centers]] and assembling [[Edge|edges]] so that the cube is "reduced" to a [[3x3x3]] puzzle. Most recent official records and fastest times on the [[4x4x4]] and [[5x5x5]] cubes have been set by speedsolvers using reduction. The one notable exception is Dan Cohen's single solve world record set at US Nationals 2009 using the [[k4]] method. The fastest unofficial times on the [[6x6x6]] and [[7x7x7]] cubes have also been set on reduction, although other methods such as [[Cage Method|Cage]] have been used to attain fast times on very large cube [[Simulator|cube simulators]] (on very big cubes there are almost only centers to solve and most time is spent looking for them so the method used does not matter that much).

The idea of reduction is applicable to other puzzles, where it may be easier to manipulate a puzzle so it functions as a simpler sub-puzzle. In most cases, reduction is used to simplify the puzzle by grouping pieces first, instead of directly solving pieces into their correct positions.

The idea of reduction can sometimes be formalized as effectively as placing a puzzle into a smaller subgroup. [[Thistlethwaite's Algorithm|Thistlethwaite's algorithm]] was based on several iterative reductions, and most fast computer solvers essentially use those approaches.

Although most solving methods involve steps that reduce the left-over puzzle portion, simply solving the puzzle into "less of a mess" (such as "reducing" a cube to the [[Last Layer|LL]] with [[Petrus]]) is not commonly considered reduction. The term is more applied to solving a puzzle into a differently interpretable puzzle, which is normally solved without resort to treating it like the original puzzle (with notable exceptions, such as [[Parity]]).

== External Links ==
* [http://www.bigcubes.com bigcubes.com Tutorial]

[[Category:Methods]]
[[Category:Big Cube Methods]]
[[Category:Cubing Terminology]]

File:Reduction.png

2010-08-13T20:18:09Z

Irontwig: 4x4 after reduction

4x4 after reduction

Columns First Methods

2010-08-13T19:49:30Z

Irontwig: mayor är borgmästare, kenneth

{{Method Infobox
|name=Columns first
|image=Columns_first.gif
|proposers=
|year=
|anames=Columns
|variants=[[Corners first]]
|steps=2 major, several sub steps
|algs=4 min
|moves=Advanced ~45-50 [[STM]]
|purpose=
* [[Speedsolving]]
}}

'''Columns first''' is a group of [[method]]s for the [[3x3x3 cube]] that in some way build four columns of three pieces each, two adjacent [[corner]]s and the and the [[edge]] between them, as the first [[step]]s. Columns are most often aligned top to bottom but two more directions are possible.

It is a great mystery why these methods are not popular at all, it is fast, effective and easy but there are very few people that uses columns.

==Columns for total noobs:==
* Solve 4 [[FL|first layer]] corners.
* Solve 4 middle layer edges using the [[LBL]] alg and it's mirror.
* Use [[Sune]] and Antisune to orient the [[LL|last layer]] [[corner]]s.
* Use [[PLL|A-PLL]] to permute the corners.
* Solve centres using M and S.
* Use M' U M and M' U2 M to solve the first layer edges.
* Use M' U M U2 M' U M to orient the last layer edges.
* Use U-PLL to permute the LL edges.

This will solve the cube but in at least 100 turns on average, probably more, there are more effective ways and using this will only complicate things, you are better of with a pure [[CF|CF method]]. The whole idea is to benefit from solving the middle layer while solving the first layer corners, that's how columns differs from CF. Take a look at this intermediate method instead:

==Intermediate columns:==
* Solve 4 F2L pairs.
* Orient last layer corners, (CO, 7 algs)
* Permute LL corners, (CP, 2 algs)
* Solve centres together with 2-3 first layer edges.
* Orient the remaining edges (EO, 5 or 9 cases depending on method)
* Permute last edges, one way is to solve the last one(s) to FL and use [[EPLL]], another is to use [[Roux]] style and put RU-LU and then permute the M-slice.

Much better, it will solve in less than 60 [[STM]], look ahead is fairly easy, and there are not more than around 20 algorithms, a method well suited for [[speedsolving]].

===Not really columns:===
One way to improve the intermediate method is to skip the CP step, always solve the last FL edge(s) after EO and end the solve using [[PLL]]. That will average around 55 STM but you will need nearly twice as many algs then.
==Advanced:==
See [[PCMS]] for an example.

==Columns for big cubes==
[[Masayuki Akimoto]] invented a columns first method for [[4x4x4]] and larger cubes some years ago that once was published at his site (that is down nowdays).

See this thread [http://www.speedsolving.com/forum/showthread.php?t=363] at [[Speedsolving.com]] for more information on that.

===See also:===
* [[Corners first]]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Cubing Terminology]]

Petrus Method

2010-08-13T19:47:43Z

Irontwig: /* Pros */ LL

{{Method Infobox
|name=Petrus
|image=Petrus_method.gif
|proposers=[[Lars Petrus]]
|year=1981
|anames
|variants
|steps=7
|moves=45 to 60
|purpose=
* [[Fewest Moves]]
* [[Speedsolving]]
}}
The '''Petrus Method''', invented by [[Lars Petrus]], is a block-building [[method]] where the [[F2L]] is solved intuitively with no [[algorithm]]s. Behind [[Fridrich]], it is currently the second most popular speed cubing method in use.

== The Steps ==

1. First, build a [[2x2x2 block]] anywhere on the cube.

2. Next, you expand the 2x2x2 block to a [[2x2x3 block]].

3. After that, you fix the "bad edges" or orient the remaining seven edges on the cube that have not been solved.

4. Then, you finish the First Two Layers (F2L). The pure Petrus approach is to create a 1x2x2 block and expand it to a 1x2x3 block to finish off the F2L, not to solve the cross piece and two corner/edge pairs.

5. Next, you permute the last layer corners, or put them in their proper places (they do not have to be oriented.)

6. Now, you orient the last layer corners, making the whole last layer a solid color.

7. Finally, you permute the last layer edges, without disturbing anything else, to solve the cube.

== Pros ==

The Petrus Method uses fewer moves than the [[Fridrich]] method and most other non-block-building methods. It is more intuitive than the Fridrich method, and it requires far less algorithms. The last layer can even be solved in one look with [[ZBLL]] or [[ZZLL]], however this drastically increases the number of algorithms one must learn.

== Cons ==

It can be sometimes hard (especially for a beginner) to optimize block building, and it's difficult to keep consistently turning throughout the solve.

== Petrus variations ==

There are several other [[sub step|substeps]] that can be used [[EJLS]], [[WV]], [[COLL]], [[JSLS]], and [[ZBLL]], which completes the entire last layer in a single algorithm.

== Petrus as a Beginner Method ==
Used as a beginner method, Petrus requires much more intuition, but also involves learning fewer algorithms. For a tutorial, see the external links below.

== External Links ==

* [http://lar5.com/cube/ Lars Petrus's tutorial]
* [http://petrus-speed.netne.net/ Petrus Speed Website]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=14014 YouTube Beginner Petrus Tutorial]
* YouTube: [http://www.youtube.com/watch?v=EQ9OrFVQw0o Petrus Tutorial] by fallofshadows
* YouTube: [http://www.youtube.com/watch?v=WqXdO2H2FTs Petrus Tutorial] by CuberChris

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Beginner Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Roux method

2010-08-13T19:45:08Z

Irontwig: /* Pros */ rotations

{{Method Infobox
|name=Roux
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames
|variants
|steps=4
|moves=[[Speedsolving|Speed]]:48, [[FM]]:28-
|purpose=
* [[Speedsolving]]
* [[Fewest Moves]]
}}

The '''Roux Method''' was invented by [[Gilles Roux]]. Unlike [[Fridrich]] and [[Petrus]], the inventor of this [[method]] has done a sub-15 second average (of 5) with it in competition.

==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 T and Y permutation) to do this.

4. [[Orient]] the 6 remaining edges (UF, UB, UF, UR, DF, DB need to be oriented correctly).

5. Solve the left and right layer edges. After this step, both the left and right side layers should be complete.

6. Solve the centers and edges in the M slice.

''See also: [[E15]]''

==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 with L, 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. Slice turns can also be slower than using a [[quarter-turn metric]].

== External Links ==

* [http://grrroux.free.fr/method/Intro.html Gilles Roux's tutorial]
* [http://rouxcentral.forummotion.com/forum.htm Roux Central Forums]
* Wikia: [http://rubiks.wikia.com/wiki/Roux_Method Roux Method]
* [http://www.speedsolving.com/forum/showthread.php?t=11506 Waffle's Roux Tutorial]

[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]