Speedsolving.com Wiki - User contributions [en]

M-CELL

2020-01-04T14:20:49Z

DarkfireZZ:

{{Method Infobox
|name=M-CELL
|image=
|proposers=[[Joseph Briggs]]
|year= 2015
|anames=
|variants= 2-OP, T-CELL, B-CELL
|steps= 3 major including F2L
|algs= 96 full.
|moves= 2-OP 60, T-CELL 45, B-CELL 40- (speed), 35- (FMC)
|purpose=
* [[Speedsolving]]
* [[FMC]]
* [[One-Handed Solving]]
* [[Solving with Feet]]
}}

'''M-CELL''' is a 2-algorithm 1-LLSLL method that can be added on to various methods as a final step it has one algorithm for solving L5C and one for L5E. Each are commutators meaning that neither affects the other so both can be recognised at the same time and executed one after each other without having to rerecognise.

==Steps==
# Solve a 1x2x3 in DL*
# Solve a 2x2x2 in DBR*
# Recognise [[L5C]] and [[L5E]] cases
# Execute in either order

(* These are part of [[SSF2L]] (Shadowslice F2L) which the method was originally proposed to be used in conjunction with)

==Variants==
* '''2OP'''- (2-OP/2 (double) Orient and Permute)
** The beginner variant so to speak, it has a 2-Look lower alg system of the method which gets the user into the habit of recognising 2 algs at the same time which can often be a barrier to entry with the larger alg sets
** Steps:
**# Recognise CO (algs found in [[MGLS]] and EO (algs from [[L5EOP]]) cases
**# Solve with two algorithms- one benefit here is that the EO can be learned intuitively
**# Recognise PL5E and PL5C- PL5E can also be learned intuitively
**# Execute PL5E and PL5C
* '''T-CELL'''- (twinned-CELL) the "normal"/ "speedsolvable" variant
** This is more or less the variant described above
** Steps
**# Recognise L5C and L5E
**# Execute L5C and L5E in either order
* '''B-CELL'''- (broken-CELL) typically for FMCesque solves
** This is essentially the same as T-CELL in terms of steps though for this one the corner and edge do not necessarily have to be in the adjacent meaning that a variety of F2L structures can be used- notably [[Heise]] though not using the centre-edge-centre one as this will block the edge position. While not recommended for speedsolving as the pieces Corner and edge in the D-layer could become hidden and impede lookahead and recognition, it can none the less produce very good FMC results as F2L can be created very efficiently and commutators for the other pieces can be inserted using commutators.

==Pros==
* 1LLSLL
* Relatively low algorithm count for a 1LLSLL especially compared to others such as CTLS or ZBLL.
* Fairly efficient and low movecount
* Requires no special setting up or conditions such as [[Edge Orientation]] (as in [[ZBLL]]), [[Corner Orientation]] (as in [[COALL]]) or [[Corner Permutation]] (as in [[2GLL]]).

==Cons==
* Many pieces mean recognition is difficult.
* 2 algorithms will always be less efficient that 1.
* Ergonomics can sometimes leave something to be desired.

==See Also==
* [https://www.speedsolving.com/forum/showthread.php?54872-Immune-System-(solving-method-potential-1LLL).html Original Method Proposal with all the variants and SSF2L]
* [[L5EOP]]
* [[MGLS]]
* [[1LLL]]
* [[ZZ-CT]]
* [[Hawaiian Kociemba]]

[[Category:3x3x3 speedsolving methods]]
[[Category: Fewest Moves Methods]]

ZBLL

2020-01-04T14:19:19Z

DarkfireZZ:

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

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

ZBLL indeed sounds like a very useful step to learn, but the main reason that it is not in wide use is that it involves a massive 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]] before you learn ZBLL, so that you will always be able to finish the cube relatively quickly even if you do not yet know the ZBLL case. Past that, the learning process is done however you'd like to do it. Many choose to skip learning the S and AS subsets due to their already very easy OLL cases. However, you will benefit if you also learn S and AS.

==Learning Approach==

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

==Edge recognition==

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

1. Recognize the orientation case.

2. Recognize the [[COLL]] case.

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

4. Apply the corresponding algorithm.

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

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

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

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

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

== Pros ==
* Smaller movecount than doing OLL/PLL
* Faster than doing OLL/PLL because you only need 1 look

== Cons ==
* There are a total of 493 algorithms
* Long and hard recognition
* Requires edge orientation before doing ZBLL

== See also ==

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

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/threads/bindedsas-algorithms.55518/ BindeDSA's Algorithms] - complete (2H and OH)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=18172 Happy New Year! Also, ZBLL Algorithms] - complete
* [http://www.ai.univ-paris8.fr/~bh/cube/solutions_567.html Bernhard Helmstetter's ZBLL algs] - complete, but excludes mirrors/inverses
* [http://www-personal.umich.edu/~dlli/Hardwick/zbll.html Chris Hardwick's ZBLL algs] - incomplete
* [http://lar5.com/cube/270/index.html Lars Petrus's One-look 2-alg ZBLL system]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]
* [http://algdb.net/ All ZBLL algs]
* [http://tading.gitee.io/zbll/ TaDing's algorithms] - 472/493 (OH)
* [https://www.speedcubingtips.eu/zbll-zborowski-bruchem-last-layer/ Speedcubingtips.eu ] Complete
[[Category:3x3x3 last layer substeps]]
[[Category:Fewest Moves Methods]]
[[Category:Acronyms]]

Keyhole F2L

2020-01-04T14:17:25Z

DarkfireZZ:

{{Method Infobox
|name=Keyhole
|image=Keyhole.gif
|proposers
|year
|anames
|variants=[[8355]]
|steps=1 substep
|moves
|purpose=
* [[Speedsolving]]
* [[Beginner method]]
}}
'''Keyhole First Two Layers''' or '''Keyhole F2L''', sometimes named '''working corner''', is a [[method]] that solves, normally, the first two bottom layers of the [[3x3x3 cube]]. It is an efficient method for inserting mid-layer edges in the 3x3x3 [[LBL]] method. Its a slight advancement on the basic [[LBL]] method, because it requires fewer moves, as well as more intuition.

== Basic Idea ==

After the bottom layer cross, only ''three'' bottom layer corners are solved. The final corner is reserved as the ''keyhole'' to be used in solving the mid layer edges efficiently. To insert a mid layer edge using the keyhole:

You start, like in normal [[LBL]] from a [[cross]], then you fill in ''three'' of the first layer [[corner]]s. From that point you solve three of the middle layer [[edge]]s using the empty corner position as the ''keyhole''. For each edge do the following:
* First position the mid-layer edge in the U-layer such that it is above the centre matching the edge's up-facing colour.
* Using a D-Turn position the bottom layer so that the unsolved corner is directly below the mid-layer edge's position.
* Now execute one of R U' R' or F U F' to insert the edge.

After three corners and edges are solved you complete [[F2L]] by first solving the last corner and finally the last edge using the normal LBL algorithm: R U R' U' F' U' F or the mirror F' U' F U R U R' depending on the current orientation of the edge.

==== Alternative Procedure ====
An alternative way to do keyhole F2L is to use this order:
* cross (doesn't have to match centers)
* 3 corners
* 4 edges
* 4th corner

For that you will need three algorithms to solve the last piece depending on it's orientation:

''List of algs...''
=== F2L 32 ===
[[Image:F2L32.png]]

{{Alg|(R U R' U')(R U R' U')(R U R')|F2L}}
{{Alg|(U R U' R')(U R U' R')(U R U' R')|F2L}}
{{Alg|U2 R d' R U R' d R'|F2L}}
{{Alg|U R d' R U2 R' d R'|F2L}}
{{Alg|R2 U R2 U R2 U2 R2|F2L}}
{{Alg|U2 R2 U2 R2 U' R2 U' R2|F2L}}

=== F2L 33 ===
[[Image:F2L33.png]]

{{Alg|(U' R U' R') U2 (R U' R')|F2L}}
{{Alg|y U' (L U' L') U2 (L U' L)|F2L}}

=== F2L 34 ===
[[Image:F2L34.png]]

{{Alg|U' (R U2' R') U (R U R')|F2L}}
{{Alg|U (R U R') U2 (R U R')|F2L}}
{{Alg|d (R' U R) U2 (R' U R)|F2L}}

== Edges-First Keyhole ==
Another way to approach keyhole is to start by inserting three edges, and then use the remaining unsolved edge position to insert three corners. The basic steps are as follows:
* Solve Cross
* Solve 3x E-slice edges
* Rotate cube to position remaining unsolved slot in FR
* Solve 3x D-layer corners by:
:# Position a D-layer corner above the slot in the U-layer
:# Rotate D-layer so that the corner's correct location is directly below the slot
:# Insert the corner using one of: '''R U R'''' or '''F' U' F''' or '''R B U2 B' R''''
If there are no corners available in the U-layer, then rotate the D-layer until an unsolved D-layer corner is above the slot, and then use R U R' to swap it into the U-layer.

==== Advantages ====
While both the corners and edges first approaches use a similar number of moves, edges-first does not require the solver to keep track of the working corner, which can be better for lookahead. If used in conjunction with [[8355]] it may also improve ease of understanding, since a similar concept is used to place the final 5 corners.

== See also ==
* [[First Two Layers]]
* [[3x3x3 beginner methods]]
* [[8355]]
* [[LBL]]

== External links ==

* [http://www.youtube.com/watch?v=VQ-qIyScA5o Arnaud van Galen's YouTube Tutorial]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=687 Keyhole Method/Working Corner method]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=21790 Edges First Keyhole]
* [http://solvethecube.110mb.com/getting_faster.html Text Tutorial by Joël van Noort]

[[Category:F2L methods]]
[[Category:3x3x3 beginner methods]]
[[Category:Fewest Moves Methods]]

Blockbuilding

2020-01-04T14:16:29Z

DarkfireZZ:

'''Blockbuilding''' is a method for intuitive solving by creating groups of blocks and joining them together. It is used in the sub-steps of many methods including: [[Petrus]], [[Heise]], [[Roux]] and [[ZZ]]. Blockbuilding is an alternative to using algorithms.

== Blockbuilding on big cubes ==
Most people use the [[reduction method]] to speedsolve the [[5x5x5 cube]] but a few use [[direct solving]] to complete the [[puzzle]]. While doing that, there are some situations that does not occur on the [[4x4x4 cube]] (or any even-layered cube). Below is a listing of some [[algorithm]]s. They are also useful for 5x5x5 [[BLD]].

=== PLLs ===
* Rw2 Fw2 U2 r2 U2 Fw2 Rw2: PLL parity (wing edges)
* x Rw2 Uw2 x U2 l2 U2 x' Uw2 Rw2 (x'): same as previous
* F2 U m' U2 m U F2: U-PLL (center edges)
* F2 U' m' U2 m U' F2: U-PLL' (center edges)
* m2 U m2 U2 m2 U m2: H-PLL (center edges)
* Fw2 m2 Fw2 U2 m2 U m2 U m2: Z-PLL (center edges)

[[Category:Terminology]]
[[Category:2x2x2 methods]]
[[Category:3x3x3 methods]]
[[Category:4x4x4 methods]]
[[Category:5x5x5 methods]]
[[Category:Fewest Moves Methods]]
[[Category:Big Cube methods]]

2x2x3 Block

2020-01-04T14:15:16Z

DarkfireZZ:

{{Substep Infobox
|name=2x2x3 Block
|image=2x2x3.png
|proposers=
|year=
|anames=2x3x3
|variants=
|subgroup=
|algs=
|moves=
|purpose=
|previous=[[2x2x2 Block cube state]]
|next=[[2x2x3 Block cube state]]
}}

The '''2x2x3 block''' is the second step of the [[Petrus Method]], but is also widely used in [[FMC]]. It is an intuitive step.

==See also==
* [[2x2x2 Block]]
* [[Block building]]

{{stub}}

[[Category:3x3x3 block substeps]]
[[Category:Fewest Moves Methods]]

2x2x2 Block

2020-01-04T14:14:28Z

DarkfireZZ:

{{Substep Infobox
|name=2x2x2 Block
|image=Petrus method.gif
|proposers=
|year=
|anames=2x2x2
|variants=
|subgroup=
|algs=
|moves=
|purpose=
|previous=[[Scrambled cube state]]
|next=[[2x2x2 Block cube state]]
}}
The '''2x2x2 block''' is the first step of the [[Petrus Method]] and the [[Tripod Method]], as well as sometimes in the [[Cross]] variant [[XCross]], but is also widely used in [[FMC]]. The block is typically built intuitively.

==See also==
* [[2x2x3 Block]]
* [[Block building]]

[[Category:3x3x3 block substeps]]
[[Category:Fewest Moves Methods]]

QSTM

2020-01-04T13:57:58Z

DarkfireZZ: added categories

'''QSTM''', short for '''Q'''uarter '''S'''lice '''T'''urn '''M'''etric, is a [[move count metric]] for the 3x3x3 in which any clockwise or counterclockwise 90-degree turn of any layer counts as one turn, and [[rotation]]s do not count as moves.

This differs from [[QTM]] in that a [[slice]] move counts as one turn, not two; and it differs from [[STM]] in that 180-degree turns in any layer count as two moves, not one.

[[God's Number]] in QSTM is likely around 23-26 moves, but the exact number has not yet been proven.

== See Also ==
* [[Move count]]
* [[Fewest Moves]]
* [[Metric]]

[[Category:Acronyms]]
[[Category:Turn metrics]]

OBTM

2020-01-04T13:56:15Z

DarkfireZZ: added categories

'''OBTM''', short for '''O'''uter '''B'''lock '''T'''urn '''M'''etric, is the official [[turn metric]] system of the [[World Cube Association]].

OBTM defines 1 move as any non-[[slice]] move done on any [[twisty puzzle]]. Outer layer moves and outer block moves (outer layer plus adjacent inner layers) turned once or more is considered as 1 turn. [[Rotation]]s are considered as 0 moves.

== See Also ==
* [[HTM]]
* [[QTM]]
* [[STM]]

== External Links ==
* [https://www.worldcubeassociation.org/regulations/ WCA Regulations]

[[Category:Acronyms]]
[[Category:Turn metrics]]

STM

2020-01-04T13:45:12Z

DarkfireZZ: Removed from "Turn metric" category since it was listed there twice

#REDIRECT [[Slice Turn Metric]]

[[Category:Acronyms]]

HTM

2020-01-04T13:41:40Z

DarkfireZZ: Removed from "Turn metric" category since it was listed there twics

#REDIRECT [[Half Turn Metric]]

[[Category:Acronyms]]

Metric

2020-01-04T13:38:41Z

DarkfireZZ: Removed a grammatically incorrect sentence and added more links

: ''[[:Category:Turn metrics]]''

A '''metric''' (more specifically, '''move count metric''' or '''turn metric''') is a convention for [[move count|counting moves]]. The same sequence of moves can have different [[move count|move counts]] depending on the metric used.

== Summary of different metrics ==
For more details, see the respective articles.
* '''HTM'''; [[HTM|Half Turn Metric]] (or Face Turn Metric): Any face turn of any angle counts as 1 turn.
* '''QTM'''; [[QTM|Quarter Turn Metric]]: Only quarter (90-degree) face turns count as 1 turn.
* '''STM'''; [[STM|Slice Turn Metric]]: Any turn of any layer, by any angle, counts as 1 turn.
* '''QSTM'''; [[QSTM|Quarter Slice Turn Metric]]: Only quarter turns of any layer, by any angle, counts as 1 turn.
* '''ATM'''; [[ATM|Axial Turn Metric]]: Any movement within the same axis counts as 1 turn.
* '''ETM'''; [[ETM|Execution Turn Metric]]: Any perceived movement counts as 1 turn.
* '''OBTM'''; [[OBTM|Outer Block Turn Metric]]: The official metric of the [[WCA]] in which all non-[[slice]] moves on all [[twisty puzzle]]s are considered 1 move and rotations are 0 moves
* '''BTM'''; [[BTM|Block Turn Metric]]: A metric for measuring movecounts on [[Bigcubes]]

== Uses ==

Metrics are used to measure the length of move sequences such as [[Algorithm|Algorithms]] or [[Reconstruction|Reconstructions]]. [[God's number]] is known to be 20 in [[HTM]] and 26 in [[QTM]]. From a mathematical standpoint, however, [[QTM]] seems a more natural choice; half-turns are visibly redundant as generators.

== Debate over metric in FMC ==
[[WCA]] uses [[HTM]] in [[FMC]]. There has been a number of debates arguing for different metrics.

== See also ==
* [[Move count]]
* [[HTM]]
* [[QTM]]
* [[STM]]
* [[QSTM]]
* [[ATM]]
* [[ETM]]
* [[OBTM]]
* [[BTM]]

== External Links ==
* [https://www.speedsolving.com/forum/threads/move-count-metrics-for-big-cubes-standards-and-preferences.23546/ SpeedSolving Forum Thread: Move count metrics for big cubes - standards and preferences]
* [https://www.cube20.org/ God's Number is 20]
* [https://www.cube20.org/qtm/ God's Number is 26 in the Quarter-Turn Metric]

[[Category:Terminology]]

2x2x2 Cube

2020-01-04T12:21:37Z

DarkfireZZ: removed broken link to "2x2x2 Cubes"

{{Puzzle Infobox|
|NAME=2x2x2
|IMAGE=Wiki 2x2x2 solved.jpg
|ALTERNATIVENAMES=Pocket Cube, Mini Cube, 2x2
|SHAPE=Cube
|MECHANISM=2x2x2
|INVENTOR=Erno Rubik
|YEAR=1981
|COMPANIES=Ideal Toy}}

The '''2x2x2 Cube''' (also known as a '''Pocket Cube''' or '''Mini Cube''' and normally referred to as the '''2x2x2''' or '''2x2''') is a twistable [[puzzle]] in the shape of a [[cube]] that is cut once along each of three axes.

The first such cube was [[Rubik's Brand|Rubik's Pocket Cube]] invented by [[Erno Rubik]] and released by [[Ideal]] Toys in 1981. In 1998 [[Chen Sen Li]] patented his [[East Sheen]] cube. Since the mid-2000s other brands began to appear such as the [[LanLan]], the [[Ghosthand 2x2x2|Ghosthand]] and the [[WitTwo]].

This puzzle has 8 [[corner]] pieces only. The 2x2x2 cube has 3,674,160 possible positions (assuming one piece is always solved from orienting the puzzle), each of which can be solved in 11 turns ([[HTM]]) / 14 turns ([[QTM]]) or fewer.

Current best 2x2x2: Valk2M, MGC 2x2

== See also ==
* [[:Category:2x2x2_beginner_methods|2x2x2 Beginner Methods]]
* [[:Category:2x2x2_speedsolving_methods|2x2x2 Speedsolving Methods]]
* [http://en.wikipedia.org/wiki/Pocket_Cube The Wikipedia article]

{{Regularcubics}}
{{Cubics}}

[[Category:2x2x2]]
[[Category:Twisty puzzles]]
[[Category:Twisty puzzles used in WCA-official events]]

File:CLS.png

2020-01-04T12:17:54Z

DarkfireZZ: DarkfireZZ uploaded a new version of File:CLS.png

== Summary ==
added CLS png

File:CLS.png

2020-01-04T12:00:43Z

DarkfireZZ: added CLS png

== Summary ==
added CLS png