Difference between revisions of "ZZ method"

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{{Method Infobox
 
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* [[One-Handed Solving]]
 
* [[One-Handed Solving]]
 
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f [[F2L]], the solver only needs to mak L, U, and R moves, which means that the solver's hands never leave the left and right sides of the cube, esulting in faster solving. In addition, edges are already oriented when the solver reaches the last lyermeaning the solver has fewer cases to deal with. The method, including both EOLine and EOCross, was origiproposed in 2003 by [[Ryan Heise]] on the [[Yahoo! Speed Solving Rubik's Cube Group|Yahoo! Group]] in[https://www.speedsolving.com/wiki/index.php/File:Ryan_Heise%27s_ZZ_Proposal.png this post]. However, it becme popular and associated with Zbigniew Zborowski after he independently created the method in 2006 and deveoped a website==The Steps==
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* '''[[EOLine]]:''' This is the most disinctive part of the ZZ method. In this step, the solver orients all the edges while placing the DF and DB edes. The two edges and the bottom centre are the "line" in [[EOLine]]. This step puts the cube intoan <L, U, R> group, meaning F, B, or D moves are not required for the remainder of the solve. Although thi step may seem like a hinderance, it speeds up the F2L and LL.
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The '''ZZ method''' is a 3x3 speedsolving method created by [[Zbigniew Zborowski]] in 2006. The method is focused both on low move count and high turning speed; during the majority of [[F2L]], the solver only needs to make L, U, and R moves, which means that the solver's hands never leave the left and right sides of the cube, resulting in faster solving. In addition, edges are already oriented when the solver reaches the last layer, meaning the solver has fewer cases to deal with. The method, including both EOLine and EOCross, was originally proposed in 2003 by [[Ryan Heise]] on the [[Yahoo! Speed Solving Rubik's Cube Group|Yahoo! Group]] in [https://www.speedsolving.com/wiki/index.php/File:Ryan_Heise%27s_ZZ_Proposal.png this post]. However, it became popular and associated with Zbigniew Zborowski after he independently created the method in 2006 and developed a website.
* '''[[ZZ F2L]]:''' The solver creates ax3x1 block on each sid of the line via blockbuilding. Because one only needs to do L, U and R moves, solvi is very quick
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* '''LL:''' The solver uses algorithms solve the remaining peces. Since he edges inthe LL wre orened during OLine, itcan be omplete in feer moves ndr with fwer algorthms to lear
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==The Steps==
==Techniques
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* '''[[EOLine]]:''' This is the most distinctive part of the ZZ method. In this step, the solver orients all the edges while placing the DF and DB edges. The two edges and the bottom centre are the "line" in [[EOLine]]. This step puts the cube into an <L, U, R> group, meaning F, B, or D moves are not required for the remainder of the solve. Although this step may seem like a hinderance, it speeds up the F2L and LL.
* '''[[Phasing]]''' During last slot, th LL edges are permuted using [[Phasing]] to perute opposte edges to be opposite using 3 different inserts. This edce te amun of LL case
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* '''[[ZZ F2L]]:''' The solver creates a 2x3x1 block on each side of the line via blockbuilding. Because one only needs to do L, U, and R moves, solving is very quick.
* '''Corner Permutation''' The first bloc be solved sily iffely or an agcan be used to permute the corners such that the rest of the solve can be dne [[2-gen]].
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* '''LL:''' The solver uses algorithms to solve the remaining pieces. Since the edges in the LL were oriented during EOLine, it can be completed in fewer moves and/or with fewer algorithms to learn.
==Variants
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There are several variations of the ZZ mthod ([https://www.speedsolving.com/threads/te-zz-xamle-solve-game.48190/page-21#post-1361812 exampleolves for each variant]), each of which reas he [[F2L]] and [[LL]] differently. When the ZZ method was propsed, the original variants on Zbigniew Zbroski's website were ZZ-a, b, c, d, and  
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==Techniques==
====Solving F2L and LL separately===
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* '''[[Phasing]]''' During last slot, the LL edges are permuted using [[Phasing]] to permute opposite edges to be opposite using 3 different inserts. This reduces the amount of LL cases.
* '''[[OCLL]] + [[PLL]]:''' LL is solvedsing OCLL to orient the LL corers, then PLL is used to permute the LL. This is the simplest of all the varints and he most used when beginning to use ZZ.  
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* '''Corner Permutation''' The first block can be solved slightly differently or an alg can be used to permute the corners such that the rest of the solve can be done [[2-gen]].  
* '''[[OCELL]] + [[CPLL]]:''' ThiHackericomebacks is similar to using [COLL]] [[EPLL]], bt mor f the aloiths ca be [2-gen]]. First the LL corners areoriented and LL edges are permuted in onestep, then the cube is completed with CPLL in the final st
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* '''ZZ-a:''' [[ZBLL]], a subset of [[1LL]] (one-look last layer), is used to solve the last layer with one alg. There are 493 cases and can be donewith less algs by taking advantage of mirrors.
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==Variants==
* '''[[COLL]] + [[EPLL]]''', or ZZ-VH (smetimes mistakenly called ZZ-a): COLL is used to orient and permute the LL corners while preserving LL edge rientation (42 algorithms), EPLL is left to permute the LL edges (4 algorithms). Often used in OH solving beause all EPLL's can be solved 2-gen.
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* '''[[CLL+1|COLL+1]]:''' This LL methodsolves the four LL corners and a single LL edge. The second step will then always be either a U-Perm orskip.
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There are several variations of the ZZ method ([https://www.speedsolving.com/threads/the-zz-example-solve-game.48190/page-21#post-1361812 example solves for each variant]), each of which treats the [[F2L]] and [[LL]] differently. When the ZZ method was proposed, the original variants on Zbigniew Zborowski's website were ZZ-a, b, c, d, and e.
* '''[[NMLL]]:''' An LL method that is cmpatible with non-matching blocks and matching blocks. The first step separates the colors blnigt te left and right layer. The second finishes permutation.
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*'''ZZ-top:''' During EOlne, orient only the cross edges and F2L edges. After ZZF2L you will end up with the same last layer as CFOP, o you can just do OLL/PLL
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====Solving F2L and LL separately====
====Influencing LL duringF2L====
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* '''[[OCLL]] + [[PLL]]:''' LL is solved using OCLL to orient the LL corners, then PLL is used to permute the LL. This is the simplest of all the variants and the most used when beginning to use ZZ.  
* '''ZZ-b:''' During lastslot, the LL edges are phased and [[ZZLL]] is used to solve the LL in one look.
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* '''[[OCELL]] + [[CPLL]]:''' This is similar to using [[COLL]] + [[EPLL]], but more of the algorithms can be [[2-gen]]. First the LL corners are oriented and LL edges are permuted in one step, then the cube is completed with CPLL in the final step.
* '''[[ZZ-reduction]]:'''During the Last Slot, the LL edges are phased and a 2-look orientation + permutation approach is ued, with the phased edges preserved in the orientation step, resulting in a reduction of PLL cases don to 9 compared to 21 in full PLL. This is the least algorithm intensive 2-look method fort layer of any [[2LLL]] method, needing 7 + 9 = 16 total algorithms.
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* '''ZZ-a:''' [[ZBLL]], a subset of [[1LLL]] (one-look last layer), is used to solve the last layer with one alg. There are 493 cases and can be done with less algs by taking advantage of mirrors.
* '''ZZ-[[WV]] and ZZ-[[S]]:''' Before the last corner-edge pair is solved, the LL corners are oriented with PLL left to be done
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* '''[[COLL]] + [[EPLL]]''', or ZZ-VH (sometimes mistakenly called ZZ-a): COLL is used to orient and permute the LL corners while preserving LL edge orientation (42 algorithms), EPLL is left to permute the LL edges (4 algorithms). Often used in OH solving because all EPLL's can be solved 2-gen.
* '''ZZ-[[WVCP]] and ZZ-SVCP]]:''' Before the last corner-edge pair is solved, the LL corners are oriented and permuted at the same ime resulting in an [[EPLL]] finish. This is similar to ZZ-VH except that the corners are solved duringinsertion of the last pair.
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* '''[[CLL+1|COLL+1]]:''' This LL method solves the four LL corners and a single LL edge. The second step will then always be either a U-Perm or a skip.
* '''ZZ-c:''' The last laer corners are oriented during insertion of the last F2L block. This system is similar to using [[WinterVariation]], but can be applied to ''any'' last block situation and uses many more algorithms. Conceptually,the comparison of ZZ-c with ZZ-WV is similar to the comparison of [[ZBLS]] with [[VH]]. This variant was roposed by [[Mitchell Stern]] and included as one of the variants on Zbigniew Zborowski's website
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* '''[[NMLL]]:''' An LL method that is compatible with non-matching blocks and matching blocks. The first step separates the colors belonging to the left and right layer. The second finishes permutation.
* '''[[ZZ-blah]]:''' The ast layer corners are ''disoriented'' during insertion of the last slot allowing the last layer to be solvd using the Pi and H subsets of [[ZBLL]].
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*'''ZZ-top:''' During EOline, orient only the cross edges and F2L edges. After ZZF2L you will end up with the same last layer as CFOP, so you can just do OLL/PLL.
* '''[[MGLS-Z]]:''' Durin last slot, only the edge is placed. LL corner orientation and the final F2L corner are then solved in one stp using [[CLS]]. Finally the solve is carily oriented. A subset of CLS is then used to orient the last slot corner alon with the LL corners. [[PLL]] to finish.
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*'''[[ZZ-CT]]:''' This vaiant solves EO and all but one F2L slot, then inserts the last edge and orients corners in one algorithm,thenrest (PLL and one corner), again in one algorithm.
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====Influencing LL during F2L====
*'''ZZ-C++:''' A hybrido ZZ-CT and ZZ-C proposed by [[Chris Tran]] where the best algorithm is chosen depending on the situat. [https://youtue/-Vp1GwnWy-Y]
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* '''ZZ-b:''' During last slot, the LL edges are phased and [[ZZLL]] is used to solve the LL in one look.
*'''ZZ-[[LSE]] or ZZ-[[4c]]:''' Insead of solving EO and a line comprising of DF and DB, solve EO and then place the edges that go to UL and UR at DF and DB. After ZZF2L, you can then do COLL and then go directly into Roux LSE step 4c, which is close to two moves more efficient than Yx09vMB33C0JyKPfXhKrXnzkrHKM/edit?usp=sharing]
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* '''[[ZZ-reduction]]:''' During the Last Slot, the LL edges are phased and a 2-look orientation + permutation approach is used, with the phased edges preserved in the orientation step, resulting in a reduction of PLL cases down to 9 compared to 21 in full PLL. This is the least algorithm intensive 2-look method for solving the last layer of any [[2LLL]] method, needing 7 + 9 = 16 total algorithms.
*'''ZZ-[[Portico]] or just [[Portico]]:''' Rather than at the start, the DF edge is solved at the end. Compared to ZZ-VH, thisads to a slightly more efficient solve an an easier first step at the price of <RULF2(M)> turning (as oosed to ZZ's <RUL>) and 12 additional algorithms.
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* '''ZZ-[[WV]] and ZZ-[[SV]]:''' Before the last corner-edge pair is solved, the LL corners are oriented with PLL left to be done.
*'''[[ZZ-Zipper]]''': Oneof 614 [[L5CO]] algorithms followed by [[L5EP]] is used toved earlier or [[Conjugated CxLL]] can be used in order to achieve 2-look LLL in 54 algorithms.  
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* '''ZZ-[[WVCP]] and ZZ-[[SVCP]]:''' Before the last corner-edge pair is solved, the LL corners are oriented and permuted at the same time resulting in an [[EPLL]] finish. This is similar to ZZ-VH except that the corners are solved during insertion of the last pair.
*'''ZZ-[[Tripod]]''': Aftr F2L-1, a 1x2x2 block is built on the top face. Then the last pair is insertpreserve the block followed by TELL, a subset of [[Tripod LL]] with edges already oriented. (More information can be found on the [[Tripod Method]] page.
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* '''ZZ-c:''' The last layer corners are oriented during insertion of the last F2L block. This system is similar to using [[Winter Variation]], but can be applied to ''any'' last block situation and uses many more algorithms. Conceptually, the comparison of ZZ-c with ZZ-WV is similar to the comparison of [[ZBLS]] with [[VH]]. This variant was proposed by [[Mitchell Stern]] and included as one of the variants on Zbigniew Zborowski's website.
====Solving Corner Permuttion during F2L====
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* '''[[ZZ-blah]]:''' The last layer corners are ''disoriented'' during insertion of the last slot allowing the last layer to be solved using the Pi and H subsets of [[ZBLL]].
These methods solve Corner Permutation leaving the cub
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* '''[[MGLS-Z]]:''' During last slot, only the edge is placed. LL corner orientation and the final F2L corner are then solved in one step using [[CLS]]. Finally the solve is completed with [[PLL]].
* '''ZZ-d:''' Just before the completion of the left block, corners are permuted and [[2GLL]] can be used to finish. Only a maximum of 2 additional moves are required to correctly solve CP. This process is calspeed solving.
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* '''[[EJLS]]:''' Similar to MGLS-Z, but using less algorithms. During the F2L last slot the edge and corner are connected and placed, but the corner is not necessarily oriented. A subset of CLS is then used to orient the last slot corner along with the LL corners. [[PLL]] to finish.
* '''ZZ-e / ZZ-Orbit:''' Corners are permuted during insertion of the last F2L's pair. Recognition is not so straight forward, but much faster than that of ZZ-d. Once performed, [[2GLL]] can be used for 1-look last layer. This has many similarities to [[CPLS]]+[[2GLL]], but wadently. ZZ-e has the alternate name of ZZ-Orbit because community member Kim Orbit was the first to completely develop the variant. Thread:[http://www.speedsolving.com/forum/show-method-has-been-COMPLETED!!!!!!!!&p=705181#post705181] Guide:[http://www.speedsolving.com/forum/showthread.php?43208-ZZ-Orbit-Guide]
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*'''[[ZZ-CT]]:''' This variant solves EO and all but one F2L slot, then inserts the last edge and orients corners in one algorithm, then solves the rest (PLL and one corner), again in one algorithm.
* '''ZZ-z: ''' After left block, CP is solved, then a 1x2ck is made on BDR and [[LPELL]] is used to permute the edges and finish F2L, and 2GLL is left to finish the solve.
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*'''ZZ-C++:''' A hybrid of ZZ-CT and ZZ-C proposed by [[Chris Tran]] where the best algorithm is chosen depending on the situation. [https://youtu.be/-Vp1GwnWy-Y]
* '''ZZ-porky v1:''' Also known as ZZ-e. The D layer corners are lready done the setup moves for ZZ-porky v1, and so execute the ZZ-porky algorithm, then solve the rest of the cube 2-gen.
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*'''ZZ-[[LSE]] or ZZ-[[4c]]:''' Instead of solving EO and a line comprising of DF and DB, solve EO and then place the edges that go to UL and UR at DF and DB. After ZZF2L, you can then do COLL and then go directly into Roux LSE step 4c, which is close to two moves more efficient than EPLL. [https://docs.google.com/spreadsheets/d/1PbdzQrIzMAaYIqhYx09vMB33C0JyKPfXhKrXnzkrHKM/edit?usp=sharing]
*'''ZZ-porky v2:''' After solving the first square of ZZF2L, place the DRB and DRF corners and AUF the last first block corner to UBL. then execute an algorithm to permut of the cube with only <RU> moves. Post: [https://www.speedsolving.com/threads/new-approach-to-zz-d.43236/]
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*'''ZZ-[[Portico]] or just [[Portico]]:''' Rather than at the start, the DF edge is solved at the end. Compared to ZZ-VH, this leads to a slightly more efficient solve and an easier first step at the price of <RULF2(M)> turning (as opposed to ZZ's <RUL>) and 12 additional algorithms.
*'''[[CPLS]] + [[2GLL]]:''' After solving ZZF2L-1 slot, insert thee. then insert the final corner while solving CP, then finish with 2GLL.
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*'''[[ZZ-Zipper]]''': One of 614 [[L5CO]] algorithms followed by [[L5EP]] is used to solve last slot and last layer. Alternatively, the last D-layer corner can be solved earlier or [[Conjugated CxLL]] can be used in order to achieve 2-look LSLL in 54 algorithms.  
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*'''ZZ-[[Tripod]]''': After F2L-1, a 1x2x2 block is built on the top face. Then the last pair is inserted using an NLS algorithm to preserve the block followed by TELL, a subset of [[Tripod LL]] with edges already oriented. (More information can be found on the [[Tripod Method]] page.)
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====Solving Corner Permutation during F2L====
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These methods solve Corner Permutation leaving the cube in a [[2-gen]] state.
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* '''ZZ-d:''' Just before the completion of the left block, corners are permuted and [[2GLL]] can be used to finish. Only a maximum of 2 additional moves are required to correctly solve CP. This process is called [[CPLS]]. However, the solver must determine the permutation of all the unsolved corners to execute this step; this is a slow process, which makes ZZ-d inappropriate for speed solving.
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* '''ZZ-e / ZZ-Orbit:''' Corners are permuted during insertion of the last F2L's pair. Recognition is not so straight forward, but much faster than that of ZZ-d. Once performed, [[2GLL]] can be used for 1-look last layer. This has many similarities to [[CPLS]]+[[2GLL]], but was developed independently. ZZ-e has the alternate name of ZZ-Orbit because community member Kim Orbit was the first to completely develop the variant. Thread:[http://www.speedsolving.com/forum/showthread.php?34994-At-last-ZZ-method-has-been-COMPLETED!!!!!!!!&p=705181#post705181] Guide:[http://www.speedsolving.com/forum/showthread.php?43208-ZZ-Orbit-Guide]
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* '''ZZ-z: ''' After left block, CP is solved, then a 1x2x2 block is made on BDR and [[LPELL]] is used to permute the edges and finish F2L, and 2GLL is left to finish the solve.
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* '''ZZ-porky v1:''' Also known as ZZ-e. The D layer corners are put in the D layer (not necessarily permuted) and alg is used to solve corner permutation. Post:[http://www.speedsolving.com/forum/showthread.php?20834-ZZ-ZB-Home-Thread&p=768029#post768029]
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*'''ZZ-Rainbow:''' A variant of ZZ-porky v1. After EOLine, place the DFR and DRB corners in place and get the Left Block pieces in the L and U layers. Then either solve the first block<LU> or do a z rotation and then solving it RU. After first block, you have already done the setup moves for ZZ-porky v1, and so execute the ZZ-porky algorithm, then solve the rest of the cube 2-gen.
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*'''ZZ-porky v2:''' After solving the first square of ZZF2L, place the DRB and DRF corners and AUF the last first block corner to UBL. then execute an algorithm to permute the corners. Followingly, insert the last first block pair using only <LU> moves, then solve the rest of the cube with only <RU> moves. Post: [https://www.speedsolving.com/threads/new-approach-to-zz-d.43236/]
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*'''[[CPLS]] + [[2GLL]]:''' After solving ZZF2L-1 slot, insert the edge. then insert the final corner while solving CP, then finish with 2GLL.
  
 
====General Variants====
 
====General Variants====
 
*'''[[ZZ-Snake Pattern]] (ZZ-SP):''' After solving the first ZZF2L block on L, solve a 1x2x3 block on the top of the cube with <RU>, then rotate with a z' and solve the LL.
 
*'''[[ZZ-Snake Pattern]] (ZZ-SP):''' After solving the first ZZF2L block on L, solve a 1x2x3 block on the top of the cube with <RU>, then rotate with a z' and solve the LL.
*'''ZZ-LOL (Line On Left):''' By solving [[EO Steps#EOEdge|EOEdge]] (EO + LF and LB edges) instead of [[EOLine]], the cube is reduced to <RUD> rather thancs in exchange for very bad lookahead.
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*'''ZZ-LOL (Line On Left):''' By solving [[EO Steps#EOEdge|EOEdge]] (EO + LF and LB edges) instead of [[EOLine]], the cube is reduced to <RUD> rather than <RUL>. This results in a standard ZZ solve offset by a z rotation with way better ergonomics in exchange for very bad lookahead.
*'''WaterZZ''': WaterZZ was inspired by [[WaterRoux]] which in turn was inspired by [[Waterman]]. Instead of an EOLine, the solve is started with [[EO Steps#EO222|EO222]] (EO + 2x2x2 block). Then, a 1x2xof 614 [[L5CO]] algorithms and then [[L6EP]] to finish off the solve.
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*'''WaterZZ''': WaterZZ was inspired by [[WaterRoux]] which in turn was inspired by [[Waterman]]. Instead of an EOLine, the solve is started with [[EO Steps#EO222|EO222]] (EO + 2x2x2 block). Then, a 1x2x2 square and a pair are solved in BR and FL, respectively. This is followed by one of 614 [[L5CO]] algorithms and then [[L6EP]] to finish off the solve.
*'''[[ZZ-EF]]''': ZZ-EF is a variant that allows for a low movecount [[ZZ F2L]] by solving pairs with incorrect corners which only have to satisfy the constraint of forming a 3-cycle on the D layer. This is followed by reducing the last layer to a 3-cycle, too, and forming the two algorithms which solve these 3-cycles.
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*'''[[ZZ-EF]]''': ZZ-EF is a variant that allows for a low movecount [[ZZ F2L]] by solving pairs with incorrect corners which only have to satisfy the constraint of forming a 3-cycle on the D layer. This is followed by reducing the last layer to a 3-cycle, too, and finishing the solve by performing the two algorithms which solve these 3-cycles.
*'''[[ZZ-Slice]]''': ZZ-Slice starts off with [[EOSlice]], followed by solving [[ZZ F2L]] in pairs. However, the pairs' corners do not have to be permuted, oh [[CPBL]]. This variant, however, averages 65-75 moves.
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*'''[[ZZ-Slice]]''': ZZ-Slice starts off with [[EOSlice]], followed by solving [[ZZ F2L]] in pairs. However, the pairs' corners do not have to be permuted, only oriented, correctly. After that, LL corners are oriented, the last six edges are permuted and the solve is finished with [[CPBL]]. This variant, however, averages 65-75 moves.
  
 
== Pros ==
 
== Pros ==
* '''Reduced Move Set''': F2L is completed using only R, U and L turns and no cube rotations are required.  This makes ZZ especia
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* '''Reduced Move Set''': F2L is completed using only R, U and L turns and no cube rotations are required.  This makes ZZ especially suited for one-handed solving.
* '''Ease of Learning''': Most of the difficulty in ZZsuming use of mirrors) are required to achieve a 2-look last layer with [[OCLL]]/[[PLL]].
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* '''Lookahead''': Pre-orientation of edges halves the F2L cases and makes edges easier to find and connect to blocks/corners. During a ZZ solve, the cube is typically held in the same orientation through out the solve which allows a memory map of pieces' correct locations to develop allowing fast/intuitive ability to place pieces without thinking/looking.
* '''Flexibility''': With edges pre-oriented many systems exist for completing the last layer in a ZZ solve, ranging from [[OCLL]]/[[PLL]] to [[ZBLL]]. A blockbuilding F2L a for the development of many short cuts and tricks as skill improves.
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* '''Efficiency''': With a blockbuilding-based F2L and pre-orientation of LL edges around 55 moves can be achieved without difficulty. Optimising F2L blockbuilding and adoption of more advanced LL systems such as [[ZBLL]] will reduce this move count significantly.
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* '''Ease of Learning''': Most of the difficulty in ZZ is confined to the EOLine stage. Intuitive blockbuilding during F2L is fairly easy to pick up and only 20 algorithms (assuming use of mirrors) are required to achieve a 2-look last layer with [[OCLL]]/[[PLL]].
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* '''Flexibility''': With edges pre-oriented many systems exist for completing the last layer in a ZZ solve, ranging from [[OCLL]]/[[PLL]] to [[ZBLL]]. A blockbuilding F2L also allows for the development of many short cuts and tricks as skill improves.
  
 
== Cons ==
 
== Cons ==
* '''Reliance on Inspection''' - ZZ makes heavy  
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* '''Reliance on Inspection''' - ZZ makes heavy use of inspection time, which is fine when 15 seconds is given, but in situations where no inspection is used it can be a drawback. For example, when using reduction on big cubes or within multi-solve scenarios starting a ZZ solve can be difficult. This isn't much more than other methods though.
 
* '''Difficulty of EOLine''' - EOLine is weird to get used to at first. In order to plan and execute in one step and takes a ''long time'' to master. New users should expect it to take in the order of months to achieve full EOLine inspection in 15 seconds. In the interim, breaking it down into two steps (EO + Line) can be used as a fall-back.
 
* '''Difficulty of EOLine''' - EOLine is weird to get used to at first. In order to plan and execute in one step and takes a ''long time'' to master. New users should expect it to take in the order of months to achieve full EOLine inspection in 15 seconds. In the interim, breaking it down into two steps (EO + Line) can be used as a fall-back.
* '''2 Extra F2L Cubies to Solve''' - The first step of Fridrich (Cross) and ZZ (EOLine) are roughly comparable in terms of move-count. The remainder of F2L in ZZ requirreedom to fully rotate the L and R faces and the use of more efficient block building compensates for this apparent disadvantage.
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* '''2 Extra F2L Cubies to Solve''' - The first step of Fridrich (Cross) and ZZ (EOLine) are roughly comparable in terms of move-count. The remainder of F2L in ZZ requires solving of two more cubies (10 in total) than Fridrich slots (8 in total). However, freedom to fully rotate the L and R faces and the use of more efficient block building compensates for this apparent disadvantage.
 
* '''Switching between L and R moves''' - On the other hand, this can feel weird. It takes some time getting used to and mastering. After one does master this though, f2l is really smooth.
 
* '''Switching between L and R moves''' - On the other hand, this can feel weird. It takes some time getting used to and mastering. After one does master this though, f2l is really smooth.
  
== Improvements =
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== Improvements ==
Other EO Steps (the most popular ones being [[EOCross]] and [[EOArrow]]) instead of [[EOLine]] can be used as a first step. EOCro made up for with its easier lookahead and reduced regrips. (See the [[EO Steps]] article for more information.)  
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Other EO Steps (the most popular ones being [[EOCross]] and [[EOArrow]]) instead of [[EOLine]] can be used as a first step. EOCross has a slightly higher movecount which is made up for with its easier lookahead and reduced regrips. (See the [[EO Steps]] article for more information.)  
  
 
== ZZ on other puzzles ==
 
== ZZ on other puzzles ==
 
The concept of orienting edges early to make the rest of the solve more ergonomic and rotationless has been applied to different puzzles. A list of puzzles and known ZZ-based methods for them is shown here:
 
The concept of orienting edges early to make the rest of the solve more ergonomic and rotationless has been applied to different puzzles. A list of puzzles and known ZZ-based methods for them is shown here:
* '''[[4x4x4]] (and other [[Big cubes]]):''' [[Z4]], [[4Z]], [[ZZ44]] and [[Mehtad]]
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* '''[[4x4x4]] (and other [[Big cubes]]):''' [[Z4]], [[4Z4]], [[ZZ44]] and [[Mehtad]]
* '''[[Megaminx]]:'''[[MegaZZ]]
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* '''[[Megaminx]]:''' [[ZZ-Spike]], [[MegaZZ]]
  
 
== Notable users ==
 
== Notable users ==

Revision as of 16:40, 16 January 2022

ZZ method
Eoline.gif
Information about the method
Proposer(s): Zbigniew Zborowski
Proposed: 2006
Alt Names: none
Variants: See #Variants
No. Steps: 3 or 4 (depending on LL)
No. Algs: 20 to 514
F2L: 0 to 21
LL: 28 to 493
Avg Moves: 45 with EOLine, 53 with EOCross
Purpose(s):


The ZZ method is a 3x3 speedsolving method created by Zbigniew Zborowski in 2006. The method is focused both on low move count and high turning speed; during the majority of F2L, the solver only needs to make L, U, and R moves, which means that the solver's hands never leave the left and right sides of the cube, resulting in faster solving. In addition, edges are already oriented when the solver reaches the last layer, meaning the solver has fewer cases to deal with. The method, including both EOLine and EOCross, was originally proposed in 2003 by Ryan Heise on the Yahoo! Group in this post. However, it became popular and associated with Zbigniew Zborowski after he independently created the method in 2006 and developed a website.

The Steps

  • EOLine: This is the most distinctive part of the ZZ method. In this step, the solver orients all the edges while placing the DF and DB edges. The two edges and the bottom centre are the "line" in EOLine. This step puts the cube into an <L, U, R> group, meaning F, B, or D moves are not required for the remainder of the solve. Although this step may seem like a hinderance, it speeds up the F2L and LL.
  • ZZ F2L: The solver creates a 2x3x1 block on each side of the line via blockbuilding. Because one only needs to do L, U, and R moves, solving is very quick.
  • LL: The solver uses algorithms to solve the remaining pieces. Since the edges in the LL were oriented during EOLine, it can be completed in fewer moves and/or with fewer algorithms to learn.

Techniques

  • Phasing During last slot, the LL edges are permuted using Phasing to permute opposite edges to be opposite using 3 different inserts. This reduces the amount of LL cases.
  • Corner Permutation The first block can be solved slightly differently or an alg can be used to permute the corners such that the rest of the solve can be done 2-gen.

Variants

There are several variations of the ZZ method (example solves for each variant), each of which treats the F2L and LL differently. When the ZZ method was proposed, the original variants on Zbigniew Zborowski's website were ZZ-a, b, c, d, and e.

Solving F2L and LL separately

  • OCLL + PLL: LL is solved using OCLL to orient the LL corners, then PLL is used to permute the LL. This is the simplest of all the variants and the most used when beginning to use ZZ.
  • OCELL + CPLL: This is similar to using COLL + EPLL, but more of the algorithms can be 2-gen. First the LL corners are oriented and LL edges are permuted in one step, then the cube is completed with CPLL in the final step.
  • ZZ-a: ZBLL, a subset of 1LLL (one-look last layer), is used to solve the last layer with one alg. There are 493 cases and can be done with less algs by taking advantage of mirrors.
  • COLL + EPLL, or ZZ-VH (sometimes mistakenly called ZZ-a): COLL is used to orient and permute the LL corners while preserving LL edge orientation (42 algorithms), EPLL is left to permute the LL edges (4 algorithms). Often used in OH solving because all EPLL's can be solved 2-gen.
  • COLL+1: This LL method solves the four LL corners and a single LL edge. The second step will then always be either a U-Perm or a skip.
  • NMLL: An LL method that is compatible with non-matching blocks and matching blocks. The first step separates the colors belonging to the left and right layer. The second finishes permutation.
  • ZZ-top: During EOline, orient only the cross edges and F2L edges. After ZZF2L you will end up with the same last layer as CFOP, so you can just do OLL/PLL.

Influencing LL during F2L

  • ZZ-b: During last slot, the LL edges are phased and ZZLL is used to solve the LL in one look.
  • ZZ-reduction: During the Last Slot, the LL edges are phased and a 2-look orientation + permutation approach is used, with the phased edges preserved in the orientation step, resulting in a reduction of PLL cases down to 9 compared to 21 in full PLL. This is the least algorithm intensive 2-look method for solving the last layer of any 2LLL method, needing 7 + 9 = 16 total algorithms.
  • ZZ-WV and ZZ-SV: Before the last corner-edge pair is solved, the LL corners are oriented with PLL left to be done.
  • ZZ-WVCP and ZZ-SVCP: Before the last corner-edge pair is solved, the LL corners are oriented and permuted at the same time resulting in an EPLL finish. This is similar to ZZ-VH except that the corners are solved during insertion of the last pair.
  • ZZ-c: The last layer corners are oriented during insertion of the last F2L block. This system is similar to using Winter Variation, but can be applied to any last block situation and uses many more algorithms. Conceptually, the comparison of ZZ-c with ZZ-WV is similar to the comparison of ZBLS with VH. This variant was proposed by Mitchell Stern and included as one of the variants on Zbigniew Zborowski's website.
  • ZZ-blah: The last layer corners are disoriented during insertion of the last slot allowing the last layer to be solved using the Pi and H subsets of ZBLL.
  • MGLS-Z: During last slot, only the edge is placed. LL corner orientation and the final F2L corner are then solved in one step using CLS. Finally the solve is completed with PLL.
  • EJLS: Similar to MGLS-Z, but using less algorithms. During the F2L last slot the edge and corner are connected and placed, but the corner is not necessarily oriented. A subset of CLS is then used to orient the last slot corner along with the LL corners. PLL to finish.
  • ZZ-CT: This variant solves EO and all but one F2L slot, then inserts the last edge and orients corners in one algorithm, then solves the rest (PLL and one corner), again in one algorithm.
  • ZZ-C++: A hybrid of ZZ-CT and ZZ-C proposed by Chris Tran where the best algorithm is chosen depending on the situation. [1]
  • ZZ-LSE or ZZ-4c: Instead of solving EO and a line comprising of DF and DB, solve EO and then place the edges that go to UL and UR at DF and DB. After ZZF2L, you can then do COLL and then go directly into Roux LSE step 4c, which is close to two moves more efficient than EPLL. [2]
  • ZZ-Portico or just Portico: Rather than at the start, the DF edge is solved at the end. Compared to ZZ-VH, this leads to a slightly more efficient solve and an easier first step at the price of <RULF2(M)> turning (as opposed to ZZ's <RUL>) and 12 additional algorithms.
  • ZZ-Zipper: One of 614 L5CO algorithms followed by L5EP is used to solve last slot and last layer. Alternatively, the last D-layer corner can be solved earlier or Conjugated CxLL can be used in order to achieve 2-look LSLL in 54 algorithms.
  • ZZ-Tripod: After F2L-1, a 1x2x2 block is built on the top face. Then the last pair is inserted using an NLS algorithm to preserve the block followed by TELL, a subset of Tripod LL with edges already oriented. (More information can be found on the Tripod Method page.)

Solving Corner Permutation during F2L

These methods solve Corner Permutation leaving the cube in a 2-gen state.

  • ZZ-d: Just before the completion of the left block, corners are permuted and 2GLL can be used to finish. Only a maximum of 2 additional moves are required to correctly solve CP. This process is called CPLS. However, the solver must determine the permutation of all the unsolved corners to execute this step; this is a slow process, which makes ZZ-d inappropriate for speed solving.
  • ZZ-e / ZZ-Orbit: Corners are permuted during insertion of the last F2L's pair. Recognition is not so straight forward, but much faster than that of ZZ-d. Once performed, 2GLL can be used for 1-look last layer. This has many similarities to CPLS+2GLL, but was developed independently. ZZ-e has the alternate name of ZZ-Orbit because community member Kim Orbit was the first to completely develop the variant. Thread:[3] Guide:[4]
  • ZZ-z: After left block, CP is solved, then a 1x2x2 block is made on BDR and LPELL is used to permute the edges and finish F2L, and 2GLL is left to finish the solve.
  • ZZ-porky v1: Also known as ZZ-e. The D layer corners are put in the D layer (not necessarily permuted) and alg is used to solve corner permutation. Post:[5]
  • ZZ-Rainbow: A variant of ZZ-porky v1. After EOLine, place the DFR and DRB corners in place and get the Left Block pieces in the L and U layers. Then either solve the first block<LU> or do a z rotation and then solving it RU. After first block, you have already done the setup moves for ZZ-porky v1, and so execute the ZZ-porky algorithm, then solve the rest of the cube 2-gen.
  • ZZ-porky v2: After solving the first square of ZZF2L, place the DRB and DRF corners and AUF the last first block corner to UBL. then execute an algorithm to permute the corners. Followingly, insert the last first block pair using only <LU> moves, then solve the rest of the cube with only <RU> moves. Post: [6]
  • CPLS + 2GLL: After solving ZZF2L-1 slot, insert the edge. then insert the final corner while solving CP, then finish with 2GLL.

General Variants

  • ZZ-Snake Pattern (ZZ-SP): After solving the first ZZF2L block on L, solve a 1x2x3 block on the top of the cube with <RU>, then rotate with a z' and solve the LL.
  • ZZ-LOL (Line On Left): By solving EOEdge (EO + LF and LB edges) instead of EOLine, the cube is reduced to <RUD> rather than <RUL>. This results in a standard ZZ solve offset by a z rotation with way better ergonomics in exchange for very bad lookahead.
  • WaterZZ: WaterZZ was inspired by WaterRoux which in turn was inspired by Waterman. Instead of an EOLine, the solve is started with EO222 (EO + 2x2x2 block). Then, a 1x2x2 square and a pair are solved in BR and FL, respectively. This is followed by one of 614 L5CO algorithms and then L6EP to finish off the solve.
  • ZZ-EF: ZZ-EF is a variant that allows for a low movecount ZZ F2L by solving pairs with incorrect corners which only have to satisfy the constraint of forming a 3-cycle on the D layer. This is followed by reducing the last layer to a 3-cycle, too, and finishing the solve by performing the two algorithms which solve these 3-cycles.
  • ZZ-Slice: ZZ-Slice starts off with EOSlice, followed by solving ZZ F2L in pairs. However, the pairs' corners do not have to be permuted, only oriented, correctly. After that, LL corners are oriented, the last six edges are permuted and the solve is finished with CPBL. This variant, however, averages 65-75 moves.

Pros

  • Reduced Move Set: F2L is completed using only R, U and L turns and no cube rotations are required. This makes ZZ especially suited for one-handed solving.
  • Lookahead: Pre-orientation of edges halves the F2L cases and makes edges easier to find and connect to blocks/corners. During a ZZ solve, the cube is typically held in the same orientation through out the solve which allows a memory map of pieces' correct locations to develop allowing fast/intuitive ability to place pieces without thinking/looking.
  • Efficiency: With a blockbuilding-based F2L and pre-orientation of LL edges around 55 moves can be achieved without difficulty. Optimising F2L blockbuilding and adoption of more advanced LL systems such as ZBLL will reduce this move count significantly.
  • Ease of Learning: Most of the difficulty in ZZ is confined to the EOLine stage. Intuitive blockbuilding during F2L is fairly easy to pick up and only 20 algorithms (assuming use of mirrors) are required to achieve a 2-look last layer with OCLL/PLL.
  • Flexibility: With edges pre-oriented many systems exist for completing the last layer in a ZZ solve, ranging from OCLL/PLL to ZBLL. A blockbuilding F2L also allows for the development of many short cuts and tricks as skill improves.

Cons

  • Reliance on Inspection - ZZ makes heavy use of inspection time, which is fine when 15 seconds is given, but in situations where no inspection is used it can be a drawback. For example, when using reduction on big cubes or within multi-solve scenarios starting a ZZ solve can be difficult. This isn't much more than other methods though.
  • Difficulty of EOLine - EOLine is weird to get used to at first. In order to plan and execute in one step and takes a long time to master. New users should expect it to take in the order of months to achieve full EOLine inspection in 15 seconds. In the interim, breaking it down into two steps (EO + Line) can be used as a fall-back.
  • 2 Extra F2L Cubies to Solve - The first step of Fridrich (Cross) and ZZ (EOLine) are roughly comparable in terms of move-count. The remainder of F2L in ZZ requires solving of two more cubies (10 in total) than Fridrich slots (8 in total). However, freedom to fully rotate the L and R faces and the use of more efficient block building compensates for this apparent disadvantage.
  • Switching between L and R moves - On the other hand, this can feel weird. It takes some time getting used to and mastering. After one does master this though, f2l is really smooth.

Improvements

Other EO Steps (the most popular ones being EOCross and EOArrow) instead of EOLine can be used as a first step. EOCross has a slightly higher movecount which is made up for with its easier lookahead and reduced regrips. (See the EO Steps article for more information.)

ZZ on other puzzles

The concept of orienting edges early to make the rest of the solve more ergonomic and rotationless has been applied to different puzzles. A list of puzzles and known ZZ-based methods for them is shown here:

Notable users

See also

External links