Difference between revisions of "L5E"
m (→Semiadvanced system for E5) 
m 

(32 intermediate revisions by 4 users not shown)  
Line 1:  Line 1:  
−  '''L5E''' is  +  {{Substep Infobox 
+  name=L5E  
+  image=  
+  proposers=  
+  year=  
+  anames=[[Last five edges]]  
+  variants=[[Sexy*+S(8355)]]n [[SexyM Beginner]], [[Commutators (pseudo EF)]]  
+  subgroup=  
+  algs= Unknown for 1 look, 5 for L5EO and 16 for L5EP  
+  moves= about 14  
+  purpose=  
+  previous=[[5 Corners Missing cube state]]  
+  next=[[Solved cube state]]  
+  }}  
+  
+  '''L5E, Last five edges''', is an experimental method that solves five [[edges]], the four in U and one in the D layer, preserving all other pieces.  
+  
+  [[ELL]] is a sub group of L5E, all ELL's may be solved in two steps using this method.  
== Description ==  == Description ==  
−  There are two main subparts. First the edges are oriented using M'UM like in Roux; there are 5 cases for this, and the worst case in Roux (6 edges) is impossible. Then the edges must be permuted; you can place FD during orientation or right after and end with [[EPLL]], or just permute all five edges in one step.  +  There are two main subparts. First the edges are oriented using M'UM like in Roux; there are 5 cases for this, and the worst case in Roux (6 edges) is impossible. Then the edges must be permuted; you can place FD during orientation or right after using [U] M' U2 M (named 'P') and end with [[EPLL]], or just permute all five edges in one step. 
−  L5E can be useful for [[Corners First]] if the Eslice, centres and three FL edges are solved after the corners. It is also useful in any method that starts with [[columns]], such as one which does the F2L pairs first and then finishes with [[CxLLCMLL]], it is an alternative to the last step of [[Roux]] if the centres are placed together with the BD edge at first, also for any LBL style, cross minus one edge at first and then the LL corners have been finished with [[CLL]] or [[CMLL]] or the same for Fridrich with 2look [[OLL]], corners first, then L5E orientation, place FD using  +  L5E can be useful for [[Corners First]] if the Eslice, centres and three FL edges are solved after the corners. It is also useful in any method that starts with [[columns]], such as one which does the F2L pairs first and then finishes with [[CxLLCMLL]], it is an alternative to the last step of [[Roux]] if the centres are placed together with the BD edge at first, also for any LBL style, cross minus one edge at first and then the LL corners have been finished with [[CLL]] or [[CMLL]] or the same for Fridrich with 2look [[OLL]], corners first, then L5E orientation, place FD using P if it was not solved and end it all in PLL as usally. 
==Intermediate system==  ==Intermediate system==  
−  ===Intuitive  +  ===Intuitive=== 
This style is not completely intuitive, because it is still necessary to know [[EPLL]]. First orient all unoriented edges, then place the FD edge to its correct position and finally end the solve in EPLL. The necessary intuitive steps are:  This style is not completely intuitive, because it is still necessary to know [[EPLL]]. First orient all unoriented edges, then place the FD edge to its correct position and finally end the solve in EPLL. The necessary intuitive steps are:  
Line 23:  Line 40:  
It is important here that the moves inside the parentheses keep the corners solved, so that they will still be correct after this algorithm. An example is the [[Uperm]], F(U P U) = F2 (U M' U2 M U) F2. F(O U') is a nice way to solve orientation and place FD all at once if the FD edge is in the middle of three unoriented edges in LL.  It is important here that the moves inside the parentheses keep the corners solved, so that they will still be correct after this algorithm. An example is the [[Uperm]], F(U P U) = F2 (U M' U2 M U) F2. F(O U') is a nice way to solve orientation and place FD all at once if the FD edge is in the middle of three unoriented edges in LL.  
−  ===Using algorithms  +  ===Using algorithms=== 
The intuitive style lets you find and understand the orientation algorithms yourself. Another approach is to learn the algorithms instead of finding them; the cases are:  The intuitive style lets you find and understand the orientation algorithms yourself. Another approach is to learn the algorithms instead of finding them; the cases are:  
Line 31:  Line 48:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:FUL Solved.jpg80px  +  IMAGE=[[Image:FUL Solved.jpg80px]] 
NAME=''Intuitive solution''  NAME=''Intuitive solution''  
ALGO=''(Possibly optimised) alg''  ALGO=''(Possibly optimised) alg''  
Line 38:  Line 55:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EO5 2 adjacent.jpg80px  +  IMAGE=[[Image:EO5 2 adjacent.jpg80px]] 
NAME=O U2 O  NAME=O U2 O  
ALGO=(M' U M) U2 (M' U M)  ALGO=(M' U M) U2 (M' U M)  
Line 46:  Line 63:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EO5 2 opposite.jpg80px  +  IMAGE=[[Image:EO5 2 opposite.jpg80px]] 
NAME=O U' O  NAME=O U' O  
ALGO=(M' U M) U' (M' U M)  ALGO=(M' U M) U' (M' U M)  
Line 53:  Line 70:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EO5 4.jpg80px  +  IMAGE=[[Image:EO5 4.jpg80px]] 
NAME=P U2 O'  NAME=P U2 O'  
ALGO=(M' U2 M) U2 (M' U' M)  ALGO=(M' U2 M) U2 (M' U' M)  
Line 61:  Line 78:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EO5 1.jpg80px  +  IMAGE=[[Image:EO5 1.jpg80px]] 
NAME=O U O'  NAME=O U O'  
ALGO=(M' U M) U (M' U' M)  ALGO=(M' U M) U (M' U' M)  
Line 68:  Line 85:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EO5 3.jpg80px  +  IMAGE=[[Image:EO5 3.jpg80px]] 
NAME=O'  NAME=O'  
ALGO=(M' U' M)  ALGO=(M' U' M)  
Line 76:  Line 93:  
 colspan="2"  <center>''All images show white on top (U) and green in front (F).''</center>   colspan="2"  <center>''All images show white on top (U) and green in front (F).''</center>  
}  }  
+  ''More algs are at the [[L5EOPL5EOP page]]''  
Sometimes this will also solve the FD edge; the images show where the FD edge must be for the algorithm to solve it, but otherwise you should simply treat the yellow sticker as white. If you learn these positions, it can also be useful to learn the mirror algorithm for the case where FD is on the opposite side from the image. The easiest example is to use O' instead of O for the case with three flipped edges on U. Just like the intuitive step, if FD is not solved use P, and either way finish with [[EPLL]].  Sometimes this will also solve the FD edge; the images show where the FD edge must be for the algorithm to solve it, but otherwise you should simply treat the yellow sticker as white. If you learn these positions, it can also be useful to learn the mirror algorithm for the case where FD is on the opposite side from the image. The easiest example is to use O' instead of O for the case with three flipped edges on U. Just like the intuitive step, if FD is not solved use P, and either way finish with [[EPLL]].  
Line 81:  Line 99:  
==Semiadvanced system==  ==Semiadvanced system==  
−  +  [[L5EOP]] is an alternative to L5E, that always solves the FD edge while orienting ('P'lace). Then the last step will always be EPLL.  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  +  ===FD placement + EPLL (L5EP)===  
−  +  Another possibility for improving the intermediate style is to permutate the last five edges in one step. This only requires 16 algorithms in total, so counting the 5 orientations creates a system that solves L5E in two short steps. Even if you know this, it is still useful to place FD without extra moves if possible, since EPLL recognition is very fast.  
−  ===FD placement + EPLL (  
−  Another possibility for improving  
We will introduce the following function:  We will introduce the following function:  
Line 108:  Line 114:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:FUL Solved.jpg80px  +  IMAGE=[[Image:FUL Solved.jpg80px]] 
NAME=''Intuitive solution''  NAME=''Intuitive solution''  
ALGO=''(Possibly optimised) alg''  ALGO=''(Possibly optimised) alg''  
Line 115:  Line 121:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 22 A.jpg80px  +  IMAGE=[[Image:EP5 22 A.jpg80px]] 
NAME=F(HPLL)  NAME=F(HPLL)  
ALGO=(y') R U2 R2 U2 R2 U2 R  ALGO=(y') R U2 R2 U2 R2 U2 R  
Line 123:  Line 129:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 22 B1.jpg80px  +  IMAGE=[[Image:EP5 22 B1.jpg80px]] 
NAME=F(ZPLL)  NAME=F(ZPLL)  
ALGO=(y') r2 U' 2x(M E2) U r2  ALGO=(y') r2 U' 2x(M E2) U r2  
Line 130:  Line 136:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 22 B2.jpg80px  +  IMAGE=[[Image:EP5 22 B2.jpg80px]] 
NAME=F(ZPLL')  NAME=F(ZPLL')  
ALGO=(y') r2 U 2x(M E2) U' r2  ALGO=(y') r2 U 2x(M E2) U' r2  
Line 138:  Line 144:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 22 H.jpg80px  +  IMAGE=[[Image:EP5 22 H.jpg80px]] 
−  NAME=[[PLL#  +  NAME=[[PLL#H PermutationHPLL]] 
ALGO=Ra U2 Ra' (y) Ra' U2 Ra  ALGO=Ra U2 Ra' (y) Ra' U2 Ra  
INFO=Swaps UR<>UL and UF<>UB  INFO=Swaps UR<>UL and UF<>UB  
Line 145:  Line 151:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 22 Z.jpg80px  +  IMAGE=[[Image:EP5 22 Z.jpg80px]] 
−  NAME=[[PLL#  +  NAME=[[PLL#Z PermutationZPLL]] 
ALGO=M2 U' 2x(M E2) U M2  ALGO=M2 U' 2x(M E2) U M2  
INFO=Swaps UR<>UB and UL<>UF  INFO=Swaps UR<>UB and UL<>UF  
Line 155:  Line 161:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 3 A.jpg80px  +  IMAGE=[[Image:EP5 3 A.jpg80px]] 
NAME=P  NAME=P  
ALGO= (M' U2 M)  ALGO= (M' U2 M)  
Line 162:  Line 168:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 3 B1.jpg80px  +  IMAGE=[[Image:EP5 3 B1.jpg80px]] 
NAME=f(d' P)  NAME=f(d' P)  
ALGO=(y') r2 U' (M' U2 M) U' r2  ALGO=(y') r2 U' (M' U2 M) U' r2  
Line 170:  Line 176:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 3 B2.jpg80px  +  IMAGE=[[Image:EP5 3 B2.jpg80px]] 
NAME=f(d P)  NAME=f(d P)  
ALGO=(y') r2 U (M U2 M') U r2  ALGO=(y') r2 U (M U2 M') U r2  
Line 177:  Line 183:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 3 U1.jpg80px  +  IMAGE=[[Image:EP5 3 U1.jpg80px]] 
−  NAME=[[PLL#  +  NAME=[[PLL#U Permutation : bUPLL]] 
ALGO=F2 U (M' U2 M) U F2  ALGO=F2 U (M' U2 M) U F2  
INFO=Cycles UF>UL>UR  INFO=Cycles UF>UL>UR  
Line 185:  Line 191:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 3 U2.jpg80px  +  IMAGE=[[Image:EP5 3 U2.jpg80px]] 
−  NAME=[[PLL#  +  NAME=[[PLL#U Permutation : aUPLL']] 
ALGO=F2 U' (M' U2 M) U' F2  ALGO=F2 U' (M' U2 M) U' F2  
INFO=Cycles UF>UR>UL  INFO=Cycles UF>UR>UL  
Line 196:  Line 202:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 5 H1.jpg80px  +  IMAGE=[[Image:EP5 5 H1.jpg80px]] 
NAME=P U P  NAME=P U P  
ALGO=(M' U2 M) U (M' U2 M)  ALGO=(M' U2 M) U (M' U2 M)  
Line 203:  Line 209:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 5 H2.jpg80px  +  IMAGE=[[Image:EP5 5 H2.jpg80px]] 
NAME=P U' P  NAME=P U' P  
ALGO=(M' U2 M) U' (M' U2 M)  ALGO=(M' U2 M) U' (M' U2 M)  
Line 211:  Line 217:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 5 Z1.jpg80px  +  IMAGE=[[Image:EP5 5 Z1.jpg80px]] 
NAME=P ZPLL  NAME=P ZPLL  
ALGO=2x(M2 U) (M U2 M')  ALGO=2x(M2 U) (M U2 M')  
Line 218:  Line 224:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 5 Z2.jpg80px  +  IMAGE=[[Image:EP5 5 Z2.jpg80px]] 
NAME=P ZPLL'  NAME=P ZPLL'  
ALGO=2x(M2 U') (M U2 M')  ALGO=2x(M2 U') (M U2 M')  
Line 226:  Line 232:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 5 U1.jpg80px  +  IMAGE=[[Image:EP5 5 U1.jpg80px]] 
NAME=P UPLL  NAME=P UPLL  
ALGO=(M' U2 M') U' (M' U2 M) U' M2  ALGO=(M' U2 M') U' (M' U2 M) U' M2  
Line 233:  Line 239:  
    
{{Casebox  {{Casebox  
−  IMAGE=[[Image:EP5 5 U2.jpg80px  +  IMAGE=[[Image:EP5 5 U2.jpg80px]] 
NAME=P UPLL'  NAME=P UPLL'  
ALGO=(M' U2 M') U (M' U2 M) U M2  ALGO=(M' U2 M') U (M' U2 M) U M2  
Line 243:  Line 249:  
}  }  
−  ==Advanced system  +  ==Advanced system== 
−  The most advanced system would be to simply solve  +  The most advanced system would be to simply solve in one step. Nobody has generated the algorithms for this yet, but it may not be a good idea because of the large number of cases and bad recognition. For the worst ones the algorithm will probably just be the same as in the 2step solution, so the benefit will be small at best. 
One case where this is useful (and doable) is to solve cases where at least one of the edges is solved at the start. Using setup turns and [[ELL]] this can be done in one step, although the recognition and setup moves might mean that this is not worth doing.  One case where this is useful (and doable) is to solve cases where at least one of the edges is solved at the start. Using setup turns and [[ELL]] this can be done in one step, although the recognition and setup moves might mean that this is not worth doing.  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
−  
==See also==  ==See also==  
+  * [[ELL]]  
+  * [[PCMS]]  
* [http://athefre.110mb.com/Step5.html Permutation of last 5 edges by Athefre]  * [http://athefre.110mb.com/Step5.html Permutation of last 5 edges by Athefre]  
+  * [https://docs.google.com/spreadsheets/d/1feWj3FOAc6cH4Zpt_zGxuwJt8w_4aSkkmxoxpYzWdBA/edit?usp=sharing L5EP Algorithm Spreadsheet]  
+  
−  +  [[Category:Experimental methods]]  
−  [[Category:Experimental  +  [[Category:3x3x3 other substeps]] 
−  [[Category:3x3x3  +  [[Category:Acronyms]] 
−  [[Category: 
Latest revision as of 19:09, 7 July 2019


L5E, Last five edges, is an experimental method that solves five edges, the four in U and one in the D layer, preserving all other pieces.
ELL is a sub group of L5E, all ELL's may be solved in two steps using this method.
Contents
Description
There are two main subparts. First the edges are oriented using M'UM like in Roux; there are 5 cases for this, and the worst case in Roux (6 edges) is impossible. Then the edges must be permuted; you can place FD during orientation or right after using [U] M' U2 M (named 'P') and end with EPLL, or just permute all five edges in one step.
L5E can be useful for Corners First if the Eslice, centres and three FL edges are solved after the corners. It is also useful in any method that starts with columns, such as one which does the F2L pairs first and then finishes with CMLL, it is an alternative to the last step of Roux if the centres are placed together with the BD edge at first, also for any LBL style, cross minus one edge at first and then the LL corners have been finished with CLL or CMLL or the same for Fridrich with 2look OLL, corners first, then L5E orientation, place FD using P if it was not solved and end it all in PLL as usally.
Intermediate system
Intuitive
This style is not completely intuitive, because it is still necessary to know EPLL. First orient all unoriented edges, then place the FD edge to its correct position and finally end the solve in EPLL. The necessary intuitive steps are:
 P = M' U2 M
 O = M' U M
 O' = M' U' M
Using that plus some U turns you can solve any case, even all ELL case. For example, O U P = (M' U M) U (M' U2 M) is a sample algorithm which solves orientation, then places FD. There is a 1 in 12 chance that EPLL is skipped; otherwise there is one algorithm left.
There is another notation which can make it shorter to write algorithms:
 F(moves) = F2 (moves) F2
It is important here that the moves inside the parentheses keep the corners solved, so that they will still be correct after this algorithm. An example is the Uperm, F(U P U) = F2 (U M' U2 M U) F2. F(O U') is a nice way to solve orientation and place FD all at once if the FD edge is in the middle of three unoriented edges in LL.
Using algorithms
The intuitive style lets you find and understand the orientation algorithms yourself. Another approach is to learn the algorithms instead of finding them; the cases are:
More algs are at the L5EOP page
Sometimes this will also solve the FD edge; the images show where the FD edge must be for the algorithm to solve it, but otherwise you should simply treat the yellow sticker as white. If you learn these positions, it can also be useful to learn the mirror algorithm for the case where FD is on the opposite side from the image. The easiest example is to use O' instead of O for the case with three flipped edges on U. Just like the intuitive step, if FD is not solved use P, and either way finish with EPLL.
Semiadvanced system
L5EOP is an alternative to L5E, that always solves the FD edge while orienting ('P'lace). Then the last step will always be EPLL.
FD placement + EPLL (L5EP)
Another possibility for improving the intermediate style is to permutate the last five edges in one step. This only requires 16 algorithms in total, so counting the 5 orientations creates a system that solves L5E in two short steps. Even if you know this, it is still useful to place FD without extra moves if possible, since EPLL recognition is very fast.
We will introduce the following function:
 f(moves) = f2 (moves) [U] f2 ... This is the same as the F() function above, but with double layer f turns. Note that sometimes the adjusting U turns are not mentioned.
Here are the algorithms for permutation of all 5 edges; make sure to use AUF to place the FD edge at the position it has in the image.

 

 

 

 

 



 

 



Advanced system
The most advanced system would be to simply solve in one step. Nobody has generated the algorithms for this yet, but it may not be a good idea because of the large number of cases and bad recognition. For the worst ones the algorithm will probably just be the same as in the 2step solution, so the benefit will be small at best.
One case where this is useful (and doable) is to solve cases where at least one of the edges is solved at the start. Using setup turns and ELL this can be done in one step, although the recognition and setup moves might mean that this is not worth doing.