Difference between revisions of "L5E"

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'''E15''' and '''E35''' are methods that solves the last six or the last eight edges of the U and D layers, first three D layer edges are done (one, BD in E15) and then the last five ones. Always preserving all corners and E-slice edges. The first part also solves the centres.
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{{Substep Infobox
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|name=L5E
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|image=
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|proposers=
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|year=
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|anames=[[Last five edges]]
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|variants=[[Sexy*+S(8355)]]n [[SexyM Beginner]], [[Commutators (pseudo EF)]]
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|subgroup=
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|algs= Unknown for 1 look, 5 for L5EO and 16 for L5EP
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|moves= about 14
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|purpose=
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|previous=[[5 Corners Missing cube state]]
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|next=[[Solved cube state]]
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}}
 +
 
 +
'''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.
  
E35 is not a compleate brute force method, it uses a combination of intuition and algorithms, an advanced user even include [[ELL]] in the method to save turns in some cases but most times you end in [[EPLL]] or 5 edge permutation. It is much as [[Roux]] last step but here orientation is done after all centres are solved to make recognition easier/faster so the M-permut used last in Roux is not really useful here (you solve centres and BD before orient instead of RU/LU after).
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== Description ==
 +
There are two main sub-parts. 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.
  
'''Short description:'''
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L5E can be useful for [[Corners First]] if the E-slice, 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 [[CxLL|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 2-look [[OLL]], corners first, then L5E orientation, place FD using P if it was not solved and end it all in PLL as usally.
* '''E3 part''' First pair up RD and LD edges, then place them together with R and L centres or simply do one at the time, the first one as a pair with the centre and the second using AUF M' U/U'/U2 M, last palce BD + B centre as a pair.
 
* '''E1 part''' As E3 but only the last edge.
 
* '''E5 part''' this part has got two main sub-parts, first orient the edges using the Roux M' U M style (5 cases, newer the worst 6 edge case of Roux). If possible also place FD during orientation, else do it after using M' U2 M and end in [[EPLL]]. You can also first orient and then permute all five edges in one go.
 
  
E35 may be used in [[CF]] if the E-slice is solved after the corners or in any method that solves columns first, like doing all pairs first and then [[CxLL|CMLL]] (or CMSLL). E15 is a good alternative to [[Roux]] last step. The E5 part is a stand alone method, it can be used togehtr with a standard [[F2L]] where the last edge for the cross is ignored and LL corners are solved after that (CLL or CMLL).
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==Intermediate system==
  
==Intermediate system for E5==
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===Intuitive===
===Intuitive:===
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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 intuitive style is not all intuitive because you need to know EPLL. First orient all unorientd edges, then place the FD edge to it's correct position and end the solve in EPLL. For that you basicly need this:
 
  
 
* P = M' U2 M
 
* P = M' U2 M
 
 
* O = M' U M
 
* O = M' U M
 
* O' = M' U' M
 
* O' = M' U' M
* O2 = P ... ''not used''
 
  
From that plus some U turns you can solve any case, (including all [[ELL]] cases), example: O U P = (M' U M) U (M' U2 M). O solves orientation U P places FD edge and then the EPLL solves permutation for the last four edges, all now in LL (if it did not skip, it is a 1:12 chance).
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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.
  
The algorithms for some cases can be shorter if you also add this to the system:
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There is another notation which can make it shorter to write algorithms:
  
* F() = F2 ( MOVES ) [u] F2
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* F(moves) = F2 (moves) F2
  
The U turn can be any U, U' U2 or no U turn depending on how U moves inside the parentesis of the "function". F(U P) makes the usual 7 turn U-PLL = F2 (U M' U2 M) U F2. F(O) is a nice way to solve orientation and place FD in one go if it is in the middle of three unoriented edges in LL, just AUF as you where about to do only O.
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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 [[U-perm]], 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:===
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===Using algorithms===
The intuitive style lets you find and understand the algorithms you need to orient the 5 cases that are possible for the orientation part but another approach is to learn the algorithms instead of finding them.
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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:
  
 
{| style="border: 1px solid #808080; color: black; background-color: #FAFAFA;" cellspacing="0" cellpadding="2"
 
{| style="border: 1px solid #808080; color: black; background-color: #FAFAFA;" cellspacing="0" cellpadding="2"
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:FUL Solved.jpg|80px|]]
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|IMAGE=[[Image:FUL Solved.jpg|80px]]
 
|NAME=''Intuitive solution''
 
|NAME=''Intuitive solution''
 
|ALGO=''(Possibly optimised) alg''
 
|ALGO=''(Possibly optimised) alg''
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EO5 2 adjacent.jpg|80px|]]
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|IMAGE=[[Image:EO5 2 adjacent.jpg|80px]]
 
|NAME=O U2 O
 
|NAME=O U2 O
 
|ALGO=(M' U M) U2 (M' U M)
 
|ALGO=(M' U M) U2 (M' U M)
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EO5 2 opposite.jpg|80px|]]
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|IMAGE=[[Image:EO5 2 opposite.jpg|80px]]
 
|NAME=O U' O
 
|NAME=O U' O
 
|ALGO=(M' U M) U' (M' U M)
 
|ALGO=(M' U M) U' (M' U M)
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EO5 4.jpg|80px|]]
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|IMAGE=[[Image:EO5 4.jpg|80px]]
 
|NAME=P U2 O'
 
|NAME=P U2 O'
 
|ALGO=(M' U2 M) U2 (M' U' M)
 
|ALGO=(M' U2 M) U2 (M' U' M)
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EO5 1.jpg|80px|]]
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|IMAGE=[[Image:EO5 1.jpg|80px]]
 
|NAME=O U O'
 
|NAME=O U O'
 
|ALGO=(M' U M) U (M' U' M)
 
|ALGO=(M' U M) U (M' U' M)
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EO5 3.jpg|80px|]]
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|IMAGE=[[Image:EO5 3.jpg|80px]]
 
|NAME=O'
 
|NAME=O'
 
|ALGO=(M' U' M)
 
|ALGO=(M' U' M)
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}}
 
}}
 
|---
 
|---
| colspan="2" | <center>''All images shows white on top (U), green in front (F) and orange left side (L).''</center>
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| colspan="2" | <center>''All images show white on top (U) and green in front (F).''</center>
 
|}
 
|}
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''More algs are at the [[L5EOP|L5EOP page]]''
  
Sometimes you will solve FD permutation while doing this, in the images the yellow sticker shows where the DF edge has to be to get solved using the given algorithms (for all other reasons, treat it as a white sticker). If you learn these position you can for some situations also learn to use the mirror algorithm when the FD edge is on the opposite side from where you normally solve it, the easiest example is to use O' (M' U' M) instead of O (M' U M). In the cases where you cannot solve FD permutation while orienting you use AUF + P to solve it, it is at the most 4 turns, then EPLL.
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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]].
 
 
==Semi advanced system for E5==
 
'''Orientations with FD permutation:'''<br>
 
In many cases you can solve FD permutation wile orienting in the same number of turns as you do only orientation. For the rest of the cases it is a bad idéa to learn algorithms because they would most times end in the same turns as do anyway to solve FD after orientation or if not the length of the algorithm is of the same length as the 2-step or at least almost. But there are a number of good cases, here is the list:
 
 
 
* ''alg'' ... (possibly optimised) MOVES ... ''orient pices'', ''permute FD''
 
 
 
* M U F(U' M') ... M d R2 d' M' d R2 ... RU and FU, FD at UF.
 
* M U' F(U M') ... M d' L2 d M' d' L2 ... LU and FU, FD at UF.
 
  
''More algs later...''
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==Semi-advanced system==
  
===EP5===
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[[L5EOP]] is an alternative to L5E, that always solves the FD edge while orienting ('P'lace). Then the last step will always be EPLL.
'''EPLL + FD permutation in one go:'''<br>
 
  
Another reason for not learning all algorithms for placing FD while orienting is that you can do the permutation for all last five edges in one go using only 12 extra algorithms above the usual 4 EPLL's, a total of 16 algs, add to that the needed 5 orientations and you got a system of 21 algorithms to solves E5 in two short steps. But it is still recomended to use as many of the short algorithms for orientation + FD permutation as possible because recognition is faster for EPLL than it is for most the of rest of the cases.
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===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.
  
Here follows the algorithms for permutation of all 5 edges (including EPLL), preceed these with AUF to place the FD edge at the position it has in the images.
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We will introduce the following function:
 
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* 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.
But first we also introduce this:
 
* -P = M U2 M'
 
And this:
 
* f() = f2 ( MOVES ) [U] f2 ... the same as the F() function above but double layer f turns.
 
  
 +
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.
  
 
{| style="border: 1px solid #808080; color: black; background-color: #FAFAFA;" cellspacing="0" cellpadding="2"
 
{| style="border: 1px solid #808080; color: black; background-color: #FAFAFA;" cellspacing="0" cellpadding="2"
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:FUL Solved.jpg|80px|]]
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|IMAGE=[[Image:FUL Solved.jpg|80px]]
 
|NAME=''Intuitive solution''
 
|NAME=''Intuitive solution''
 
|ALGO=''(Possibly optimised) alg''
 
|ALGO=''(Possibly optimised) alg''
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 22 A.jpg|80px|]]
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|IMAGE=[[Image:EP5 22 A.jpg|80px]]
 
|NAME=F(H-PLL)
 
|NAME=F(H-PLL)
 
|ALGO=(y') R U2 R2 U2 R2 U2 R
 
|ALGO=(y') R U2 R2 U2 R2 U2 R
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 22 B1.jpg|80px|]]
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|IMAGE=[[Image:EP5 22 B1.jpg|80px]]
 
|NAME=F(Z-PLL)
 
|NAME=F(Z-PLL)
 
|ALGO=(y') r2 U' 2x(M E2) U r2
 
|ALGO=(y') r2 U' 2x(M E2) U r2
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 22 B2.jpg|80px|]]
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|IMAGE=[[Image:EP5 22 B2.jpg|80px]]
|NAME=F(Z'-PLL)
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|NAME=F(Z-PLL')
 
|ALGO=(y') r2 U 2x(M E2) U' r2
 
|ALGO=(y') r2 U 2x(M E2) U' r2
 
|INFO=Swaps UL<->DF and UR<->UB
 
|INFO=Swaps UL<->DF and UR<->UB
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 22 H.jpg|80px|]]
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|IMAGE=[[Image:EP5 22 H.jpg|80px]]
|NAME=[[PLL#H_Permutation|H PLL]]
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|NAME=[[PLL#H Permutation|H-PLL]]
 
|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
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|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 22 Z.jpg|80px|]]
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|IMAGE=[[Image:EP5 22 Z.jpg|80px]]
|NAME=[[PLL#Z_Permutation|Z PLL]]
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|NAME=[[PLL#Z Permutation|Z-PLL]]
 
|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
 
}}
 
}}
 
|---
 
|---
| colspan="2" | <center>'''Three cycle permutations'''</center>
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| colspan="2" | <center>'''3-cycle permutations'''</center>
 
|---
 
|---
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 3 A.jpg|80px|]]
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|IMAGE=[[Image:EP5 3 A.jpg|80px]]
 
|NAME=P
 
|NAME=P
 
|ALGO= (M' U2 M)
 
|ALGO= (M' U2 M)
|INFO=Cycles UF->DF->UB->UF
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|INFO=Cycles UF->DF->UB
 
}}
 
}}
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 3 B1.jpg|80px|]]
+
|IMAGE=[[Image:EP5 3 B1.jpg|80px]]
 
|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
|INFO=Cycles UL->UB-DF->UL
+
|INFO=Cycles UL->UB->DF
 
}}
 
}}
 
|---
 
|---
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 3 B2.jpg|80px|]]
+
|IMAGE=[[Image:EP5 3 B2.jpg|80px]]
 
|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
|INFO=Cycles UR->UB->DF-UR
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|INFO=Cycles UR->UB->DF
 
}}
 
}}
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 3 U1.jpg|80px|]]
+
|IMAGE=[[Image:EP5 3 U1.jpg|80px]]
|NAME=[[PLL#U_Permutation_:_b|U PLL]] / F(U P)
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|NAME=[[PLL#U Permutation : b|U-PLL]]
 
|ALGO=F2 U (M' U2 M) U F2
 
|ALGO=F2 U (M' U2 M) U F2
|INFO=Cycles UF->UL-UR->UF
+
|INFO=Cycles UF->UL->UR
 
}}
 
}}
 
|---
 
|---
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 3 U2.jpg|80px|]]
+
|IMAGE=[[Image:EP5 3 U2.jpg|80px]]
|NAME=[[PLL#U_Permutation_:_a|U' PLL]] / F(U' P)
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|NAME=[[PLL#U Permutation : a|U-PLL']]
 
|ALGO=F2 U' (M' U2 M) U' F2
 
|ALGO=F2 U' (M' U2 M) U' F2
|INFO=Cycles UF->UR-UL->UF
+
|INFO=Cycles UF->UR->UL
 
}}
 
}}
|<small>''Empty''</small>
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|<center> </center>
 
|---
 
|---
| colspan="2" | <center>'''Five cycle permutations'''</center>
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| colspan="2" | <center>'''5-cycle permutations'''</center>
 
|---
 
|---
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 5 H1.jpg|80px|]]
+
|IMAGE=[[Image:EP5 5 H1.jpg|80px]]
 
|NAME=P U P
 
|NAME=P U P
 
|ALGO=(M' U2 M) U (M' U2 M)
 
|ALGO=(M' U2 M) U (M' U2 M)
|INFO=Cycles UF->UL->UR-DF->UB-UF
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|INFO=Cycles UF->UL->UR->DF->UB
 
}}
 
}}
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 5 H2.jpg|80px|]]
+
|IMAGE=[[Image:EP5 5 H2.jpg|80px]]
 
|NAME=P U' P
 
|NAME=P U' P
 
|ALGO=(M' U2 M) U' (M' U2 M)
 
|ALGO=(M' U2 M) U' (M' U2 M)
|INFO=Cycles UF-UR-UL-DF-UB-UF
+
|INFO=Cycles UF->UR->UL->DF->UB
 
}}
 
}}
 
|---
 
|---
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 5 U1.jpg|80px|]]
+
|IMAGE=[[Image:EP5 5 Z1.jpg|80px]]
|NAME=
+
|NAME=P Z-PLL
|ALGO=
+
|ALGO=2x(M2 U) (M U2 M')
|INFO=
+
|INFO=Cycles UF->UR->UB->UL->FD
 
}}
 
}}
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 5 U2.jpg|80px|]]
+
|IMAGE=[[Image:EP5 5 Z2.jpg|80px]]
|NAME=
+
|NAME=P Z-PLL'
|ALGO=
+
|ALGO=2x(M2 U') (M U2 M')
|INFO=
+
|INFO=Cycles UF->UL->UB->UR->DF
 
}}
 
}}
 
|---
 
|---
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 5 Z1.jpg|80px|]]
+
|IMAGE=[[Image:EP5 5 U1.jpg|80px]]
|NAME=
+
|NAME=P U-PLL
|ALGO=
+
|ALGO=(M' U2 M') U' (M' U2 M) U' M2
|INFO=
+
|INFO=Cycles UF->DF->UB->UL->UR
 
}}
 
}}
|---
 
 
|
 
|
 
{{Casebox
 
{{Casebox
|IMAGE=[[Image:EP5 5 Z1.jpg|80px|]]
+
|IMAGE=[[Image:EP5 5 U2.jpg|80px]]
|NAME=
+
|NAME=P U-PLL'
|ALGO=
+
|ALGO=(M' U2 M') U (M' U2 M) U M2
|INFO=
+
|INFO=Cycles UF->DF->UB->UR->UL
 
}}
 
}}
 
|
 
|
| colspan="2" | <center>''White on top (U), green in front (F) and orange left side (L). Darker pieces changes positions.''</center>
+
|---
 +
| colspan="2" | <center>''These images have white on top (U) and green in front (F). Darker pieces change positions.''</center>
 
|}
 
|}
  
==Advanced system for E5==
+
==Advanced system==
The advanced style is to create algorithms for all extra ELL cases that solves E5 in one go. This has not ben done by anybody yet, it's your chance to get famous, create the system and post the algorithms with descriptions here =)
+
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 2-step 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.
 +
 
 +
==See also==
 +
* [[ELL]]
 +
* [[PCMS]]
 +
* [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]
  
Don't think about it, it is so many cases and for the worst ones you will end up in an alg having exaclty the same turns as you do 2-step anyway. Also, the one step approach has got much slower recognition, the benefit of trying to learn is wery small, just a lot of work.
 
  
One exeption: It is possible to solve all but the 5-cycles using setup turns + [[ELL]] but that is not really useful because of the slowness in recognition, setting up (max 2 turns, possibly AUF and F2) and restore (max 3 turns possibly AUF, F2 and possibly AUF again).
+
[[Category:Experimental methods]]
 +
[[Category:3x3x3 other substeps]]
 +
[[Category:Acronyms]]

Latest revision as of 19:09, 7 July 2019

L5E
[[Image:]]
Information
Proposer(s):
Proposed:
Alt Names: Last five edges
Variants: Sexy*+S(8355)n SexyM Beginner, Commutators (pseudo EF)
Subgroup:
No. Algs: Unknown for 1 look, 5 for L5EO and 16 for L5EP
Avg Moves: about 14
Purpose(s):
Previous state: 5 Corners Missing cube state
Next state: Solved cube state

5 Corners Missing cube state -> L5E step -> Solved cube state


The L5E step is the step between the 5 Corners Missing cube state and the 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

There are two main sub-parts. 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 E-slice, 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 2-look 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 U-perm, 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:

Basic orientations
FUL Solved.jpg
Intuitive solution

(Possibly optimised) alg

Comment
EO5 2 adjacent.jpg
O U2 O

(M' U M) U2 (M' U M)

Orients UL and UB.
EO5 2 opposite.jpg
O U' O

(M' U M) U' (M' U M)

Orients UF and UB.
EO5 4.jpg
P U2 O'

(M' U2 M) U2 (M' U' M)

Orients UR, UF, UL and UB
EO5 1.jpg
O U O'

(M' U M) U (M' U' M)

Orients FD and UB
EO5 3.jpg
O'

(M' U' M)

Orients FD, UR, UF and UL
All images show white on top (U) and green in front (F).

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.

Semi-advanced 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.

Double two cycle permutations
FUL Solved.jpg
Intuitive solution

(Possibly optimised) alg

Comment
EP5 22 A.jpg
F(H-PLL)

(y') R U2 R2 U2 R2 U2 R

Swaps UF<->DF and UR<->UL
EP5 22 B1.jpg
F(Z-PLL)

(y') r2 U' 2x(M E2) U r2

Swaps UR<->DF and UL<->UB
EP5 22 B2.jpg
F(Z-PLL')

(y') r2 U 2x(M E2) U' r2

Swaps UL<->DF and UR<->UB
EP5 22 H.jpg
H-PLL

Ra U2 Ra' (y) Ra' U2 Ra

Swaps UR<->UL and UF<->UB
EP5 22 Z.jpg
Z-PLL

M2 U' 2x(M E2) U M2

Swaps UR<->UB and UL<->UF
3-cycle permutations
EP5 3 A.jpg
P

(M' U2 M)

Cycles UF->DF->UB
EP5 3 B1.jpg
f(d' P)

(y') r2 U' (M' U2 M) U' r2

Cycles UL->UB->DF
EP5 3 B2.jpg
f(d P)

(y') r2 U (M U2 M') U r2

Cycles UR->UB->DF
EP5 3 U1.jpg
U-PLL

F2 U (M' U2 M) U F2

Cycles UF->UL->UR
EP5 3 U2.jpg
U-PLL'

F2 U' (M' U2 M) U' F2

Cycles UF->UR->UL
5-cycle permutations
EP5 5 H1.jpg
P U P

(M' U2 M) U (M' U2 M)

Cycles UF->UL->UR->DF->UB
EP5 5 H2.jpg
P U' P

(M' U2 M) U' (M' U2 M)

Cycles UF->UR->UL->DF->UB
EP5 5 Z1.jpg
P Z-PLL

2x(M2 U) (M U2 M')

Cycles UF->UR->UB->UL->FD
EP5 5 Z2.jpg
P Z-PLL'

2x(M2 U') (M U2 M')

Cycles UF->UL->UB->UR->DF
EP5 5 U1.jpg
P U-PLL

(M' U2 M') U' (M' U2 M) U' M2

Cycles UF->DF->UB->UL->UR
EP5 5 U2.jpg
P U-PLL'

(M' U2 M') U (M' U2 M) U M2

Cycles UF->DF->UB->UR->UL
These images have white on top (U) and green in front (F). Darker pieces change positions.

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 2-step 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.

See also