Difference between revisions of "ELL"

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(Cleaned up a little. Now getting algs from places to finish the page. Also, I'll add them to the Alg Database.)
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ELL is also used for a method of solving the last layer edges on larger cubes. Since there are 8 of each type of [[wing]], though, ELL for larger cubes requires more than one algorithm.
 
ELL is also used for a method of solving the last layer edges on larger cubes. Since there are 8 of each type of [[wing]], though, ELL for larger cubes requires more than one algorithm.
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== Deducing the number of cases ==
  
 
For orientation, there are 4 possibilities.
 
For orientation, there are 4 possibilities.
  
1. [[OLL #28]]
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1. [[OLL #28]] -- this OELL can be situated in 4 ways
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[[File:O28.gif]]
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2. [[OLL #57]] -- this OELL can be situated in 2 ways
  
2. [[OLL #57]]
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[[File:O57.gif]]
  
3. [[OLL #20]]
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3. [[OLL #20]] -- this OELL is symmetrical
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[[File:O20.gif]]
  
 
4. All edges oriented correctly.
 
4. All edges oriented correctly.
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For permutation, there are also 4 possibilities.
 
For permutation, there are also 4 possibilities.
  
1. [[Ua permutation]]
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1. [http://www.speedsolving.com/wiki/index.php/PLL#U_Permutation_:_a Ua permutation] -- this EPLL can be situated in 4 ways
  
2. [[Ub permutation]]
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[[File:U1.gif]]
  
3. [[Z permutation]]
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2. [http://www.speedsolving.com/wiki/index.php/PLL#U_Permutation_:_b Ub permutation] -- this EPLL can be situated in 4 ways
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[[File:U.gif]]
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3. [http://www.speedsolving.com/wiki/index.php/PLL#Z_Permutation Z permutation] -- this EPLL can be situated in 2 ways
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[[File:Z.gif]]
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4. [http://www.speedsolving.com/wiki/index.php/PLL#H_Permutation H permutation] -- this EPLL can be situated in 1 way
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[[File:H.gif]]
  
4. [[H permutation]]
 
  
Both U permutations can be oriented in 4 ways, the Z permutation in 2 ways, and the H permutation is always the same, so 1 orientation.
 
  
 
Because OLL #20 always is symmetrical, for this orientation, there are 5 possible ELL cases.
 
Because OLL #20 always is symmetrical, for this orientation, there are 5 possible ELL cases.
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These are the two U-perms (one case for each), the Z-perm (1 case), the H-perm (which is 1 case anyways), and the solved EPLL.
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OLL #28 has two orientations: The incorrectly oriented edges on UL and UR, and on UF and UB. This means that there are 8 ELL cases possible.
 
OLL #28 has two orientations: The incorrectly oriented edges on UL and UR, and on UF and UB. This means that there are 8 ELL cases possible.
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These are the two U-perms (two cases for each), the Z-perm (two cases), the H-perm (one case), and the solved EPLL.
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OLL #57 has four orientations. This means that there are 12 possible ELL cases.
 
OLL #57 has four orientations. This means that there are 12 possible ELL cases.
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We have 5 possibilities if all edges are correctly oriented, one of which is the solved position.  
 
We have 5 possibilities if all edges are correctly oriented, one of which is the solved position.  
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The cases for this follow the same principle of the cases for OLL #20 since solved OELL is symmetrical as well.
  
 
In total we have 30 ELL cases.
 
In total we have 30 ELL cases.

Revision as of 22:39, 2 May 2010

Edges of Last Layer, or normally ELL, is a method that solves the last layer edges of the 3x3x3 in one algorithm as the last step in the solution, normally after performing CLL to solve the last layer corners.

ELL is also used for a method of solving the last layer edges on larger cubes. Since there are 8 of each type of wing, though, ELL for larger cubes requires more than one algorithm.

Deducing the number of cases

For orientation, there are 4 possibilities.

1. OLL #28 -- this OELL can be situated in 4 ways

O28.gif

2. OLL #57 -- this OELL can be situated in 2 ways

O57.gif

3. OLL #20 -- this OELL is symmetrical

O20.gif

4. All edges oriented correctly.

For permutation, there are also 4 possibilities.

1. Ua permutation -- this EPLL can be situated in 4 ways

U1.gif

2. Ub permutation -- this EPLL can be situated in 4 ways

U.gif

3. Z permutation -- this EPLL can be situated in 2 ways

Z.gif

4. H permutation -- this EPLL can be situated in 1 way

H.gif


Because OLL #20 always is symmetrical, for this orientation, there are 5 possible ELL cases. These are the two U-perms (one case for each), the Z-perm (1 case), the H-perm (which is 1 case anyways), and the solved EPLL.

OLL #28 has two orientations: The incorrectly oriented edges on UL and UR, and on UF and UB. This means that there are 8 ELL cases possible. These are the two U-perms (two cases for each), the Z-perm (two cases), the H-perm (one case), and the solved EPLL.

OLL #57 has four orientations. This means that there are 12 possible ELL cases.


We have 5 possibilities if all edges are correctly oriented, one of which is the solved position. The cases for this follow the same principle of the cases for OLL #20 since solved OELL is symmetrical as well.

In total we have 30 ELL cases.

The ELLs wil be denoted by the cycles, beginning with the UF sticker. When there are 2 cycles, there will be started with UL. If that is not possible, they will start with UB. When an edge is correctly permuted, but incorrectly oriented, it will be denoted by the notation of that edge, between parenthesis.

ELL 1: UF-BU-UF UL-RU-UL: (R2' U2 Lw) D2 (x) U2' (R2 F) (R2 (U2'(x')) D2 (x) R' U2 R2 U

ELL 2: (UF, UB, UL, UR): U R2 U2' R' F2 U2' R2' F R Lw F2 D2 R F2 R2'

ELL 3: UF-LU-UR-FU (UB): F U R U' R' Bw' R2 (z') R' U' R' F R F' U R U2

ELL 4: UF-RU-UL-FU (UB): U R' U' R' F R F' y' R' U2 R2 U2' R2' U' R2 U' R' U y R U

ELL 5: UF-RU-UF UL-BU-UL: R2' U2 Lw D x U2' R2' U2 F2 R2 U2' R2' F R' U2' R2

ELL 6: (UF, UB): R F R U R' F' R' F U' y' R2' U2 R U' R' U' R

ELL 7: UF-BU-UF UL-UR-UL: R' U2 R U' R' U' R' F R2 U R' U' R' F' R2

ELL 8: UF-RU-FU UL-BU-FU: R2' U R' U' R F R2 U R U' F' U R2

ELL 9: UF-LU-RU-FU (UB): U' F R2 U' R' F U R2 U' R' F' U R U F' U

ELL 10: UF-RU-LU-FU (UB): R' F2 U F R' U' F2 U F R U' F' U' R

ELL 11: UF-RU-BU-UF: R U R' U' M' U R U' r'

ELL 12: UF-BU-UR-UF: L R' U' R U M U' R' U

To be continued.

See Also

External Links

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