Difference between revisions of "PBL"

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'''Permutation of both layers''', abbreviated as '''PBL''', is a [[step]] used in a number of [[2x2x2]] methods (and thus [[corners first]] methods). Specifically, the [[Ortega method]] and the [[Guimond method]], perhaps the two most popular advanced [[2x2x2]] methods, both finish with a PBL step. When solving only corners, PBL has five unsolved cases, which can be recognized by the number of adjacent color pairs on each side that are correctly permuted (a solved side has 4 pairs, an adjacent corner swap has 1 pair, and a diagonal corner swap has 0 pairs), so the unsolved cases (denoted by counting number of color pairs on top and bottom) are 0+0, 1+0, 1+1, 4+0, and 4+1. [[Algorithm]]s for PBL (for 2x2x2 or CF) can be found at the [[Template:CxLLnav|CxLL]] pages (the grey cases in the topmost line).
+
'''Permutation of both layers''', abbreviated as '''PBL''', is a [[step]] used in a number of [[2x2x2]] methods (and thus [[corners first]] methods). Specifically, the [[Ortega method]] and the [[Guimond method]], perhaps the two most popular advanced [[2x2x2]] methods, both finish with a PBL step. When permuting only corners, PBL has five unsolved cases, which can be recognized by the number of "bars" (adjacent color pairs) on each side that are correctly permuted (a solved layer has 4 bars, an adjacent corner swap has 1 bar, and a diagonal corner swap has 0 bars), so the unsolved cases (denoted by counting number of bars on top and bottom layers) are 0+0, 1+0, 1+1, 4+0, and 4+1. [[Algorithm]]s for PBL (for 2x2x2 or CF) can be found at the [[Template:CxLLnav|CxLL]] pages (the grey cases in the topmost line).
  
 
It is actually possible, in theory, to do PBL in one step for [[3x3x3]] or [[Square-1]] - in this case we would be permuting not only corners but the whole layers. No [[speedcubing]] method actually uses this, though, because there are about 800 cases in total and recognition is very difficult. For the [[Square-1]], many methods do PBL in two steps, by first solving the [[corner]]s of both layers and then doing the [[edges]] of both layers. Even though two layers are being permuted at once, though, solvers conventionally refer to the steps as simply [[CP]] and [[EP]].
 
It is actually possible, in theory, to do PBL in one step for [[3x3x3]] or [[Square-1]] - in this case we would be permuting not only corners but the whole layers. No [[speedcubing]] method actually uses this, though, because there are about 800 cases in total and recognition is very difficult. For the [[Square-1]], many methods do PBL in two steps, by first solving the [[corner]]s of both layers and then doing the [[edges]] of both layers. Even though two layers are being permuted at once, though, solvers conventionally refer to the steps as simply [[CP]] and [[EP]].
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<table cellspacing='5' cellpadding='5'><tr>
 
<table cellspacing='5' cellpadding='5'><tr>
 
<td valign='top'>
 
<td valign='top'>
==== Swap UF Corners (1+4) ====
+
==== Swap U-layer Adj. Corners (1+4) ====
 
 
[[Image:PBL1.gif]]
 
* y' x U2 R' U' R U2 L' U R' U' R2
 
* (R' F R') B2 R F' (R' B2 R2)  ([[PLL#A_Permutation_:_a|A Permutation]])
 
* U' x' R2 U2 R' U' R U2 L' U R'
 
* y' R2 F2 R' U' R F2 R' U R'
 
* y' (U') R' U L' U2 R U' R' U2 R L
 
* y' R U R' U' R' F R2 U' R' U' R U R' F'  ([[PLL#T_Permutation_:_t|T Permutation]])
 
* y' R U2 R' U' R U2 L' U R' U' L
 
* y2 R' U L' U2 R U' R' U2 R2 B' (Ja Permutation)
 
* y' R2 U R2' U' R2 y' R2' U' R2 U R2 U'
 
  
 +
[[Image:2x2_PBL_image1.png]]
 +
* y R' F R F' R U2 R' U R U2 R'
 +
* y' R2 F2 R U R' F2 R F' R
 +
* y2 R' F R' F2 R U' R' F2 R2
 +
* y R U2 R' U' R U2 L' U R' U' L ([[PLL#Jb_Permutation_:_jb|Jb Permutation]])
 +
* y R U R' U' R' F R2 U' R' U' R U R' F'  ([[PLL#T_Permutation_:_t|T Permutation]])
 +
* y R U2 R' U' R U2 R' F R' F' R
 
</td>
 
</td>
  
 
<td valign='top'>
 
<td valign='top'>
==== Swap U-Layer Diagonal (0+4) ====
+
==== Swap U-Layer Opp. Corners (0+4) ====
[[Image:PBL2.gif]]
+
[[Image:2x2_PBL_image2.png]]
* (R U' R' U') F2 (U' R U R') D R2
+
* R U' R' U' F2 U' R U R' U F2
* (R U' R' U') F2 (U' R U R' U) F2
+
* F R' F' R U R U' R' F R F' U' R' U' R
* L' U L D R2 D R' U' R D' R2
+
* R U2 R' U2 R' F R F' R U' R' F R' F' R
 +
* R U R U' R' F R' F' R U R' U' R' F R F'
 
* F R U' R' U' R U R' F' R U R' U' R' F R F' ([[PLL#Y_Permutation|Y Permutation]])
 
* F R U' R' U' R U R' F' R U R' U' R' F R F' ([[PLL#Y_Permutation|Y Permutation]])
* R' U L' U2 R U' x' U L' U2 R U' L
 
* [R' U R' U'] y [R' F'] [R2 U' R' U] [R' F R F]
 
 
</td>
 
</td>
 +
 +
</tr>
 +
<tr>
  
 
<td valign='top'>
 
<td valign='top'>
==== Swap UF + DF Corners (1+1) ====
+
==== Swap Adj. + Adj. Corners (1+1) ====
[[Image:PBL3.gif]]
+
[[image:2x2_PBL_image3.png]]
* R2 U' R2' (U2' + y) R2 U' R2'
+
* R2 U' B2 U2 R2 U' R2
* R2' U' R2 U2' F2 U' R2
+
* y2 R2 U' R2 U2 F2 U' R2
* R2' U' R2 U2' x' U2 x' U' R2
+
</td>
* R2 U F2 U2 R2 U R2
+
 
* y2 R2 U' B2 U2' R2' U' R2
+
<td valign='top'>
* z' U2 L U2 (L' R') U2 R U2
+
==== Swap Opp. + Opp. Corners (0+0) ====
 +
[[Image:2x2_PBL_image4.png]]
 +
 
 +
* R2 F2 R2
 +
* R2 B2 R2
 +
* x R2 U2 R2 x'
 
</td>
 
</td>
  
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<td valign='top'>
 
<td valign='top'>
==== Swap U + D Diagonal (0+0) ====
+
==== Swap Adj. + Opp. Corners (1+0) ====
[[Image:PBL4.gif]]
+
[[Image:2x2_PBL_image5.png]]
  
* R2' F2 R2
+
* R' F R' F2 R U' R
* R2 B2 R2'
+
* y2 R' U R' F2 R F' R
* (R L) U2 (R' L')
+
* R U' R F2 R' U R'
 +
* y R2 D R2 D' R2 D R2 D' R2
 
</td>
 
</td>
  
 
<td valign='top'>
 
<td valign='top'>
==== Swap UB Corners + D-Layer Diagonal (1+0) ====
+
==== Swap Opp. + Adj. Corners (0+1) ====
[[Image:PBL5.gif]]
+
[[Image:2x2_PBL_image6.png]]
 +
* y R2 U R2 U' R2 U R2 U' R2
 +
* y R2 U' R2 U R2 U' R2 U R2
 +
</td>
 +
 
 +
</tr>
 +
<tr>
  
* [R U' R] F2 [R' U R']
+
<td valign='top'>
* [R U' L] U2 [R' U R']
+
==== Swap D-layer Adj. Corners (4+1) ====
* y2 [R' U L'] U2 [R U' L]
+
[[Image:2x2_PBL_image7.png]]
* x2 y' R2 U' R2 U R2 U' R2 U R2
+
* y R2 U' R' U R' F2 R F' R' F2
* x2 R D' L U2 L' D R'
+
* R2 F2 U' R2 U R2 U' R2 U R2
* x2 R D' L U2 R' F U'
 
 
</td>
 
</td>
  
 
<td valign='top'>
 
<td valign='top'>
==== Swap UB + DB Corners (1+1) ====
+
==== Swap D-layer Opp. Corners (4+0) ====
[[Image:PBL6.gif]]
+
[[Image:2x2_PBL_image8.png]]
* R2 U' B2 U2' R2' U' R2
+
* R U' R' U' F2 U' R U R' U R2 B2
* R2 U' F2 U2' R2' U' F2
+
* F R2 U2 R' U R U2 R2 F R F' R' F'
* R2 U R2 U2 F2 U F2
 
* R2' U R2 U2 y' R2' U R2
 
* L2' U F2' U2 R2' U R2'
 
 
</td>
 
</td>
  
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</table>
 
</table>
  
The first two algorithms (Y perm and A perm) only affect the top layer, and because of that, they can be used in LBL methods.
+
The first two algorithms (J perm and Y perm) only affect the top layer, and because of that, they can be used in LBL methods.
  
 
Note that D moves are the same as U + y, just a different notation, what you do for real is something in between. The effect of it is that you transform F moves to R or L (D R makes the same turns as U F + y').
 
Note that D moves are the same as U + y, just a different notation, what you do for real is something in between. The effect of it is that you transform F moves to R or L (D R makes the same turns as U F + y').
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== External links ==
 
== External links ==
 +
* [https://docs.google.com/document/d/1HxfCoJcEREP_DEHmK_Yafi7UtMaaeLlIqRZk1OVl6mU/edit?usp=sharing AlgoCuber's PBL Algs]
 
* [https://web.archive.org/web/20111108120705/http://www.dtwoner.110mb.com/index.php?p=1_40_PBL David Woner's PBL algs]
 
* [https://web.archive.org/web/20111108120705/http://www.dtwoner.110mb.com/index.php?p=1_40_PBL David Woner's PBL algs]
 
* [http://www.cubewhiz.com/ortegapbl.php Bob Burton's PBL algs]
 
* [http://www.cubewhiz.com/ortegapbl.php Bob Burton's PBL algs]

Latest revision as of 20:13, 16 April 2023

Permutation of both layers, abbreviated as PBL, is a step used in a number of 2x2x2 methods (and thus corners first methods). Specifically, the Ortega method and the Guimond method, perhaps the two most popular advanced 2x2x2 methods, both finish with a PBL step. When permuting only corners, PBL has five unsolved cases, which can be recognized by the number of "bars" (adjacent color pairs) on each side that are correctly permuted (a solved layer has 4 bars, an adjacent corner swap has 1 bar, and a diagonal corner swap has 0 bars), so the unsolved cases (denoted by counting number of bars on top and bottom layers) are 0+0, 1+0, 1+1, 4+0, and 4+1. Algorithms for PBL (for 2x2x2 or CF) can be found at the CxLL pages (the grey cases in the topmost line).

It is actually possible, in theory, to do PBL in one step for 3x3x3 or Square-1 - in this case we would be permuting not only corners but the whole layers. No speedcubing method actually uses this, though, because there are about 800 cases in total and recognition is very difficult. For the Square-1, many methods do PBL in two steps, by first solving the corners of both layers and then doing the edges of both layers. Even though two layers are being permuted at once, though, solvers conventionally refer to the steps as simply CP and EP.

Algorithms

Swap U-layer Adj. Corners (1+4)

2x2 PBL image1.png

  • y R' F R F' R U2 R' U R U2 R'
  • y' R2 F2 R U R' F2 R F' R
  • y2 R' F R' F2 R U' R' F2 R2
  • y R U2 R' U' R U2 L' U R' U' L (Jb Permutation)
  • y R U R' U' R' F R2 U' R' U' R U R' F' (T Permutation)
  • y R U2 R' U' R U2 R' F R' F' R

Swap U-Layer Opp. Corners (0+4)

2x2 PBL image2.png

  • R U' R' U' F2 U' R U R' U F2
  • F R' F' R U R U' R' F R F' U' R' U' R
  • R U2 R' U2 R' F R F' R U' R' F R' F' R
  • R U R U' R' F R' F' R U R' U' R' F R F'
  • F R U' R' U' R U R' F' R U R' U' R' F R F' (Y Permutation)

Swap Adj. + Adj. Corners (1+1)

2x2 PBL image3.png

  • R2 U' B2 U2 R2 U' R2
  • y2 R2 U' R2 U2 F2 U' R2

Swap Opp. + Opp. Corners (0+0)

2x2 PBL image4.png

  • R2 F2 R2
  • R2 B2 R2
  • x R2 U2 R2 x'

Swap Adj. + Opp. Corners (1+0)

2x2 PBL image5.png

  • R' F R' F2 R U' R
  • y2 R' U R' F2 R F' R
  • R U' R F2 R' U R'
  • y R2 D R2 D' R2 D R2 D' R2

Swap Opp. + Adj. Corners (0+1)

2x2 PBL image6.png

  • y R2 U R2 U' R2 U R2 U' R2
  • y R2 U' R2 U R2 U' R2 U R2

Swap D-layer Adj. Corners (4+1)

2x2 PBL image7.png

  • y R2 U' R' U R' F2 R F' R' F2
  • R2 F2 U' R2 U R2 U' R2 U R2

Swap D-layer Opp. Corners (4+0)

2x2 PBL image8.png

  • R U' R' U' F2 U' R U R' U R2 B2
  • F R2 U2 R' U R U2 R2 F R F' R' F'

The first two algorithms (J perm and Y perm) only affect the top layer, and because of that, they can be used in LBL methods.

Note that D moves are the same as U + y, just a different notation, what you do for real is something in between. The effect of it is that you transform F moves to R or L (D R makes the same turns as U F + y').

See also


External links