PBL

2009-12-28T08:01:46Z

DWoner:

'''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 pairs on each side that are correctly permuted (a solved side has 4 pairs, an adjacent swap has 1 pair, and an opposite swap has 0 pairs), so the unsolved cases 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]].

== Algorithms ==
<table cellspacing='5' cellpadding='5'><tr>
<td valign='top'>
==== Swap UF Corners ====
[[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]])

</td>

<td valign='top'>
==== Swap U-Layer Diagonal ====
[[Image:PBL2.gif]]
* R U' R' U' F2 U' R U R' D R2
* F R U' R' U' R U R' F' R U R' U' R' F R F' ([[PLL#Y_Permutation|Y Permutation]])
</td>

<td valign='top'>
==== Swap UF + DF Corners ====
[[Image:PBL3.gif]]
* R2 U' R2' (U2' + y) R2 U' R2'
* R2 U F2 U2 R2 U R2
</td>

</tr>
<tr>

<td valign='top'>
==== Swap U + D Diagonal ====
[[Image:PBL4.gif]]

* R2 F2 R2
</td>

<td valign='top'>
==== Swap UB Corners + D-Layer Diagonal ====
[[Image:PBL5.gif]]

* R U' R F2 R' U R'
</td>

<td valign='top'>
==== Swap UB + DB Corners ====
[[Image:PBL6.gif]]
* R2 U' B2 U2' R2' U' R2
* R2' U R2 U2 y' R2' U R2
</td>

</tr>
</table>

== See Also ==
* [[Ortega]]
* [[Guimond]]
* [[OLL (2x2x2)]]

== External Links ==
* [http://dtwoner.110mb.com/index.php?p=1_40_PBL David Woner's PBL algs]

[[Category:Methods]]
[[Category:2x2x2 Methods]]
[[Category:2x2x2 Speedsolving Methods]]
[[Category:Algorithms]]
[[Category:Sub Steps]]
[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
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PBL