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 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. 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 UF Corners

PBL1.gif

  • y' x U2 R' U' R U2 L' U R' U' R2
  • (R' F R') B2 R F' (R' B2 R2) (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' (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'

Swap U-Layer Diagonal

PBL2.gif

  • (R U' R' U') F2 (U' R U R') D R2
  • (R U' R' U') F2 (U' R U R' U) F2
  • L' U L D R2 D R' U' R D' R2
  • F R U' R' U' R U R' F' R U R' U' R' F R F' (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]

Swap UF + DF Corners

PBL3.gif

  • R2 U' R2' (U2' + y) R2 U' R2'
  • R2' U' R2 U2' F2 U' R2
  • R2' U' R2 U2' x' U2 x' U' R2
  • R2 U F2 U2 R2 U R2
  • y2 R2 U' B2 U2' R2' U' R2
  • z' U2 L U2 (L' R') U2 R U2

Swap U + D Diagonal

PBL4.gif

  • R2' F2 R2
  • R2 B2 R2'
  • (R L) U2 (R' L')

Swap UB Corners + D-Layer Diagonal

PBL5.gif

  • [R U' R] F2 [R' U R']
  • [R U' L] U2 [R' U R']
  • y2 [R' U L'] U2 [R U' L]
  • x2 y' R2 U' R2 U R2 U' R2 U R2
  • z2 R D' L U2 L' D R'
  • x2 R D' L U2 R' F U'

Swap UB + DB Corners

PBL6.gif

  • R2 U' B2 U2' R2' U' R2
  • R2 U R2 U2 F2 U F2
  • R2' U R2 U2 y' R2' U R2
  • L2' U F2' U2 R2' U R2'

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.

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