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4x4 Parity algorithms PDF

All 25 parity cases, top-ranked algorithm first.

Columns

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OLL parity

  • OLL parity: Basic case
    OLL parity: Basic
    r U2xr U2r U2 r'U2 l U2 r' U2r U2 r'U2 r'
    r2 B2 U2 l U2r' U2 rU2 F2 r F2 l' B2 r2
  • OLL parity: Pure case
    OLL parity: Pure
    2R' U2 2L F2 2L' F2 2R2 U2 2R U2 2R' U2 F2 2R2 F2
    r' U' rU' r U r'r' U' r'r'U2rU2r'U2rU2 r U'r U r' U'r U2 r'
  • OLL parity: M case
    OLL parity: M
    2R2 U2 2R2 u2 2R2 u2 r U2xr U2r U2 r'U2 l U2 r' U2r U2 r'U2 r'
    2R2 U2 2R2 u2 2R2 u2 r' U2 l F2 l' F2 r2 U2r U2 r'U2 F2 r2 F2

PLL parity

  • PLL parity: M case
    PLL parity: M
    r2 F2 U2 2R2 UR' U' R UR' D R D' R F2 U r2
    R U R' U'R' F R2 U'R' U'R U R' F'2R2 U2 2R2 u2 2R2 u2
  • PLL parity: OPP Parity case
    PLL parity: OPP Parity
    2R2 U2 2R2 u2 2R2 u2
    Ur2 U2r U2 r'r' U2 r2 U2r U2 r'r'
    r2 F2 U2 r2 R2 U2 F2 r2
  • PLL parity: Adj Parity case
    PLL parity: Adj Parity
    R' U R U'2R2 U2 2R2 u2 2R2 u2 U'R' U' R
    r U r'R U' r'U'rUrU'r'U'r'R Ur U R' U'R'
  • PLL parity: CwO case
    PLL parity: CwO
    u2 2R2 u2 2R2 U2 2R2U R' U' RU' RU R U' R'UR U R'R' U' R'
    r2 U2R U' R'U r U2 r'r' U2 r'r' U2 rR' U' R UR' U' RR U' r2
    r2 U' R2U' R' U RU' rR' U2 rr U2 r'r' U2 r UR' U' RU2 r2
  • PLL parity: CcwO case
    PLL parity: CcwO
    u2 2R2 u2 2R2 U2 2R2R' U' R U'RU R U' R'UR U R'R' U' R'
    r2 U R'R' U RU' R' U Rr' U2 rr U2 rr U2 r' U'R U R'U2 r2
    r2 U2R' U RU' r' U2 rr U2 r'r' U2 Rr' UR' U' R UR2 U r2
  • PLL parity: W case
    PLL parity: W
    UR2 u2 B2 R2 u2 B2 R2 U R2 B2 R2 U B2 u2
    R' U R' U' R'U' R' U RU r2 U2 2R2 u2 2R2 u2
    UR2 U R' U'R'R' U RU rr U2 R'r U2 R'r2 U2 r2 U2r U2 r'r'
  • PLL parity: Pj case
    PLL parity: Pj
    U'zrr U2 R'U2R' U2 RxU2 r2 U2 B2L U2 L'U2 r2 U2z'
    R U R' U'R' F R2 U'R' U'R U R' F'U' 2L2 U2 2L2 u2 2L2 u2
    R U R' U'R' F R2 U'R' U'R U R' F'U' 2R2 U2 2R2 u2 2R2 u2
  • PLL parity: Ba case
    PLL parity: Ba
    Uu2 2L2 u2 2L2 U2 2L2 UR U R' F'R U R' U'R' F R2 U'R'
    z'U2 B2 ll U2 L'B2 l2 L B2L U2 l'l' L U2z
    Ux'r2 U2 r2 u2 2R2 u2 F 3r U' R U2 L' U R'
  • PLL parity: Bb case
    PLL parity: Bb
    xr2 U2 r2 u2 2R2 u2 B 3r' U R' U2 L U' R
    z'U2 F2 l'l' U2 LF2 l2 L' F2L' U2 ll L' U2z
    2R2 U2 2R2 u2 2R2 u2 R' UL'U2RU'R'U2LR
  • PLL parity: Ca case
    PLL parity: Ca
    u2 2R2 u2 2R2 U2 r'r' F R URU' R' F' RU2R' U2 R
    u'R U R'u' r2 U2 r2 RD'R U R'DR U r'r' uR U' R'u
    2R2 U2 2R2 u2 2R2 u2 R'R'FRURU'R'F'RU2R' U2 R
  • PLL parity: Cb case
    PLL parity: Cb
    R' U2 RU2R' F R UR'U' R' F' rr U2 2R2 u2 2R2 u2
    U2u'R U R'u' rr U' R'D'R U' R'DR' r2 U2 r2 uR U' R'u
    2R2 U2 2R2 u2 2R2 u2 R U'R' U' R URDR'U'RD'R'U2 R'
  • PLL parity: Da case
    PLL parity: Da
    z'U2 l2 L U2 L F2 l2 L F2L' U2 ll F2 U2z
    U'R' U L' U2 R U' 3r B r2 U2 r2 u2 2R2 u2x'
    U'L' U R' U2 LU' L' U2 LR U' 2R2 U2 2R2 u2 2R2 u2
  • PLL parity: Db case
    PLL parity: Db
    z'U2 l2 L' U2 L' B2 l2 L' B2L U2 l'l' B2 U2z
    R U R' F'R U R' U'R' F R2 U'R' u2 2R2 u2 2R2 U2 2R2
    R U R' F'R U R' U'R' F R2 U'R' 2R2 U2 2R2 u2 2R2 u2
  • PLL parity: Ka case
    PLL parity: Ka
    3l' U R'D2R U' R'D2x'r2 U2 2R2 u2 2R2 u2
  • PLL parity: Kb case
    PLL parity: Kb
    r2 F2 U2 r2 R2 U2xR'D'RU2R'DRr2x'
    3r U' LD2L' U LD2x'l2 U2 2L2 u2 2L2 u2
  • PLL parity: Pa case
    PLL parity: Pa
    R U R' F'R U R' U'R' F R2 U'R' U' 2R2 U2 2R2 u2 2R2 u2
    d2 R2 D B2 d2 D' B2 D' R2 d2 D' B2 L2 U' L2
    r2D'r U2 r'Dr U2 r U r U2 rDr' U2 rD'r2
  • PLL parity: Pb case
    PLL parity: Pb
    2R2 U2 2R2 u2 2R2 u2R U R' F'R U R' U'R' F R2 U'R'
    U2L2 U L2 B2 d2 D R2 D B2 d2 D B2 D' R2 d2
    U2r2Dr' U2 rD'r' U2 r' U' r' U2 r'D'r U2 r'Dr2
  • PLL parity: Diag C case
    PLL parity: Diag C
    FRU'R'U'RUR'F'U' 2R2 U2 2R2 u2 2R2 u2 U'R U R' U'R' F R F'
    F2L' U2 LR U2 R'F2l2 F2 U2 l2 L' U2 F2 l2
    r2 R U2R U2 R'U2r U2 r'r' U2 r2 U2 L r U2R' U2 RU2 L' r2
  • PLL parity: Q case
    PLL parity: Q
    zr2 u2 R2 u2 FR U R' U'R U R' U'R U R' U'F' U2 R2 u2 r2z'
    R2 U B2 u2 R2 U' B2 u2 U B2 U2 R2 u2 U' R2
    zF2 r2 R' F2 R2 U2 r2R U2 R'F2 r'r' U2 RF2z'
  • PLL parity: Sa case
    PLL parity: Sa
    FRU'R'U'RUR'F'R U R' U'R' F R F'U' 2R2 U2 2R2 u2 2R2 u2
    zU2R' U2 rr B2R U2 r'r'R' U2 RR B2 r2 R U2z'
  • PLL parity: Sb case
    PLL parity: Sb
    FRU'R'U'RUR'F'R U R' U'R' F R F'2R2 U2 2R2 u2 2R2 u2
    UzU2R U2 r'r' F2R' U2 rrR U2 R'R' F2 r2 R' U2z'
  • PLL parity: X case
    PLL parity: X
    r2 F2 U2 r2 F'U' R' U RU' R' U RU' R' U RF R2 U2 F2 r2
    u2 l2 U' B' U B U2F U' F'U F' L2 F l2 U2 l2 u2
    x'R U' R'DR U R'D'R U R'DR U' R'D'x2R2 U2 2R2 u2 2R2 u2