4x4x4 parity algorithms

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Parity (also known as Orientation Parity and Permutation Parity) on the 4x4x4 is a common situation (occurring in 3/4 of all solves) where two or four edge pieces need to be cycled. This is considered difficult because in most methods the centers are solved before the edges, and there is no efficient or intuitive way to swap those edges (and no others) without affecting the centers. Because of how common and difficult this case is, many algorithms have been developed. This page attempts to list all efficient algorithms. Solutions listed which are not as efficient as others in their categories are at least relatively efficient for their specific effect on the cube or for the move set they are confined to.


Introduction

  • The shortest odd parity fix (PLL Parity algorithms are even parity fixes for wing edges) algorithm which preserves the colors of the centers is simply:
Speedsolving Logo tiny.gif Alg (r U2)4 r /(13,9)

For those who are familiar with commutators and conjugates, this quick parity fix can be represented as

Speedsolving Logo tiny.gif Alg [r: [U2, r [r2 U2: r]] /(13,9)]

In fact, we can do the same 4-cycle of wing edges with just a conjugate alone.

Speedsolving Logo tiny.gif Alg [r2 d' r2 Uw2 S': r' /(17,11)]


The phrase "there is more than one way to solve any given problem" holds true with tackling 4x4x4 parity situations. In fact, there are different categories of parity algorithms, and algorithms can consist of different move patterns (the move set of one algorithm might be entirely different than the algorithm above and/or below it).

This page not only contains commonly practiced speedsolving algorithms, but it also contains algorithms which illustrate the veracity of the 4x4x4 cube parity algorithm domain.


NOTES

  • Algorithms with a lower btm (block half turn) move count are listed first in each category.
  • All algorithms can be applied to the 6x6x6 if instead of turning the outer 2 layers, you turn the outer 3 layers. For slice moves, instead of turning 1 slice layer, you turn 2 slices.



Contents

PLL Parity (WCA Notation)

PLL Parity in Two Opposite Edges ("Oriented")

Speedsolving Logo tiny.gif Alg r2 U2 r2 Uw2 r2 u2 /(12,6)
Speedsolving Logo tiny.gif Alg r2 U2 r2 Uw2 r2 Uw2 /(12,6)
Speedsolving Logo tiny.gif Alg (Rw2 R2') U2 (Rw2 R2') Uw2 (Rw2 R2') Uw2 /(12,6)
Speedsolving Logo tiny.gif Alg Uw2 Rw2 U2 (Rw2 R2') U2 Rw2 Uw2 /(14,7)
Speedsolving Logo tiny.gif Alg Uw2 Rw2 U2 r2 U2 Rw2 Uw2 /(14,7)
Speedsolving Logo tiny.gif Alg Rw2 B2 U2 r2 U2 B2 Rw2 /(14,7)


PLL Parity in Two Adjacent Edges ("Oriented")

Speedsolving Logo tiny.gif Alg R2 D' x r2 U2 r2 Uw2 r2 u2 x' D R2 /(18,10)
Speedsolving Logo tiny.gif Alg R2 D' x Rw2 F2 U2 r2 U2 F2 Rw2 x' D R2 /(20,11)
Speedsolving Logo tiny.gif Alg F2 U Rw2 U2 F2 r2 F2 U2 Rw2 U' F2 /(20,11)
Speedsolving Logo tiny.gif Alg y' R' F l E F2 E' l' r' E F2 E' r F' R y /(16,14)
Speedsolving Logo tiny.gif Alg y' R' F l E' F2 E l' r' E' F2 E r F' R y /(16,14)
Speedsolving Logo tiny.gif Alg (Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw) /(22,17)


PLL Parity in Two Opposite Edges ("Unoriented")

Speedsolving Logo tiny.gif Alg F2 l E F2 E' l' r' E F2 E' r F2 /(16,12)
Speedsolving Logo tiny.gif Alg F2 l E' F2 E l' r' E' F2 E r F2 /(16,12)
Speedsolving Logo tiny.gif Alg y R' U F' r2 U2 r2 Uw2 r2 u2 F U' R y' /(18,12)
Speedsolving Logo tiny.gif Alg r U2 l D2 l' U2 M U2 r D2 r' U2 l' /(19,13)
Speedsolving Logo tiny.gif Alg y' R' F U' Rw2 U2 F2 r2 F2 U2 Rw2 U F' R y /(20,13)
Speedsolving Logo tiny.gif Alg y R' U F' Rw2 F2 U2 r2 U2 F2 Rw2 F U' R y' /(20,13)


PLL Parity in Two Adjacent Edges ("Unoriented")

Speedsolving Logo tiny.gif Alg R B r2 U2 r2 Uw2 r2 u2 B' R' /(16,10)
Speedsolving Logo tiny.gif Alg (R B Rw2 F2 U2) r2 (U2 F2 Rw2 B' R') /(18,11)
Speedsolving Logo tiny.gif Alg ((Lw r') U Rw2 U2 F2) r2 (F2 U2 Rw2 U' (Lw' r)) /(18,11)


Adjacent Two Corner Swap

Speedsolving Logo tiny.gif Alg R U' R B2 L' D L B2 R2 U r2 F2 r2 Fw2 r2 f2 /(25,16)
Speedsolving Logo tiny.gif Alg B2 L U L' B2 R D' r2 F2 r2 Fw2 r2 f2 R D R2 /(25,16)
Speedsolving Logo tiny.gif Alg z r2 U2 R' U2 R' U2 R x U2 Rw2 U2 B2 L U2 L' U2 Rw2 U2 z' y' /(29,17)
Speedsolving Logo tiny.gif Alg z' Rw2 x U2 R' U2 x' U2 R' U2 R U2 L' x U2 Rw2 U2 Rw2 U2 Rw2 x' U2 Rw2 z U /(33,19)
Speedsolving Logo tiny.gif Alg r2 U2 r2 Uw2 r2 u2 y' R U R' U' R' F R2 U' R' U' R U R' F' y /(27,20)
Speedsolving Logo tiny.gif Alg z' x Rw2 R' U2 Rw' U2 Rw2 U2 Rw2 U2 L Rw' U2 R' U2 R U2 L' R U2 R U2 Rw2 x' z /(35,22)
Speedsolving Logo tiny.gif Alg z' x Rw2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' R U2 R U2 Rw2 x' z /(35,22)


Adjacent Two Corner Swap (Only Two X-Center Piece Exchange on the Supercube)

Speedsolving Logo tiny.gif Alg U Rw2 Bw2 Rw F Rw' Bw2 Rw F' L2 r U' b2 U L' F' L U' b2 U L' F M x /(29,23)
Speedsolving Logo tiny.gif Alg z' Fw' L2 Uw F' U R U' F r2 F' U R' U' F r2 Fw Uw' L Uw Fw' Uw' L Fw L z /(27,24)
Speedsolving Logo tiny.gif Alg z' Fw' L2 Uw r2 F' U R U' F r2 F' U R' U' F Fw Uw' L Uw Fw' Uw' L Fw L z /(27,24)
Speedsolving Logo tiny.gif Alg Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' Rw' F Rw2 U' Rw' U' /(28,26)
Speedsolving Logo tiny.gif Alg Rw' U' R U r U' R' U R2 U R' U' r U r' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F' /(28,26)
Speedsolving Logo tiny.gif Alg Rw' U' R U r U' R' U R2 U R' U' r U R U' Lw Uw2 Rw' U' Rw Dw2 Rw' U Rw' F' x y2 /(29,26)
Speedsolving Logo tiny.gif Alg U Rw2 Bw2 Rw F Rw' Bw2 Rw F' D' f' D F2 D' f D F2 Rw L F' L' f' L F L' f /(31,26)
Speedsolving Logo tiny.gif Alg Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' R' F' r' F R F' r2 B' R B r' B' R' B /(29,27)
Speedsolving Logo tiny.gif Alg Rw U R' U' r' U R U' R2 U' R U r' U' R' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U /(29,28)


Opposite/Diagonal Two Corner Swap

Speedsolving Logo tiny.gif Alg Rw2 f2 U2 Fw2 U' Rw2 U2 Fw2 U Fw2 R2 U2 F2 Rw2 U /(27,15)
Speedsolving Logo tiny.gif Alg Rw2 F2 U2 y Rw2 U' Rw2 U D Lw2' U' Lw2' y' r2 U2 F2 Rw2 U /(27,16)
Speedsolving Logo tiny.gif reParity z (R2' Uw2' R2 U R2') y (R2 U2 R2' U' R2) y' (R2' Uw2' R2 (Dw' u) R2) Uw2 U2 y' z' /(29,16)
Speedsolving Logo tiny.gif Alg r2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 Rw' r' U2 F2 Rw2 U2 /(30,17)
Speedsolving Logo tiny.gif Alg r2 B2 R' U2 Rw2 U2 B2 R' B2 r2 U2 Rw2 B2 U2 R' U2 Rw2 /(31,17)
Speedsolving Logo tiny.gif Alg r2 U2 r2 Uw2 r2 Uw2 L' U R' U2 L U' L' R U R' U2 L U' R U /(29,21)
Speedsolving Logo tiny.gif Alg Rw2 R U2 R U2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' Rw2 /(35,22)


Opposite/Diagonal (Only Two X-Center Piece Exchange on the Supercube)

Speedsolving Logo tiny.gif Alg F r2 F' U R' U' F r2 Fw Uw' L Uw Fw' Uw' L Fw L Fw' L2 Uw F' U R U' /(27,24)
Speedsolving Logo tiny.gif Alg F Rw' F Rw2 U' Rw' U' Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' F' /(30,28)


Impure Dedge Flips (OLL Parity)(Turn the inner and outer layers simultaneously)

  • Unless mentioned otherwise, the algorithms in this section are written in SiGN notation in which lowercase letters mean to move the inner and outer layer at the same time (wide turns).
  • Purpose of the notation. Besides its great application to larger cube sizes, it allows us to write wide turn algorithms more simply and compactly.

OLL Parity

Speedsolving Logo tiny.gif cmowlaparity x' r2 U2 l' U2 r U2 r U2 x' U r U' F2 U r' U r2 x /(23,16)
Speedsolving Logo tiny.gif Alg r U2 x U2 F' r' F U2 F' r F r U2 r' U2 x' r' U2 r' /(23,17)
Speedsolving Logo tiny.gif lucasparity r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r' /(25,17)
Speedsolving Logo tiny.gif lucasparity r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r' /(25,17)
Speedsolving Logo tiny.gif Alg r U2 r2 U2 x' U r U' F2 U r' U' l' U2 r U2 r' U2 r' /(25,18)
Speedsolving Logo tiny.gif Alg r2 B2 3d' r' 3d r U2 r' 3d' r U' y' r' U2 r' U2 r B2 r2 /(25,18)


OLL Parity + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg_1(v1) r' U2 r' U2 l U2 r' U2 r U2 x U2 r2 U2 r' U2 r /(25,16)
Speedsolving Logo tiny.gif Alg_1(v2) l U2 l U2 r' U2 l U2 l' U2 x U2 l2 U2 l U2 l' /(25,16)
Speedsolving Logo tiny.gif Alg_2(v1) r U2 r' U2 r U2 r U2 l' U2 r U2 r' U2 x' U2 r2 /(25,16)
Speedsolving Logo tiny.gif Alg_2(v2) l' U2 l U2 l' U2 l' U2 r U2 l' U2 l U2 x' U2 l2 /(25,16)
Speedsolving Logo tiny.gif Alg_3(v1) r2 U2 x' U2 r' U2 r U2 l' U2 r U2 r U2 r' U2 r /(25,16)
Speedsolving Logo tiny.gif Alg_3(v2) l2 U2 x' U2 l U2 l' U2 r U2 l' U2 l' U2 l U2 l' /(25,16)
Speedsolving Logo tiny.gif Alg_4(v1) r U2 r' U2 r2 U2 x U2 r U2 r' U2 l U2 r' U2 r' /(25,16)
Speedsolving Logo tiny.gif Alg_4(v2) l' U2 l U2 l2 U2 x U2 l' U2 l U2 r' U2 l U2 l /(25,16)
Speedsolving Logo tiny.gif Alg_5(v1) Rw U2 Rw U2 Rw U R Rw U2 R2 U Rw U Rw2 R U Rw U' Rw /(23,19)(WCA)
Speedsolving Logo tiny.gif Alg_5(v2) Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' Rw2 R' U' Rw' U Rw' /(23,19)(WCA)


Impure Dedge Flips with Wide Turns/Pure Flips with Inner Layer Turns (SiGN Notation)

OLL Parity

  • If the following group of algorithms is executed using WCA notation (where lowercase = inner layer turns), pure one dedge flips will result.
  • Note that all 26 possible (25,15) solutions (excluding mirrors and inverses) of this category are listed.
Speedsolving Logo tiny.gif Frédérick_Badie(v1) r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2 /(25,15)
Speedsolving Logo tiny.gif Frédérick_Badie(v2) r' U2 r U2 l' U2 l2 F2 r F2 l' U2 F2 r2 F2 /(25,15)
Speedsolving Logo tiny.gif Frédérick_Badie(v3) r B2 r' U2 r U2 r2 F2 r' D2 l D2 B2 r2 F2 /(25,15)
Speedsolving Logo tiny.gif Frédérick_Badie(v4) r B2 r' U2 r U2 l2 B2 r' U2 l U2 F2 l2 F2 /(25,15)
Speedsolving Logo tiny.gif Frédérick_Badie(v5) r B2 l' B2 l U2 r2 F2 l' F2 r U2 F2 l2 F2 /(25,15)
Speedsolving Logo tiny.gif Alg.2(v1) r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 B2 /(25,15)
Speedsolving Logo tiny.gif Alg.2(v2) r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 B2 /(25,15)
Speedsolving Logo tiny.gif Alg.2(v3) r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 B2 /(25,15)
Speedsolving Logo tiny.gif Alg.2(v4) r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 B2 /(25,15)
Speedsolving Logo tiny.gif Alg.2(v5) r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 B2 /(25,15)
Speedsolving Logo tiny.gif Alg.3(v1) r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.3(v2) r2 B2 U2 l U2 l' B2 r B2 U2 r U2 r' B2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.3(v3) r2 F2 D2 r' D2 r F2 l' F2 D2 l' D2 l F2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.3(v4) r2 F2 D2 r' D2 l D2 l' D2 B2 l' B2 r F2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.3(v5) r2 B2 U2 r B2 r' B2 l U2 F2 r F2 l' B2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.3(v6) r2 F2 D2 l' F2 l F2 r' D2 B2 l' B2 r F2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.3(v7) r2 B2 U2 r B2 l' D2 r D2 B2 l U2 r' B2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.3(v8) r2 F2 D2 l' F2 r U2 l' U2 F2 r' D2 l F2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.4(v1) r2 B2 U2 l' U2 r U2 r' U2 B2 r' B2 l B2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.4(v2) r2 B2 U2 l' U2 l F2 r' F2 U2 r' U2 r B2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.4(v3) r2 F2 D2 r D2 r' B2 l B2 D2 l D2 l' F2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.4(v4) r2 F2 D2 r D2 l' D2 l D2 F2 l F2 r' F2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.4(v5) r2 B2 U2 r' F2 r F2 l' U2 B2 r' B2 l B2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.4(v6) r2 B2 U2 r' F2 l D2 r' D2 F2 l' U2 r B2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.4(v7) r2 F2 D2 l B2 r' U2 l U2 B2 r D2 l' F2 r2 /(25,15)
Speedsolving Logo tiny.gif Alg.4(v8) r2 F2 D2 l B2 l' B2 r D2 F2 l F2 r' F2 r2 /(25,15)
Speedsolving Logo tiny.gif cmowlaparity x' r2 U2 l' U2 r U2 l F2 U r U' F2 U r' U r2 x /(23,16)
Speedsolving Logo tiny.gif Alg r U2 F2 D' r' D F2 D' r D r F2 r' F2 r' U2 r' /(23,17)
Speedsolving Logo tiny.gif lucasparity r U2 r U2 r' U2 r U2 l' U2 l F2 r' F2 r' U2 r' /(25,17)
Speedsolving Logo tiny.gif Alg r2 U2 l' U2 r U2 r' U2 r U2 r' x' U2 r' U2 r2 F2 l x /(27,17)
Speedsolving Logo tiny.gif Alg r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r' /(27,18)
Speedsolving Logo tiny.gif Alg r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r' U2 l' r' U2 l /(27,18)


OLL Parity + PLL Parity (Double Parity) (SiGN Notation)

  • If the following group of algorithms is executed using WCA notation (where lowercase = inner layer turns), pure one dedge flips + PLL Parity will result.
Speedsolving Logo tiny.gif Alg r2 B2 r' U2 r' U2 x' U2 r' U2 r U2 r' U2 r2 U2 x /(25,15)
Speedsolving Logo tiny.gif Alg r U2 r' U2 r U2 r U2 r' x U2 r U2 r' U2 x' U2 r2 U2 /(27,17)


Pure Flips (WCA Notation)

(Algorithms in SiGN Notation are labeled.)

OLL Parity: One Dedge Flip

Speedsolving Logo tiny.gif cmowlaparity x' Rw2 U2 Lw' U2 r U2 Rw U2 x' U r U' F2 U r' U Rw2 x /(23,16)
Speedsolving Logo tiny.gif Alg x' Rw2 U2 Lw' U2 r U2 Rw U2 x' U' r U F2 U' r' U' Rw2 x /(23,16)
Speedsolving Logo tiny.gif Alg Rw Uw2 x' U D r y Uw2 Rw2 Uw r Uw' Rw2 Dw r' u D' x Uw2 Rw' /(22,17)
Speedsolving Logo tiny.gif Alg Rw U2 F2 D' r' D F2 D' r D Rw F2 r' F2 Rw' U2 Rw' /(23,17)
Speedsolving Logo tiny.gif Alg Rw U2 F2 D r' D' F2 D r D' Rw F2 r' F2 Rw' U2 Rw' /(23,17)
Speedsolving Logo tiny.gif lucasparity Rw U2 Rw U2 r' U2 r U2 l' U2 l F2 r' F2 Rw' U2 Rw'/ (25,17)
Speedsolving Logo tiny.gif Holy_Grail z Dw' M D Lw' Uw' r' Uw Lw Uw' Lw2' Bw' r' Bw Rw' R' u y' M' Uw x2 z' /(19,18) Cube Camera Icon.png[1]
Speedsolving Logo tiny.gif Alg Rw' E Uw2 Fw Uw Rw' r' Fw' r Fw Rw Uw' Fw' Uw r Uw E' Rw /(19,18)
Speedsolving Logo tiny.gif Alg Lw' S Bw2 Dw r Dw' Bw Dw r' Dw' r' Bw' r Bw r Bw S' Lw /(19,18)
Speedsolving Logo tiny.gif Alg Lw' F' b' Rw' Bw' Rw u Rw' Bw Rw u2 Bw' u Bw u b F Lw /(19,18)
Speedsolving Logo tiny.gif Alg Rw2 F' r U' R U' r' U R' U r' F' U2 r' U2 r F2 Rw2 /(23,18)
Speedsolving Logo tiny.gif Alg z r f2 3u U y' 2R' u2 y' l2 u' 2R' u l2 u' 2R 3u' u' U' x' u2 r' z /(23,18)(SiGN)
Speedsolving Logo tiny.gif Alg Rw2 B2 U' b' U r U2 r' U' b U' Rw' U2 r' U2 Rw B2 Rw2 /(25,18)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U2 x' U r U' F2 U r' U' Lw' U2 r U2 Rw' U2 Rw' /(25,18)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U2 x' U' r U F2 U' r' U Lw' U2 r U2 Rw' U2 Rw' /(25,18)
Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 r' U2 Rw U2 l' U2 r U2 r' U2 (Rw' l) Rw' U2 Rw' /(27,18)
Speedsolving Logo tiny.gif Alg r2 U2 r2 U2 r U2 r U2 r' U2 B2 U' r' U B2 U' r U' /(27,18)
Speedsolving Logo tiny.gif Alg r2 U2 r2 U2 r U2 r U2 r' U2 B2 U r' U' B2 U r U /(27,18)
Speedsolving Logo tiny.gif Alg Rw' E Uw b' Uw r Uw r' Uw' b Uw r' Uw' r Uw r Uw E' Rw /(19,19)
Speedsolving Logo tiny.gif Alg Rw' E Uw' r' Uw Lw' Uw' Fw Rw' Fw' r' Fw r Rw Fw' Uw Lw E' Rw /(19,19)
Speedsolving Logo tiny.gif Alg Rw' D' u' Uw' Rw f Rw' Uw Rw f' Rw' f' Uw' f Uw f u D Rw /(19,19)
Speedsolving Logo tiny.gif Alg Rw' E R Uw' Fw' u' Fw Uw2 Bw' Uw Fw' u' Fw U' Bw Uw' R' E' Rw /(20,19)
Speedsolving Logo tiny.gif Alg Dw' F' z Rw2 B2 x' l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l u' U Rw2 D Rw z' /(24,19)
Speedsolving Logo tiny.gif Alg Rw' E r' f' Dw' f' Dw Fw Lw' f Fw Dw' f' Dw Fw' Lw F' r E' Rw /(20,20)
Speedsolving Logo tiny.gif Alg Uw Fw' D r' Dw b Dw b' Dw' r Dw b' Dw' b Dw b Dw2 D' Fw Uw' /(21,20)
Speedsolving Logo tiny.gif Alg Fw' U' l u2 Lw Bw' Lw' u Lw Uw Bw u' Bw' Uw' Bw Lw' u l' U Fw /(21,20)
Speedsolving Logo tiny.gif Alg Rw U L F' U l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l Uw' U' F L' U' Rw' /(23,20)
Speedsolving Logo tiny.gif Alg Bw' R' u Rw' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' Rw u' R Bw /(21,21)
Speedsolving Logo tiny.gif Alg Bw' R' u Rw' l' Dw Bw' Dw' l Dw Lw Bw l' Bw' Lw' Bw Dw' Rw u' R Bw /(21,21)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw' U L u l Uw' r' Uw l' u' L' U' Fw r2 Uw' z /(23,22)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw' f' U L U' f r' f' U L' U' f Fw r2 Uw' z /(23,22)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw' f' L Fw R' F' r' F R Fw' L' f Fw r2 Uw' z /(23,22)


One Dedge Flip + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg_1 r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l y2 /(21,14)
Speedsolving Logo tiny.gif Alg_2(v1) r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 B2 /(25,15)
Speedsolving Logo tiny.gif Alg_2(v2) r2 F2 r U2 r U2 F2 r F2 r' F2 r F2 r2 F2 /(25,15)
Speedsolving Logo tiny.gif Alg_3 Rw2 B2 U2 l r2 U2 r' U2 r U2 F2 r F2 l' B2 Rw2 /(26,16)
Speedsolving Logo tiny.gif Alg_4 r' U2 r' U2 l U2 r' U2 r U2 M' U2 r2 U2 r' U2 r /(26,17)
Speedsolving Logo tiny.gif Alg_5 r' U2 r U2 r' U2 r' U2 l U2 r' U2 r U2 M' U2 r2 /(26,17)
Speedsolving Logo tiny.gif Alg_6 (F d' S r F Rw2 f2 u' r2 Uw2 S') r (S Uw2 r2 u f2 Rw2 F' r' S' d F') /(31,23)
Speedsolving Logo tiny.gif Alg_7 (B Lw2 U' L' U r u2 b' r2 Bw2 E) r (E' Bw2 r2 b u2 r' U' L U Lw2 B') /(31,23)
Speedsolving Logo tiny.gif Alg_8 r' U' R' U' r' U R U r U2 r' U' R' U' r2 U R U r U2 r U2 r' U2 /(29,24)


One Dedge Flip + Adjacent PLL Parity (Adjacent Double Parity)

Speedsolving Logo tiny.gif Alg (r2 F Rw' F') U2 r U2 r U2 r U2 r2 (F Rw F' r2) /(23,16)
Speedsolving Logo tiny.gif Alg (Rw' z' L' U r F) U2 r U2 r U2 r U2 r2 (F' r' U' L z Rw) /(23,18)
Speedsolving Logo tiny.gif Alg (x' r2 U' Rw U) M' U2 r' U2 r' U2 r' U2 l r (U' Rw' U r2 x) /(24,18)
Speedsolving Logo tiny.gif Alg R B r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l y2 B' R' /(25,18)
Speedsolving Logo tiny.gif Alg (R B r2 B2) r' U2 r' U2 B2 r' B2 r B2 r' (B2 r2 B R') /(27,18)
Speedsolving Logo tiny.gif Alg Rw U2 x U' Rw R U' r U2 r U2 r U2 r2 U' Rw' R' U x' U2 Rw' /(25,19)
Speedsolving Logo tiny.gif Alg Rw2 U x' U2 r U2 r' F2 l F2 U' L' U' l U L U l' x U' Rw2 /(25,19)
Speedsolving Logo tiny.gif Alg r2 F' R' F' U2 l F2 D2 r D2 l' F' r' F' U2 F Rw F r2 /(26,19)
Speedsolving Logo tiny.gif Alg M' U F2 r' B2 r B2 r F2 r' U' r' F R' F r F' R F' l /(24,20)
Speedsolving Logo tiny.gif Alg (Rw2 U x') U2 r U2 l' U2 l U2 M U' L' U' l U L U l' (x U' Rw2) /(26,20)
Speedsolving Logo tiny.gif Alg Rw2 F L F U2 l F2 D2 r D2 l' F r' F U2 F' r L' F' Rw2 /(27,20)
Speedsolving Logo tiny.gif Alg (z' Rw' U' Rw' l' U L') U r U2 r U2 r U2 r2 U (L U' l Rw U Rw z) /(25,21)
Speedsolving Logo tiny.gif Alg (Rw2 F' L F r f2 u' r2 Uw2 S') r (S Uw2 r2 u f2 r' F' L' F Rw2) /(29,21)
Speedsolving Logo tiny.gif Alg (x' Lw2 F' L2 F r f2 u' r2 Uw2 S') r (S Uw2 r2 u f2 r' F' L2 F Lw2 x) /(31,21)



Other ELL Cases (WCA Notation)

4-Cycles in Two Opposite Edges

Checkerboard pattern (Adj. 2-swap 2-Swap + Two Flip)

Speedsolving Logo tiny.gif Alg_1 (f2 u' r2 Uw2 S') r (S Uw2 r2 u f2) /(17,11)
Speedsolving Logo tiny.gif Alg_2 f2 M2 f2 l2 U2 r S2 r' S2 r' U2 r2 /(21,12)
Speedsolving Logo tiny.gif Alg_3(v1) r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r /(21,13)
Speedsolving Logo tiny.gif Alg_3(v2) l' U2 l2 U2 l U2 l' U2 l U2 l2 U2 l' /(21,13)
Speedsolving Logo tiny.gif Alg_3(v3) r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r' /(21,13)
Speedsolving Logo tiny.gif Alg_3(v4) l U2 l2 U2 l' U2 l U2 l' U2 l2 U2 l /(21,13)


Bowtie/Hourglass (Adj. 2-swap + Pll Parity)

Speedsolving Logo tiny.gif Alg_1 r2 U2 l' U2 l F2 U2 r2 U2 r F2 r' F2 r' F2 /(25,15)
Speedsolving Logo tiny.gif Alg_2(v1) r' U2 r U2 l' U2 r U2 l F2 r' F2 r F2 r2 F2 /(25,16)
Speedsolving Logo tiny.gif Alg_2(v2) l U2 l' U2 r U2 l' U2 r' F2 l F2 l' F2 l2 F2 /(25,16)
Speedsolving Logo tiny.gif Alg_3 (B' R Uw' u' r' f2 Rw2 E) f (E' Rw2 f2 r u Uw R' B) /(21,17)
Speedsolving Logo tiny.gif Alg_4 r U2 l' U2 r U2 r U2 r' U2 r U2 r2 U2 M U2 r' /(26,17)
Speedsolving Logo tiny.gif Alg_5 r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r' /(26,17)


4-Cycles in Two Adjacent Edges

Checkboard Pattern

Speedsolving Logo tiny.gif Alg (R2 Uw' u' r' f2 Rw2 E) f (E' Rw2 f2 r u Uw R2) /(21,15)
Speedsolving Logo tiny.gif Alg (Rw' F2 M2 F) l' U2 l' U2 l2 U2 l' U2 (F' M2 F2 Rw) /(25,16)
Speedsolving Logo tiny.gif Alg (Rw U2 M2 U') M U2 r' U2 r2 U2 r' U2 l' (U M2 U2 Rw') /(26,17)


Bowtie/Hourglass

Speedsolving Logo tiny.gif Alg (L' Fw' f' l' u2 Lw2 S') u (S Lw2 u2 l f Fw L) /(19,15)
Speedsolving Logo tiny.gif Alg (Lw' U2 M2 U' x) r' U2 r' U2 r2 U2 r' U2 (x' U M2 U2 Lw) /(25,16)
Speedsolving Logo tiny.gif Alg R B r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r' B' R' /(25,17)
Speedsolving Logo tiny.gif Alg (l' U2 M2 U) M' U2 r U2 r2 U2 r U2 l (U' M2 U2 l) /(26,17)


2-Cycles in Two Opposite Edges

Adjacent 2-swap

Speedsolving Logo tiny.gif Alg_1 r2 D2 r' D2 l D2 l' D2 B2 l' B2 r' /(19,12)
Speedsolving Logo tiny.gif Alg_2(v1) r U2 r U2 x U2 r U2 l' x' U2 l U2 r2 /(19,12)
Speedsolving Logo tiny.gif Alg_2(v2) l' U2 l' U2 x U2 l' U2 r x' U2 r' U2 l2 /(19,12)
Speedsolving Logo tiny.gif Alg_3(v1) r U2 r U2 M' U2 r U2 r' U2 l U2 r2 /(20,13)
Speedsolving Logo tiny.gif Alg_3(v2) l' U2 l' U2 M' U2 l' U2 l U2 r' U2 l2 /(20,13)
Speedsolving Logo tiny.gif Alg_4 Rw' U2 r' U2 (Rw' l) U2 r' U2 r U2 l' U2 Rw2 /(20,13)
Speedsolving Logo tiny.gif Alg_5 z' Lw U' r Uw Lw' Uw' r Fw r Fw' r2 Uw Lw u' Lw' z /(16,15)
Speedsolving Logo tiny.gif Alg_6 l2 D' f' D r D2 r' D' f D' l' F2 r' F2 l' /(19,15)
Speedsolving Logo tiny.gif Alg_7 b u Bw' Rw' f' Rw Bw Rw' f2 Uw' f' Uw f' Rw u' b' /(17,16)
Speedsolving Logo tiny.gif Alg_8 Rw U2 r U2 Rw U2 Rw2 F r F' Rw2 U2 Rw2 F r' F' /(23,16)
Speedsolving Logo tiny.gif Alg_9 Fw' Uw r' Uw' Fw Uw r' Fw' f' L f r' f' L' f Fw r2 Uw' /(19,18)


Opposite/diagonal 2-swap

Speedsolving Logo tiny.gif Alg_1(v1) l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r z2 /(21,14)
Speedsolving Logo tiny.gif Alg_1(v2) r S2 U2 r' U2 r U2 l' U2 l F2 r' B2 l' z2 /(21,14)
Speedsolving Logo tiny.gif Alg_2 r2 B2 U2 r' U2 r2 B2 r' U2 r2 U2 B2 r' B2 /(25,14)
Speedsolving Logo tiny.gif Alg_3 r2 B2 U2 r U2 r2 B2 r' U2 r2 U2 B2 r' B2 /(25,14)
Speedsolving Logo tiny.gif Alg_4 Uw Lw' Uw' l' Uw Lw2 Dw' Lw Uw' l' Uw L' Dw Lw' Uw' /(16,15)
Speedsolving Logo tiny.gif Alg_5 Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw' /(16,15)
Speedsolving Logo tiny.gif Alg_6 Uw Lw' Bw' r' Bw Lw2 Bw' Rw Fw' r' Fw R' Bw Lw' Uw' /(16,15)
Speedsolving Logo tiny.gif Alg_7 Fw' L2 Uw b' Uw' Lw2 Uw L' Uw b' Uw' Lw Uw' l2 Fw /(18,15)
Speedsolving Logo tiny.gif Alg_8 Fw Uw' B2 Lw u' Lw' Bw2 Rw2 d' Rw' d Rw' b2 Uw Fw' /(19,15)
Speedsolving Logo tiny.gif Alg_9 Uw Rw' F2 Rw' f Rw Bw2 Lw2 u Lw u' Rw u2 Rw Uw' y2 /(19,15)
Speedsolving Logo tiny.gif Alg_10 Rw2 F2 U2 r U2 x U2 Rw2 U2 r' U2 l r U2 l' U2 x' /(25,15)
Speedsolving Logo tiny.gif Alg_11 Fw' L U' f Uw2 Lw2 Dw r Dw' Lw2 Uw f' Uw U L' Fw /(19,16)
Speedsolving Logo tiny.gif Alg_12(v1) l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r /(25,16)
Speedsolving Logo tiny.gif Alg_12(v2) r U2 r' U2 r' U2 l U2 r' U2 r U2 F2 r2 F2 l' /(25,16)
Speedsolving Logo tiny.gif Alg_13 r F2 D2 l D2 F r2 U2 r2 F r' F' r2 U2 r2 F /(25,16)
Speedsolving Logo tiny.gif Alg_14 r U2 r' U2 r' U2 l U2 r' U2 r U2 M' U2 r2 U2 r' /(26,17)
Speedsolving Logo tiny.gif Alg_15 Uw' Lw' Fw R' Fw' d' Fw R Fw' Lw2 Fw2 Rw' u' Rw Fw2 Lw' b Uw /(21,18)
Speedsolving Logo tiny.gif Alg_16 x' l' Uw Rw' Uw' l Uw Fw Uw B' l2 B r' B' l2 B Uw' Fw' Rw Uw' x /(21,19)


2-Cycles in Two Adjacent Edges

Case 1 (Close Adjacent "unoriented")

Speedsolving Logo tiny.gif Alg l2 r' U B2 U' r U B2 Lw U2 r U2 Lw' U' l2 /(21,15)
Speedsolving Logo tiny.gif Alg x' l2 F U2 l U2 r' U2 r U2 F2 r F2 l' F' l2 x /(23,15)
Speedsolving Logo tiny.gif Alg r U2 r U2 F' L F' r F L' F l' U2 l U2 r2 /(21,16)
Speedsolving Logo tiny.gif Alg x' l2 F U2 l U2 r' U2 r U2 (l' Rw) U2 r U2 Rw' F' l2 x /(24,16)
Speedsolving Logo tiny.gif Alg z' F Lw2 b Uw' Rw Uw b' Uw' b' Rw' b Rw b Rw' Uw Lw2 F' z /(19,17)
Speedsolving Logo tiny.gif Alg z' F Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2 F' z /(19,17)
Speedsolving Logo tiny.gif Alg z' F Lw2 z Lw' Bw r' Bw' Lw Bw Rw' Dw' r' Dw Rw r Fw' Lw2 F' z /(19,17)
Speedsolving Logo tiny.gif Alg Rw b' Uw2 Rw' Uw' f Uw Rw Uw' f Rw' f Rw f2 Uw' b Rw' /(19,17)
Speedsolving Logo tiny.gif Alg r2 U2 l U2 r' U2 r U2 F' L F' r F L' F l' r2 /(23,17)


Case 2 (Far Adjacent "unoriented")

Speedsolving Logo tiny.gif Alg l2 r' U' B2 U r U' B2 Lw U2 r U2 Lw' U l2 /(21,15)
Speedsolving Logo tiny.gif Alg x Rw2 F' U2 l U2 r' U2 r U2 F2 r F2 l' F Rw2 x' /(23,15)
Speedsolving Logo tiny.gif Alg r U2 r U2 F R' F r F' R F' l' U2 l U2 r2 /(21,16)
Speedsolving Logo tiny.gif Alg x Rw2 F' U2 l U2 r' U2 r U2 (l' Rw) U2 r U2 Rw' F Rw2 x' /(25,16)
Speedsolving Logo tiny.gif Alg Lw l b Uw' Rw Uw b' Uw' b' Rw' b Rw b Rw' Uw Lw' l' /(17,17)
Speedsolving Logo tiny.gif Alg Lw l z Lw' Bw r' Bw' Lw Bw Rw' Dw' r' Dw Rw r Fw' Lw' l' /(17,17)
Speedsolving Logo tiny.gif Alg Rw l Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' l' Rw' /(17,17)
Speedsolving Logo tiny.gif Alg Rw' l' x' U2 l U2 r' U2 r U2 x U R U r U' R' U' Rw /(21,17)
Speedsolving Logo tiny.gif Alg r2 U2 l U2 r' U2 r U2 F R' F r F' R F' l' r2 /(23,17)
Speedsolving Logo tiny.gif Alg z Dw' (M R') D Lw' Uw' r' Uw Lw Uw' Lw2' Bw' r' Bw Rw' R' u y' (M' R) Uw x2 z'/(19,18)


Case 3 ("Oriented" Case)

Speedsolving Logo tiny.gif Alg Lw2 b Uw' Rw Uw b' Uw' b' Rw' b Rw b Rw' Uw Lw2 /(17,15)
Speedsolving Logo tiny.gif Alg Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2 /(17,15)
Speedsolving Logo tiny.gif Alg Lw2 z Lw' Bw r' Bw' Lw Bw Rw' Dw' r' Dw Rw r Fw' Lw2 /(17,15)
Speedsolving Logo tiny.gif Alg Rw2 f Uw' Bw Dw r' Dw' r' Bw' r Bw r Bw' Uw Rw2 /(17,15)
Speedsolving Logo tiny.gif Alg z' Fw' l' Uw' Bw2 Uw' r Uw Bw2 Uw2 r Uw r' Uw2 l Fw z /(19,15)
Speedsolving Logo tiny.gif Alg Uw Rw' Uw' r' Uw Rw Bw' Rw' r' Uw' r' Uw R r' Bw Uw' /(16,16)
Speedsolving Logo tiny.gif Alg Bw L' Dw' l Dw Lw Bw' Lw L Dw' l Dw Lw2 Fw u' Fw' /(17,16)
Speedsolving Logo tiny.gif Alg Uw' Fw l' Fw' Uw Fw l' Uw2 R Uw l' Uw' R' Uw2 l2 Fw' /(19,16)
Speedsolving Logo tiny.gif Alg r' Uw Lw Uw' r2 Fw2 Lw' Fw r' Fw' Lw Fw2 r' Uw Lw' Uw' /(19,16)
Speedsolving Logo tiny.gif Alg z' Lw Uw' r Uw Lw' Uw' r Fw2 L' Fw' r Fw L Fw2 r2 Uw z /(19,16)
Speedsolving Logo tiny.gif Alg Bw' Uw2 r' Dw l' Dw' r Uw' Lw2 Uw' r' Uw Lw2 Uw' r Bw /(19,16)
Speedsolving Logo tiny.gif Alg z' Uw Lw' Uw2 r Uw' l Uw r' Uw2 L Uw' Bw2 Uw l Uw' Bw2 z /(20,16)
Speedsolving Logo tiny.gif Alg x l2 U2 r U2 r' F2 l F2 U L U l U' L' U' l x' /(21,16)
Speedsolving Logo tiny.gif Alg l2 r' U F2 U' l U F2 Rw U2 l U2 Rw' U' l r /(21,16)
Speedsolving Logo tiny.gif Alg R B r U2 r U2 x U2 r U2 l' x' U2 l U2 r2 B' R' /(23,16)
Speedsolving Logo tiny.gif Alg x l' U L U l' U' L' U' x U2 l' U2 l U2 r' U2 l r x2 /(21,17)
Speedsolving Logo tiny.gif Alg x r U' R' U' r U R U M' U2 r U2 r' U2 l U2 r2 x' /(22,17)
Speedsolving Logo tiny.gif Alg x' f' Uw Rw' Fw' r' Fw Rw Uw' f r' Uw Rw' Fw' r' Fw Rw Uw' r2 x /(19,18)
Speedsolving Logo tiny.gif Alg r' U' F2 U r' U' F2 r' F' R' F' r' F R F r U r2 /(21,18)
Speedsolving Logo tiny.gif Alg z' r' Uw Bw Uw' Bw L Bw r Bw' L' Bw' Uw Bw' Lw Uw' r Uw Lw' Uw' z /(19,19)
Speedsolving Logo tiny.gif Alg l' Uw Rw' Uw' l Uw Fw Uw B' Rw2 F r' F' Rw2 B Uw' Fw' Rw Uw' /(21,19)



Summary of 2-Cycle and 4-Cycle ELL Case Movecounts

  • Since there is disagreement among cubers about whether lowest q moves or lowest btm moves defines the "optimal algorithm", the table below categorizes all 2-cycle and 4-cycle ELL cases on the 4x4x4 by the average of q moves and btm.
  • Algorithms optimal in btm need not be the algorithm with the lowest average of q and btm, and algorithms optimal in q turns need not be the algorithm with the lowest average of q and btm. Therefore, the average for a given case might be from an algorithm optimal in q moves, optimal in btm moves, or optimal in both.
  • Of course, this ranking is based off of required moves. It is not based off of the amount of time it takes to solve a case.
  • These results will change in the future if shorter algorithms are found for any of these cases.
  • The table shows that the "worst case" is Adjacent Double Parity, and that the "easiest case" is the Checkerboard Pattern (in two opposite edges).



OLL Parity Algorithms Which Don't Preserve F3L (WCA Notation)

  • One advantage of having access to algorithms which don't preserve the first three layers of the 4x4x4 is that the optimal algorithms require less moves than algorithms which preserve the first three layers, which might be of interest to certain cubers.
  • Unlike algorithms which preserve the first three layers, which are at minimum 14 block half turns and 19 block quarter turns, some algorithms in this section are 13 block half turns and some are just 15 block quarter turns.
  • All of the 13 btm algorithms in this section have many variations, but yet all variations are the same as the few algorithms listed below. The following "translations" of the 13 btm algorithms work on all cube sizes (the first version, at least, for those with more than one version). For a list of more variations of the 13 btm algorithms (but definitely not all possible variations), see http://www.speedsolving.com/forum/showthread.php?26564-4x4x4-edge-parity-is-there-a-shorter-alg-that-doesn-t-preserve-corners&p=531938&viewfull=1#post531938
  • A few of the algorithms are in SiGN Notation: they are labeled.

OLL Parity

Complete 3x3x3 Scrambles

Speedsolving Logo tiny.gif Alg Rw B U2 B' r B2 l B2 r B' D2 B Rw/(17,13)
Speedsolving Logo tiny.gif Alg r U F2 U' l F2 2R U2 r U B2 U' r/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg r U' F2 U l F2 2R U2 r U' B2 U r/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg Uw M R D R' Fw f E' l' E Fw b E F Lw/(15,15)
Speedsolving Logo tiny.gif Alg r U2 r' U2 r D2 r D2 r' F L' F' U' r' D2 r/(21,16)(SiGN)
Speedsolving Logo tiny.gif Alg r U2 r' U2 r D2 r D2 r' F L' F' U' l' F2 l/(21,16)(SiGN)
Speedsolving Logo tiny.gif Alg r U2 r' U2 r D2 r D2 l' U L' U' B' l' U2 l x'/(21,16)(SiGN)
Speedsolving Logo tiny.gif Alg r U2 r' U2 r D2 r D2 l' U L' U' B' r' F2 r/(21,16)(SiGN)


More than 1 F3L Slot Destroyed (Not Petrus)

Speedsolving Logo tiny.gif Alg r' U2 F U2 F' U2 r' U2 r' U2 r' F U2 F' r'/(21,15)(SiGN)
Speedsolving Logo tiny.gif Alg Rw U D' R2 U' R2 D x' U2 Lw U2 Lw U2 Lw F' U2 F Lw/(22,16)
Speedsolving Logo tiny.gif Alg Rw F U2 F' Rw U2 Rw U2 Rw R U2 F U2 F' U2 r/(22,16)
Speedsolving Logo tiny.gif Alg Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' F U' B' U' S Dw' z'/(20,17)
Speedsolving Logo tiny.gif Alg Lw U' L' R U2 L U Lw U2 Lw U2 Lw U' R' U2 R U r x'/(22,18)
Speedsolving Logo tiny.gif Alg Lw U' L' R' U2 L U Lw U2 Lw U2 Lw U' R U2 R' U Lw R/(23,19)


FR F3L Slot Destroyers

Speedsolving Logo tiny.gif Alg r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r'/(21,15)
Speedsolving Logo tiny.gif Alg l U2 F' U2 F U2 l U2 l U2 l F' U2 F l/(21,15)
Speedsolving Logo tiny.gif Alg r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r'/(21,17)
Speedsolving Logo tiny.gif Alg l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l'/(21,17)
Speedsolving Logo tiny.gif Alg l U2 l' F U R U' Lw' D2 r D2 r U2 Rw' U2 Lw F/(22,17)
Speedsolving Logo tiny.gif Alg Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F r' U2 r F/(22,17)
Speedsolving Logo tiny.gif Alg Rw U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'/(24,18)
Speedsolving Logo tiny.gif Alg Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 r'/(24,18)
Speedsolving Logo tiny.gif Alg Rw U2 R U R' U2 R U r U2 Rw U2 Rw U R U2 R' U' Rw/(24,19)


Just Corners are Permuted

Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw R2/(22,18)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U r U2 Rw R U2 r U R U2 R' U' Rw/(22,18)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U r U2 Rw R U2 r U R' U2 R U' Rw/(22,18)
Speedsolving Logo tiny.gif Alg Rw R U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw/(24,18)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw R2 U2 r U2 Rw U R' U2 R U' Rw R2/(24,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw R2/(24,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U' R U2 r U2 Rw U2 r U R U2 R' U' Rw/(24,19)


Petrus Parities (Destroy 2 Adjacent Faces)

Speedsolving Logo tiny.gif Alg_1 r B' U2 B r B2 l B2 r B D2 B' r/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg_1(v2) x' r' U F2 U' l' U2 r' U2 r' F' U2 F r'/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg_1(v3) x' r' U F2 U' l' U2 r' U2 l' U' B2 U r' x'/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg_1(v4) x' r' U F2 U' l' U2 r' 3d2 r' U' F2 U l' x/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg Rw U2 Rw' U2 Rw D2 r D2 l' U L' U' B' l' U2 l x'/(21,16)
Speedsolving Logo tiny.gif Alg Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw'/(21,17)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw/(21,17)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw U2 Rw U2 r U R U2 R' U' Rw/(21,17)
Speedsolving Logo tiny.gif Alg Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw'/(21,17)
Speedsolving Logo tiny.gif Alg Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F Rw' U2 Rw F/(22,17)
Speedsolving Logo tiny.gif Alg Rw U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw/(23,17)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw'/(25,17)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 r2 U R2 U' Rw'/(25,17)
Speedsolving Logo tiny.gif Alg Rw U' R2 U2 R2 U r U2 r U2 r U R2 U2 R2 U' Rw/(25,17)
Speedsolving Logo tiny.gif Alg Rw' U R U2 R' U' r' U2 Rw' U2 Rw' F' U' R' U' R F Rw'/(21,18)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw/(23,18)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U Rw U2 r U2 Rw R2 U R U2 R' U' Rw/(23,18)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U Rw U2 Rw R2 U2 Rw U R' U2 R U' Rw/(23,18)
Speedsolving Logo tiny.gif Alg Rw U R U' Rw2 R U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 Rw'/(24,18)
Speedsolving Logo tiny.gif Alg Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R2 U' R2 U2 R2 U Rw'/(24,18)
Speedsolving Logo tiny.gif Alg Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'/(24,18)
Speedsolving Logo tiny.gif Alg Rw U R' U Rw U2 r U2 r U' Rw' U R U R' U2 Rw U' Rw/(22,19)
Speedsolving Logo tiny.gif Alg Rw U R' U r U2 r U2 Rw U' Rw' U R U R' U2 Rw U' Rw/(22,19)
Speedsolving Logo tiny.gif Alg Rw U' Rw U2 R' U R U Rw' U' r U2 Rw U2 Rw U R' U Rw/(22,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw R U2 r U2 Rw R U R' U2 R U' Rw/(23,19)
Speedsolving Logo tiny.gif Alg Rw U' Rw U2 R' U R U Rw' U' Rw U2 r U2 Rw U R2 U Rw/(23,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U' R' U2 r U2 Rw U2 r U R' U2 R U' Rw/(24,19)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U' R' U2 r U2 Rw U2 r U R U2 R' U' Rw/(24,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U r U2 Rw U2 Rw U R U2 R' U R' U2 Rw/(24,19)
Speedsolving Logo tiny.gif Alg Rw U R' U2 R' U2 R U Rw R U2 Rw U2 Rw U R U2 R' U' Rw/(25,20)


OLL Parity + PLL Parity (Double Parity)

Complete 3x3x3 Scrambles

Speedsolving Logo tiny.gif Alg_1 r F2 U2 l F U' R U' r2 B2 r' B2 r2/(19,13)(SiGN)
Speedsolving Logo tiny.gif Alg_2 r F2 U2 l F' U L' U r2 B2 r' B2 r2/(19,13)(SiGN)
Speedsolving Logo tiny.gif Alg r F2 U2 l F U' (L' R) U' r2 B2 r' B2 r2/(19,13)(SiGN)
Speedsolving Logo tiny.gif Alg r F2 U2 l F' U (L' R) U r2 B2 r' B2 r2/(19,13)(SiGN)
Speedsolving Logo tiny.gif reParity r U2 l' U2 x' (r' U2 l U2)2 l'/(19,13)
Speedsolving Logo tiny.gif Alg Uw R' b E' d' L' b L u' b2 Uw M' B' Uw/(15,15)
Speedsolving Logo tiny.gif Alg Uw S L B' R u d f' u d L B' R S Uw/(15,15)
Speedsolving Logo tiny.gif Alg Uw S L' F R' u d f' u d L' F R' S Uw/(15,15)
Speedsolving Logo tiny.gif Alg Rw' U2 r U2 Rw' x' U2 r' U' R' U' Rw' U2 Rw U R U' Rw x/(21,17)


Affect M Layer Only

Speedsolving Logo tiny.gif Alg r U2 r' U2 r' D2 r D2 r' B2 r B2 r'/(19,13)
Speedsolving Logo tiny.gif Alg r U2 r' U2 M' l' U2 r U2 l' U2 r U2 l'/(20,14)
Speedsolving Logo tiny.gif reParity(v2) r U2 l' U2 l r2 U2 l U2 r' U2 l U2 l r2/(23,15)


FR F3L Slot Destroyers

Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 Rw U Rw U2 R' U Rw U Rw2 R U Rw U' Rw/(21,18)


Petrus Parities (Destroy 2 Adjacent Faces)

Speedsolving Logo tiny.gif Alg_1(v2) l' U2 F2 l' U' F R' F l2 U2 r U2 l2 U' x'/(20,14)(SiGN)
Speedsolving Logo tiny.gif Alg_1(v3) l' U2 F2 l' U' F 3l' U l2 x' U2 r U2 l2 U' x'/(20,14)(SiGN)
Speedsolving Logo tiny.gif Alg_2(v2) r U2 F2 r U' F R' F r2 U2 l' U2 r2 U' x'/(20,14)(SiGN)
Speedsolving Logo tiny.gif Alg_2(v3) r U2 F2 r U' F 3l' U r2 x' U2 l' U2 r2 U' x'/(20,14)(SiGN)
Speedsolving Logo tiny.gif Alg Rw' U Rw' U' Rw2 R' U' Rw' U' R U2 Rw' U' Rw' U2 Rw' U2 Rw'/(21,18)
Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 Rw' U' R' Rw2 U2 r U' R' U' Rw U2 r2 U Rw2/(24,18)
Speedsolving Logo tiny.gif Pochmann Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw'/(24,19)


OLL Parity Algorithms Which Don't Preserve F3L or the Colors of the Centers (WCA Notation)

  • These algorithms are least practical when it comes to use of parity algorithms, and therefore they are mentioned here mainly for theoretical purposes only. They have fewer moves than any other OLL Parity algorithm forms.

OLL Parity

Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r' B2 Rw2 /(15,11)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r' B2 Rw2 /(15,11)
Speedsolving Logo tiny.gif Alg Rw2 U f U' B2 U f' U l B2 Rw2 /(15,11)
Speedsolving Logo tiny.gif Alg Uw S B D B' R f' R M E R Fw /(12,12)


OLL Parity + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg Uw F R B' U f' E U M' U Fw /(11,11)
Speedsolving Logo tiny.gif Alg l' B' u B' D2 B u' B' l D2 l' /(13,11)
Speedsolving Logo tiny.gif Alg Uw L U B U' d Fw2 u' Fw2 L' Uw2 y /(14,11)
Speedsolving Logo tiny.gif Alg Uw L U B d Fw2 u' Fw2 U' L' Uw2 y /(14,11)
Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r B2 Rw2 /(15,11)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r B2 Rw2 /(15,11)
Speedsolving Logo tiny.gif Alg Rw2 U f U' B2 U f' U l' B2 Rw2 /(15,11)
Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 Rw U2 Rw2 U' R U Rw2 U R U' Rw2/(21,15)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U' Rw2 U' R2 U' Rw'/(21,15)


  • Although the following isn't specifically "OLL Parity", where dedge preservation is important, it is the briefest 2-cycle algorithm yet to be found. It also doesn't preserve F3L or the centers.
Speedsolving Logo tiny.gif Alg Lw' F' R2 F2 u' F' Lw /(9,7)


Cage Method/Sandwich Method Algorithms (WCA Notation)

  • These algorithms are for fixing the wing edges, but they do not preserve the centers.

Single Dedge Flip

Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r' U2 B2 Rw2 /(17,12)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r' U2 B2 Rw2 /(17,12)
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U y r U2 F2 Rw2 /(17,12)
Speedsolving Logo tiny.gif Alg Lw2 (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw2 /(17,13)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U B2 D2 l D2 Rw2 /(19,13)
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U' D2 y l D2 F2 Rw2 /(19,13)
Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 l' U2 l U2 r' F2 r F2 Rw2 /(21,13)
Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 l' U2 l U2 r' B2 l B2 Rw2 /(21,13)
Speedsolving Logo tiny.gif Alg l U2 l' U2 Lw2 F2 r' F2 Rw2 U2 l' U2 r x2 /(21,13)
Speedsolving Logo tiny.gif Alg r2 Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' r /(15,14)
Speedsolving Logo tiny.gif Alg x r R' U' Rw U' r U Rw' r' U R U' r U r' x' /(15,15)


OLL Parity + PLL Parity (Double Parity)

  • Most of these algorithms are exactly the same as the single dedge flip ones except that the extra quarter turn is inverted.
Speedsolving Logo tiny.gif Alg Rw' F' u F' D2 F u' F' l D2 F2 Rw /(15,12)
Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r U2 B2 Rw2 /(17,12)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r U2 B2 Rw2 /(17,12)
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U y r' U2 F2 Rw2 /(17,12)
Speedsolving Logo tiny.gif Alg Lw2 (Dw' u) r' U L2 U' r D' r U D L2 y' Lw2 /(17,13)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U B2 D2 l' D2 Rw2 /(19,13)
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U' D2 y l' D2 F2 Rw2 /(19,13)
Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 l' U2 l U2 r' F2 r' F2 Rw2 /(21,13)


Adjacent Double Parity

Speedsolving Logo tiny.gif Alg [r2 U Rw' U R U: r'/(15,13)]
Speedsolving Logo tiny.gif Alg [r2 F' U2 F r U2: r'/(19,13)]
Speedsolving Logo tiny.gif Alg Rw F' Rw' F' U2 F r F' U2 r F R F Rw'/(16,14)
Speedsolving Logo tiny.gif Alg l2 U' Lw U r2 U2 r U2 r U2 r U Lw' U l2/(21,15)


In Two Adjacent Edges (in the M ring)

Adjacent 2-Swap

Speedsolving Logo tiny.gif Alg r' U r U F2 U' r' U F2 U2 /(13,10)
Speedsolving Logo tiny.gif Alg r' U' r U' F2 U r' U' F2 U2 /(13,10)
Speedsolving Logo tiny.gif Alg y' U2 R2 U l U' R2 U l' U y r /(13,10)
Speedsolving Logo tiny.gif Alg F2 U2 l U2 r' U2 r U2 l' F2 r /(17,11)
Speedsolving Logo tiny.gif Alg r U' Rw U' R' U r U' R U r' Rw' U /(13,13)


Opposite/Diagonal 2-Swap (The majority are nearly the same as the one dedge flip algorithms.)

Speedsolving Logo tiny.gif Alg Rw U r' U' B2 U r U r' U2 B2 Rw' /(15,12)
Speedsolving Logo tiny.gif Alg Rw U' r' U B2 U' r U' r' U2 B2 Rw' /(15,12)
Speedsolving Logo tiny.gif Alg Rw (Dw u') l U' R2 U l' U y r U2 F2 Rw' /(17,12)
Speedsolving Logo tiny.gif Alg x' U Rw' U r' U' Rw r U' R' U r' U' R x /(13,13)
Speedsolving Logo tiny.gif Alg x' R U Rw' U r' U' Rw r U' R' U r' U' x /(13,13)
Speedsolving Logo tiny.gif Alg r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' /(13,13)
Speedsolving Logo tiny.gif Alg Lw' (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw /(15,13)
Speedsolving Logo tiny.gif Alg Rw U' r' U B2 U' r U B2 D2 l D2 Rw' /(17,13)
Speedsolving Logo tiny.gif Alg Rw (Dw u') l U' R2 U l' U' D2 y l D2 F2 Rw' /(17,13)
Speedsolving Logo tiny.gif Alg Rw U2 r U2 l' U2 l U2 r' F2 r F2 Rw' /(19,13)
Speedsolving Logo tiny.gif Alg Rw U2 r U2 l' U2 l U2 r' B2 l B2 Rw' /(21,13)


In Two Opposite Edges (in the M Ring)

Adjacent 2-Swap

Speedsolving Logo tiny.gif Alg y Lw' Uw' r Fw r Fw' r2 Uw Lw Uw' r Dw /(13,12)


Opposite/Diagonal 2-Swap (These are the same as the single dedge flips but without first and last moves.)

Speedsolving Logo tiny.gif Alg U r' U' B2 U r U r' U2 B2 /(13,10)
Speedsolving Logo tiny.gif Alg U 'r' U B2 U' r U' r' U2 B2 /(13,10)
Speedsolving Logo tiny.gif Alg (Dw' u) r' U L2 U' r D' r' U D L2 y' /(13,11)
Speedsolving Logo tiny.gif Alg U' r' U B2 U' r U B2 D2 l D2 /(15,11)
Speedsolving Logo tiny.gif Alg (Dw u') l U' R2 U l' U' D2 y l D2 F2 /(15,11)
Speedsolving Logo tiny.gif Alg U2 l U2 r' U2 r U2 l' F2 r F2 /(17,11)
Speedsolving Logo tiny.gif Alg U2 r U2 l' U2 l U2 r' F2 r F2 /(17,11)
Speedsolving Logo tiny.gif Alg U2 r U2 l' U2 l U2 r' B2 l B2 /(17,11)


4-Cycles in Adjacent Edges (in the M ring)

Checkboard Pattern 4-cycle (Adj. 2-swap 2-Swap + Two Flip)

Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 Rw2 /(9,5)


Bowtie/Hourglass (Adj. 2-swap + Pll Parity)

Speedsolving Logo tiny.gif Alg r U2 r' U2 x' U2 r U2 r2 U2 r' U2 r' x /(19,12)


Supercube/Blindfold Solving Algorithms (WCA Notation)

Supercube Safe PLL Parity

In Two Opposite Edges ("Oriented)

Speedsolving Logo tiny.gif Alg r2 U2 B2 l r U2 M' U2 r2 B2 U2 /(19,11)
Speedsolving Logo tiny.gif Alg r2 U2 r U2 r2 U2 r2 U2 r U2 r2 U2 /(22,12)
Speedsolving Logo tiny.gif Alg r' F U' R F' U l r U' F R' U F' l' /(14,14)


In Two Adjacent Edges ("Oriented")

Speedsolving Logo tiny.gif Alg R' F l E F2 E' l' r' E F2 E' r F' R /(16,14)
Speedsolving Logo tiny.gif Alg R' F l E' F2 E l' r' E' F2 E r F' R /(16,14)


Supercube Safe OLL Parity

Single Dedge Flip

Speedsolving Logo tiny.gif Alg r' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U r /(27,23)
Speedsolving Logo tiny.gif Alg Rw2 U2 r' U2 r' U' l r u2 l' r' U l r u2 x U2 l' U2 r U2 r' U2 Rw2 x' /(33,23)


2-Cycles in Two Opposite Edges

Adjacent 2-swap

Speedsolving Logo tiny.gif Alg r' U' r' U r U r' U' r' U' r D b2 r' b2 r U2 D' r U' /(23,20)
Speedsolving Logo tiny.gif Alg U2 l' U2 r U2 r' U2 x' U2 r' U2 r' U' l r u2 l' r' U l r u2 x /(29,21)


Opposite/diagonal 2-swap

Speedsolving Logo tiny.gif Alg x' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U x /(25,21)
Speedsolving Logo tiny.gif Alg Rw U2 r' U2 r' U' l r u2 l' r' U l r u2 x U2 l' U2 r U2 r' U2 Rw' x' /(31,23)


2-Cycles in Two Adjacent Edges

Case 1 (Close "Unoriented" Case)

Speedsolving Logo tiny.gif Alg r' U' r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r2 /(25,21)


Case 2 (Far Adjacent "Unoriented" Case)

Speedsolving Logo tiny.gif Alg r' U r' U r U' r U' r' D b2 r b2 r' D' U2 r' U' r U' r2 /(25,21)


Case 3 ("Oriented" Case)

Speedsolving Logo tiny.gif Alg r' U' r U' r' D b2 r b2 r' D' U2 r' U' r U' r U r' U r2 /(25,21)


Two X-Center Piece Swap Algorithms

  • These algorithms, and other algorithms like them, are used to make two corner swap algorithms which only swap two X-center pieces on the 4x4x4 supercube.
Speedsolving Logo tiny.gif Alg Rw U' Lw Uw2 Rw' U Rw Uw2 x Rw2 U /(13,10)
Speedsolving Logo tiny.gif Alg Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F' /(15,14)
Speedsolving Logo tiny.gif Alg Rw U Lw' U' Lw U Rw' U' Lw' U Lw Rw U' Rw' U' /(15,15)
Speedsolving Logo tiny.gif Alg Rw' U' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U /(15,15)


2-Gen Algorithms (WCA Notation)

  • These algorithms are longer than optimal solutions, but they touch a smaller portion of the cube during execution.
  • The solutions listed are believed to be optimal for this intense move restriction.

One Dedge Flip

(U,r)

Speedsolving Logo tiny.gif Alg r U2 r' U2 r U2 r U r U r U2 r2 U2 r U2 r U r' U' r2 U2 /(31,22)
Speedsolving Logo tiny.gif Alg r U2 r' U2 r U2 r U' r U' r U2 r2 U2 r U2 r U' r' U r2 U2 /(31,22)
Speedsolving Logo tiny.gif Alg r2 U r' U' r U2 r U2 r2 U2 r U' r U' r U2 r U2 r' U2 r U2 /(31,22)
Speedsolving Logo tiny.gif Alg r2 U' r' U r U2 r U2 r2 U2 r U r U r U2 r U2 r' U2 r U2 /(31,22)


(U, Rw)

Speedsolving Logo tiny.gif Alg Rw' U' Rw U' Rw U Rw2 U' Rw2 U2 Rw U2 Rw' U2 Rw U2 Rw U' Rw U Rw' U' Rw U2 Rw' U2 /(34,26)
Speedsolving Logo tiny.gif Alg Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U Rw U Rw' U' Rw U2 Rw' U2 /(34,26)


(U, Rw, r)

  • Although the following algorithm is not 2-gen and is one move longer than the optimal (U, Rw) solutions, it can be applied to larger cube sizes by

1) Letting Rw be the right half of the even cube and the right half + the central slice on odd cubes.

2) Applying the r' and r2 only on this slices which are to be affected.

Speedsolving Logo tiny.gif Alg Rw U2 Rw U Rw U2 Rw U2 Rw' U2 Rw' U r' U' Rw U2 Rw U2 Rw' U2 Rw' U r2 U2 Rw' U2 Rw' /(37,27)

(Similar to other algorithms in this page, the (U, Rw) solutions cannot be applied to the 4x4x4, but the above algorithm can be applied to all big cubes.)



External Links

OLL Parity Algorithms

OLL Parity Algorithms which don't preserve F3L

PLL Parity Algorithms

SuperCube Parity Algorithms

Miscellaneous