OLL parity

Flip a single dedge on a 4x4: the case a 3x3 cannot have.

What it is

Solved as a 3x3 after reduction, a 4x4 can show an odd number of flipped edges: OLL parity. It comes from the inner slices, so the fix is an algorithm of wide moves that flips one dedge while keeping the first three layers.

Recognition

Make the top cross as on a 3x3, then: Count the last-layer dedges showing no top colour on top: one or three means OLL parity; none, two or four means no parity: an ordinary 3x3 OLL.

How to read the diagrams

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Basic

Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'

17 HTM · 4 algs

Pure

2R' U2 2L F2 2L' F2 2R2 U2 2R U2 2R' U2 F2 2R2 F2

22 HTM · 4 algs

M Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw' M'

21 HTM · 4 algs

Source: SpeedCubeDB, https://speedcubedb.com/a/4x4/OLLParity, retrieved 2026-10-24: case names, groups, setups and images, and the top-voted algorithms per case with their votes. Every algorithm shown was checked by the logic engine; rejected ones are listed in docs/db-exclusions.md.