4×4 parity: OLL and PLL explained
Recognise and solve both parity cases produced by the reduction method: a single apparently flipped edge during OLL, or two apparently swapped edges during PLL.
What is 4×4 parity?
Reduction makes a 4×4 behave almost like a 3×3: you build six centres and pair the 24 wing pieces into 12 edges, then solve those groups as though they were ordinary 3×3 pieces.
The reduced cube can nevertheless reach two types of state that are impossible on a physical 3×3. These are called OLL parity and PLL parity. Both are completely solvable; each simply needs an algorithm which temporarily uses the inner layers.
OLL parity: one paired edge appears flipped
On a 4×4, an edge consists of two separate wing pieces. OLL parity occurs when the two wings in one paired edge are exchanged, making the combined edge appear flipped. A single flipped edge cannot occur on a 3×3, so no ordinary 3×3 OLL algorithm can repair it.
Recognise it early
During edge orientation, a normal OLL position has zero, two or four yellow edges facing upwards. That produces the familiar dot, L, line or cross. If the number of upward-facing yellow edges is odd—one or three—you have OLL parity.
Recommended algorithm
Hold the affected paired edge at the top-front.
Rw2 B2 U2 Lw U2 Rw' U2 Rw U2 F2 Rw F2 Lw' B2 Rw2Show move-by-move notation images
Faster alternative: Lucas parity
This is longer to read but can flow more naturally once learned. The x is a whole-cube rotation.
Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'Show move-by-move notation images
Emergency method
If you have not yet learnt a full parity algorithm, this repeated sequence changes the parity state, but it destroys some completed edge pairing. You must then repair the final four edges and redo the 3×3 stage.
Rw U2 Rw U2 Rw U2 Rw U2 Rw U2Show move-by-move notation images
PLL parity: two paired edges are swapped
PLL parity occurs when two reduced edge pairs are transposed. On a 3×3, two edges cannot be swapped by themselves: an edge permutation must involve at least three edges, unless corners are also permuted.
If you know full PLL, parity is recognisable immediately because the stickers do not match any legal PLL case. If you are using a beginner method, finish solving the corners first and then look for the two transposed edges.
PLL parity algorithm
Rw2 R2 U2 Rw2 R2 Uw2 Rw2 R2 Uw2Each Rw2 R2 pair is most efficiently performed as a half-turn of the inner right slice only: the two outer-layer half-turns cancel.
Show move-by-move notation images
Incorrect centres: not parity
A 4×4 has no fixed centres, so a beginner can accidentally build a centre using the wrong colour scheme. You will usually notice this when the cross is complete but the first F2L pair appears impossible to place.
Check the opposite pairs—white/yellow, green/blue and red/orange—and the clockwise order of the four side colours. If the cross is on the bottom, this algorithm exchanges the required centre relationship:
R2 L2 Uw2 R2 L2 Uw2Show move-by-move notation images
Quick recognition table
| Appearance | What it means | What to do |
|---|---|---|
| One paired edge appears flipped | OLL parity | Hold it at top-front and use an OLL-parity algorithm. |
| An odd number of yellow edges faces upwards | OLL parity during edge orientation | Do parity immediately, then recognise ordinary OLL again. |
| Two opposite paired edges need swapping | PLL parity | Hold them at top-front and top-back and use the PLL-parity algorithm. |
| Two adjacent paired edges appear swapped | The same underlying PLL parity | Use AUF or a normal PLL setup to place the parity swap front/back, or use a dedicated adjacent algorithm. |
| Cross colours make every F2L pair impossible | Incorrect centre colour scheme | Correct the centres; this is not parity. |
Common mistakes
- Confusing an unpaired last edge with OLL parity.
- Waiting until the entire OLL has been attempted before fixing parity.
- Holding the affected edge anywhere other than top-front.
- Mixing lowercase slice notation with explicit wide-turn notation.
- Turning only the outer layer when the algorithm requires Rw, Lw or Uw.
- Losing count during repeated U2 turns.
- Treating each unusual PLL appearance as a different kind of parity.
- Assuming an incorrect centre colour scheme caused ordinary parity.
Advanced: can OLL parity be avoided?
Yes. The parity state is linked to the parity of the wing permutation and the number of inner-layer quarter turns used while constructing the centres. After the centres are complete, ordinary edge-pairing sequences use inner turns in cancelling pairs and therefore preserve that OLL-parity state.
With ARP tracing, a solver traces the wing cycles during inspection and determines the required parity of the first-three-centres solution. If the trace requires even parity, those centres are completed using an even number of inner-layer quarter turns; if it requires odd parity, an odd number is used. The practical difficulty is completing that trace and planning the centres within WCA inspection.
Another advanced approach is to learn parity-specific OLL and PLL subsets. Instead of fixing parity and then solving a normal last-layer case, one specialised algorithm handles both at once.
This deserves its own guide: the eventual OLL Parity Avoidance tutorial can explain good and bad wings, cycle breaks, solved/flipped edges, ARP scoring and centre-turn control without overwhelming somebody who only wants to finish their first 4×4 solve.
4×4 parity printable summary
Hold the affected edges as shown before beginning.
OLL parity
Recognition: one paired edge appears flipped, or an odd number of last-layer edges is oriented.
Hold: affected edge at top-front.
Rw2 B2 U2 Lw U2 Rw' U2 Rw U2 F2 Rw F2 Lw' B2 Rw2PLL parity
Recognition: two paired edges must swap by themselves.
Hold: swapped edges at top-front and top-back.
Rw2 R2 U2 Rw2 R2 Uw2 Rw2 R2 Uw2Incorrect centres
Recognition: the cross is solved but the side colour scheme makes F2L impossible.
Hold: cross on the bottom.
R2 L2 Uw2 R2 L2 Uw2Notation
Rw/Lw/Uw: turn two layers together.
R2: turn only the outer right face by 180°.
x: rotate the entire cube as an R move.
A parity algorithm deliberately uses inner layers to leave the reduced 3×3 state space. Continue with ordinary OLL or PLL afterwards.