Parity
Sometimes edges have an odd number of targets. That leaves your corners in an odd permutation — a single two-corner swap that 3-cycles can never fix on their own. You resolve it with one extra J-perm between edges and corners, then adjust your corner memo.
When Does Parity Happen?
A 3x3 cube permutation must be even overall. If your edge cycle has an odd number of targets, your corner cycle will be “off” by one swap. You detect this during memo: count your edge targets.
Rule:
Odd number of edge targets → parity exists. Apply the parity alg between edges and corners.
Parity Algorithm
This is the same J-perm you use for edges. Run it once after your edge targets and before corners: it swaps the leftover two edges and two corners, and leaves the centers untouched. Because it moves two corners, you adjust your corner memo to match (see below).
Compensating Your Corner Memo
The parity J-perm swaps two corners as a side effect, so your traced corner sequence is now “off” by that swap. The standard fix is simple:
Rule:
When you have parity, swap your first two corner targetsbefore solving corners. The parity alg's corner swap then cancels cleanly.
Exactly which two corners the alg disturbs depends on your buffer and setup conventions — the “first two targets” rule is the common shortcut, but verify it against your own scheme the first few times, the same way you sanity-check a trace on the full-solve simulator.
Full Solve Flow with Parity
- Memorize edges and corners separately, counting your edge targets.
- If the edge count is odd, you have parity — swap your first two corner targets in memo before you start.
- Solve all edge targets using J-perms.
- If you have parity: apply the parity J-perm
R U R' F' R U R' U' R' F R2 U' R' U'once, now — between edges and corners. - Solve all corner targets using Y-perms.
- Remove blindfold and celebrate.