= = = ZZ METHOD WINTER VARIATION = = =

Algorithms found by Cube Explorer, compiled by Jack Eisenmann


This page contains algorithms for the Winter variation of the ZZ method. The Winter variation allows the solver to fix the orientation of the 4 last layer corners while simultaneously placing the last corner-edge pair. The algorithms were chosen with these priorities:


  1. 1.Find optimal sequences.

  2. 2.Choose algorithms which use U/R, L/U/R, or the fewest sides possible.

  3. 3.Choose algorithms which break up things in a way which is easy to follow (keep corner-edge pairs together; this aids memorization).


For each case listed below, the empty slot is located at RF, and the corner-edge pair which goes in that slot is represented by the horizontal blue bar. The edges are not included in the pictures. Each case is associated with a letter which often looks like the case (this is comparable with the letter naming convention for PLL cases). The pictures depict the U face of the cube.


The average move count for all the algorithms is 8.07. For OLL in the ZZ-VH variety, the move count is 11.37, including the 3 moves to insert the c/e pair. On average, the Winter variation requires 3.30 fewer moves.

A case (9 moves):

U F' R (U2 R' U2 R') F R

Breaks the <F2,B2,L,U,R,D> group. First places FD c/e pair diagonally opposite of U c/e. Then U c/e is placed, and FD c/e is repositioned.


B case (10 moves):

U' R2 F2 R2 U R U' R (F2 R2)

Difficult to follow; use brute memorization. U c/e placement comes at U R U'.


C case (4 moves):

U R U2 R'

A very basic case. Placement is U2 instead of U'.


D case (10 moves):

(R U' R') L U2 L' U' L U' L'

Standard U c/e placement + Anti Sune w/ LB c/e. There are a few cases like this where R U' R' are the most efficient moves.


E case (10 moves):

(R U' R') L' U2 L U L' U L

Similar to D; Standard placement + Anti Sune w/ LF c/e.


F case (8 moves):

U R U' R' U R U2 R'

This algorithm resembles a Double Sune. The U c/e is toggled around the U face via 2-gen until it is placed.


G case (8 moves):

U2 L (U' R U) L' U R'

LB c/e is first placed adjacent to U c/e. R slot is then aligned, LB c/e is repositioned, and U c/e is placed.


H case (7 moves):

R U R' U' R U' R'

Similar to F; U c/e pair toggles around until it's placed. Seems like Anti Double Sune.


I case (9 moves):

U F2 L F2 L' (U' L' U L)

Places U c/e upside-down in F, then repositions LF c/e pair.


J case (8 moves):

U R' U' R2 U' R2 U2 R

Bruno. RB c/e is placed parallel to U c/e, then U c/e is inserted into its slot, and RB c/e is repositioned.


K case (10 moves):

(U R U2) R2 U2 R U R' U R

Combination of C and Anti Sune w/ RB c/e.


L case (8 moves):

U (L' U R U' L) U2 R'

U c/e pair is hidden in LB slot while LF c/e pair bobs up; LF c/e then toggles while R slot is aligned, LF c/e is repositioned, and U c/e is placed.


M case (10 moves):

(U R U2) R2 U' R U' R' U2 R

Similar to K. Combination of C and Sune w/ RB c/e.


N case (9 moves):

U' (R' F2 R F2) U L' U L

U c/e is sledge-hammered in with double F turns. This results in the displacement of the LF c/e, which is repositioned with a slight toggle.

 
O case (7 moves):

L' U2 (R U R') U2 L

This algorithm breaks up the U c/e pair while the LF c/e comes up. The broken U c/e is quickly fixed and placed at the same time with R U R', then the LF c/e is directly repositioned.


P case (7 moves):

R2 D (R' U' R) D' R2

Begins by placing FD c/e adjacent to the R block. U c/e is then placed, and the first few moves are undone.


Q case (3 moves):

R U' R'

The MOST BASIC CASE. If you get Q, you should think to yourself, "Oh happy day! I only need to make 3 moves!"


R case (10 moves):

U R' U L (U' R2 U) L' U R'

The U face becomes crowded during this algorithm's execution. First the RB c/e is placed parallel to the U c/e. Next, the LB c/e is placed perpendicular to the 2 other c/e pairs in U. Then the RB c/e is placed, and the RF slot is aligned for the U c/e. Before the U c/e is placed, the LB c/e is repositioned. THEN the U c/e can be put into its slot.


S case (9 moves):

(R' D' R) U (R' D R2) U2 R'

The DBL (surprise!) c/e first goes into the FR slot. The U c/e moves to the left, and the DBL c/e is repositioned by undoing the first few moves. Lastly, the U c/e is placed.


T case (9 moves):

R U R D (R' U2 R) D' R2

Vaguely similar to P. First, the RB c/e is placed diagonally opposite the U c/e with some toggling. Next, the FD c/e is placed adjacent to the R block. The U c/e is directly placed, and the FD c/e is repositioned.


U case (9 moves):

R U R2 U' R2 U' R2 U2 R

Bruno. Similar to J, but with different initial moves.


V case (9 moves):

B' (R U' R') B U' B' U2 B

This algorithm breaks the <F2,B2,L,U,R,D> group. First, the LB c/e is placed parallel to the U c/e with an unusual B move. The U c/e is then placed into its slot, the LB c/e pair is toggled around w/ the B face (Sune style), and lastly it is repositioned.


W case (9 moves):

R' F2 (D' L2 D' L2) D2 F2 R

This algorithm is really weird. Memorize the moves. U c/e is first tossed all over the place, then is placed with D2.


X case (10 moves):

L' U2 (R U' R' U' R U')R' L

The beginning is similar to O, but after the U c/e pair is broken and fixed, it toggles around before it is placed.


Y case (9 moves):

(R U' R2) U' R U' R' U2 R

Similar to M, except with direct U c/e placement at the beginning. This is followed by Sune w/ RB c/e.


Z case (6 moves):

B' (R U' R') U B

Similar to V, but without toggling. The <F2,B2,L,U,R,B> is broken at the beginning when B is turned, dislodging the LB c/e. Then the U c/e is directly placed, and the DBL c/e is repositioned.


& case (9 moves):

(R U' R2) U2 R U R' U R

Similar to Y. Standard c/e placement + Anti Sune w/ RB c/e.