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Winter Variation

WV (Winter Variation) is a method for solving the last F2L pair and orienting the corners when the edges are already oriented. This will result in an automatic OLL skip since the edges are oriented already. Keep in mind that in order to take full advantage of this, you should be able to mirror these algs into the FL pair or BR pair. Since all edges are already oriented, every case could be solved with only <R,U> but for many cases it is shorter and more practical to include F, L, or D turns. Most of these algorithms are pretty intuitive and I've given an explanation of each case. Notice that in many cases it's easiest to just insert the pair and finish with a Sune or Antisune, but only if the pair is inserted correctly. There is a similar set of algs known as the Summer Variation, but the recognition is a bit more difficult and I haven't learned those.

These are the 27 Winter Variation cases for inserting the last connected pair while orienting the last layer corners and the algorithms I use for them.These algorithms appear EXACTLY as I perform them when I am solving the last layer, in speedcubing notation with rotations included in the algorithm. It should be noted that these are the algorithms that I find easiest to perform. However, you may find other algorithms better-suited for your own hands, so it is recommended to try many different algorithms for the same situation to find which one works best for your own style of cubing.

In each diagram, yellow is the color of the upper face. A yellow "bar" indicates that the last layer color is facing that direction in that location. Grey denotes that a particular piece is not oriented correctly. The pair to be entered is the red/green pair.

Three Corners Oriented Correctly

# Diagram Algorithm Comments
01 [U'] (L' U2) (R U' R' U2) L Take out the FL pair, insert the FR pair, and then reinsert the FL pair.

Two Corners Oriented Correctly

# Diagram Algorithm Comments
02 [U] (R U' R') This is the simplest case. Just insert the pair as normal.
03 (R' F) (R U) (R U') (R' F') This is a pretty easy case similar to a ZBF2L alg for inserting a connected pair.
04 [U] (R2 D) (R' U' R D' R2) After the first 3 moves, you can see the pair being inserted. This case is similar to the U COLL case.
05 [U] (R U' R') U (R' U' R U' R' U2 R) Just insert the pair, AUF, and do a Sune from the back right.
06 (R U' R' U2) (R U' R' U2) (R U R') This is just two fast triggers and a pull to insert.
07 [U] (R U R' U') (R U' R') This is just the end of a double Antisune.

One Corner Oriented Correctly

# Diagram Algorithm Comments
08 [U2] (R U' R') (U R U2 R') This is just the end of a double Sune.
09 [U2] F' (R U2) (R' U2) (R' F R) This is a pretty decent case that reminds me a little bit of the Ra permutation.
10 (R' F) (R2 U R' U') (R U R' U') F' This is a sledgehammer into double sexy.
11 [U2] (R' U' R2 U') (R2 U2 R) Take out the BR pair, insert the FR pair, and then reinsert the BR pair.
12 (R' F2 R F2) (U L' U L) This is a modified sledgehammer and then a reinsertion of the FL pair.
13 [U2] (R U2) (R2 U' R U') (R' U2 R) This is an insertion of the pair using U2 right into a Sune from the back right.
14 [U2] (R2 D) (R' U2 R D' R2) This is the same as Case #04 except with a U2 instead of a U' to insert the pair.
15 (L' U) (R U' R') L Just do L, insert the pair, and undo the L.
16 [U2] L' (R U R' U') L (R U2 R') Just do L, sexy move, undo L, and insert the pair using U2.
17 [U2] R U2 R' This is the second nicest case.  Insert the pair with a U2 instead of just U'.
18 (R' F' R U2) (R U2 R' F) This is just the inverse of Case #09.
19 (R' F2) (R2 U' R' U') (R U R' F2) This is a pretty cool alg and it flows kind of nicely.

No Corners Oriented Correctly

# Diagram Algorithm Comments
20 [U] (R U' R') U' (R U R' U) (R U2 R') Just insert the pair, AUF, and do a Sune.
21 [U] (R U') (R2 U2) (R U R' U R) This is an insertion of the pair into an Antisune from the back right.
22 [U] (R2 D) (R' U R D') (R' U2 R') This is the same alg as a U COLL except a U2 was replaced with a U.
23 (R2 U) (R' U R' U') (R U R U2 R2) This is a pretty neat alg that flows kind of nicely.
24 [U2] (R U' R' U) (R U' R' U) (R U2 R') This is just the end of a triple sune.
25 [U2] (R U2) (R2 U2 R U) (R' U R) This is just an insertion with a U2 into an Antisune from the back right.
26 [U] (R U') (R2 U' R U') (R' U2 R) This is just an insertion into a Sune from the back right.
27 [U] (R U R' U') (R U R' U') (R U' R') This is just the end of a double Antisune.  Do a double sexy and insert the pair.