A Pairs Commutator Insertion by Sebastian Tronto

Scramble: B2 D2 L F2 R D2 L B2 R2 F D R’ B’ L R D’ F2 L’ D2
Solution: R’ B R2 B2 L B’ R2 L2 F R2 B’ L’ U B2 U’ L’ F’ L2 F’ L’ U L2 U’ L F2 L D2 R2 (28 HTM)

Explanation (with my NISS notation, move in brackets are done on inverse scramble):
R’ B //2x2x1 (2/2)
(R2 D2) //Expand to 3x2x1 (2/4)
(U B2 U’ L B) //Another (pseudo) 3x2x1 (5/9)
R2 B2 L //Roux Blocks (3/12)
(R2 F’ L2 R2 B) //All but 3 edges and 3 corners (5/17)

Final Skeleton (for normal scramble) + insertion:
R’ B R2 B2 L B’ R2 L2 F R2 B’ L’ U B2 U’ * D2 R2
* L’ F’ L2 F’ L’ U L2 U’ L F2 L //3 corners and 3 edges (11/28)

The insertion is a setup + 9 moves pair 3-cycle: [L': [F2: [F L2 F’, Rw’]].

I have explored some other starts, but the only one (except for the one above) that gave some nice continuation was this:
D R’ D2 R2 //2x2x1 (4/4)
D L D //2x2x2 (3/7)
B U’ B’ //2x2x3 (3/10)
L F’ L’ //More blocks (3/13)
F’ U2 F2 U’ //Pseudo F2L-1 (4/17)
F U2 R U R2 F2 R F2 //All but 3 corners (8/25)

I’ve kept this as a backup partial solution, planning to quickly look for a 3 corner insertion in case I was left with only 5 minutes or so.
When I have finally found that “All but 3 corners and 3 edges” skeleton I had only 10 minutes to find insertions. I knew it was probably going to be better than the backup skeleton, but maybe 10 minutes weren’t enough. In a competition I would have probably looked for a 3 corners insertion in the backup solution (I don’t like risking a DNF, especially now that FMC is a Mo3 event) and be satisfied with a 30 moves solution (optimal insertion found by IF, but for a single corners 3-cycle it’s pretty easy to find optimal insertions). But, since it was only practice, I decided to go for the (I thought) double insertion on the other skeleton. Both corner and edges were awfully placed during the whole skeleton, the best I could find was 7+8 for a 32 moves total, until right before the end, when I saw that the edges and corners could be solved with a pairs commutator after a setup move.
In case you don’t know, pairs commutators work exactly like corners commutators, but at some point you use a wide turn. A few examples can be found on Ryan Heise’s website, at this page (Strategy #1: pair 3-cycles).
BTW, if you set the “other” option on IF, it finds an even better insertion (while using only the “corners 3-cycle” and “edges 3-cycle” options it gives 30 HTM as the best solution).

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>