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What is that first insertion? I've never seen something like that before. I guess a better question is if this is something intuitive that I just need to think about more or is it some set alg that you have down for this very occasion?

What is that first insertion? I've never seen something like that before. I guess a better question is if this is something intuitive that I just need to think about more or is it some set alg that you have down for this very occasion?

If you use Rniss at that point, the cube is an F2L-1. That insert is the optimal alg to solve the F2L pair which I learnt a while back. I saw it this way, although the setup to sexy way of viewing it is valid too, but perhaps less obvious to find

Not really an answer, but I once wrote a NISS block solver and I think it managed to solve a fixed 2×2×2 block (i.e. not colour neutral) in at most 5 moves >90% of the time. (Let me check again; don't quote me on this yet.)

And yes, knowing three of those will give the fourth.

E: Ran 40 solves (fixed block, as mentioned above).
4 moves: 8
5 moves: 21
6 moves: 11
So ">90%" was an exaggeration. For CN block, this seems to suggest that it's almost always possible to do it in at most 5 moves, 4 if you're somewhat lucky. Without NISS/premoves, this is the distribution.

Cologne Open 2018, Scramble 2 -- Best result on this at the comp was 28 (?)

R' U' F R2 B D2 U2 B D2 L2 B2 R2 F' D' L' F R' B2 L R2 F D R' U' F

24

B' // 2 pairs [1/1]
F' D' // sq + 3 pairs [2/3]
(B2 R) // sq + 123 [2/5]
(F D2 F2) // 222 + 123 [3/8]
B' U' (U) // F2L-1 [3/11]
(L' B' L' B) // F2L [4/15]
(B' U' L' U L B L2) // 3c [7-2/20]

Skeleton: B' F' D' B' U' L2 B' L' U' L U L B L U' F2 D2 F' ^ R' B2

^ - F2 R' B' R F2 R' B R [8-4/24]

Solution: B' F' D' B' U' L2 B' L' U' L U L B L U' F2 D2 F R' B' R F2 R' B' (24)

27.00 mean for last week's forum weekly comp, with three lucky solutions.

Spoiler: #1: 25 moves

scramble: R' U' F D2 R B2 R F2 D2 U2 L' D2 U2 R2 D' L' R' B L' B2 F2 D2 F D' R' U' F

L' U2 R' D B' F' D' B' U' L2
U2 R' U L U' R U F U F'
U L' U' L' B

L' U2 R' D B' // two squares (5/5)
F' D' B' U' L2 // more blocks (5/10)
(B' L2 U' L') // F2L (4/14)
(L U L' U L U' F U' F' L') // fish (10-5/19)
(L U' R' U L' U' R U2) // chips (8-2/25)

The last layer edge case is the one with edges permuted + two opposite edges flipped. One optimal alg for this is a cancellation of fruruf into Antisune, which also solves the OLLCP case for diag-pi with opposite flip. The mirror/inverse alg solve the same last layer case (at two different angles); one of the angles leads to ab4c and the other leads to ab3c. One of the 3c angles also cancels 5 moves, so of course that's the one I used. Might be the first or second time I'm using this alg in FMC.

The L3C alg at the end (which is just a Niklas + AUF) is also the optimal 3c insertion.

A 31-move solution I found near the end of the attempt (i.e. useless but interesting I guess):
(L' F2 L R F' R F2 D F) // 223 (9/9)
D' B2 D // EO (3/12)
(L' B' L' B2) // F2L-corner; AUF+ab4c2e (4/16)
(B D2 R2 U F U' R2 D B' D) // edges; AUF+ab3c (10-1/25)
(D' R D L D' R' D L2) // finish (8-2/31)

Could also have done a different 10-move EP alg to cancel one more move to get 24 to 5c, but that's even more useless. (The optimal EP alg if you can destroy one slot's corner is 9 moves iirc, but I don't have that one memorised.)

Spoiler: #2: 29 moves

scramble: R' U' F D F2 B' R F B2 D2 R' L F' R2 F2 L2 U2 D' F2 U F2 B2 U' R' U' F

U R L U' L2 U L U B2 U'
B R B R2 F' L F U2 L' U'
L U' L2 U2 L R' B' D L2

(L2 D' B R2) // p222 (4/4)
U R L U' L2 U L U B2 U' B2 // F2L-1 (11/15)
B' R B R2 // unexpected blocks; pF2L (4-1/18)
(R') // F2L (1-1/18)
(L' U2 L2 U L' U L U2 F' L' F) // 1LLL (11/29)

Literally couldn't find a single good skeleton on this, but I lucked out on the 1LLL. (Mirror of the OLLCP alg I normally use for this case; the normal RUF 3-gen OLLCP alg cancels one move, but leads to a U perm.)

Backup (34):
... B2 // F2L-1
B' R B R' U2 B' R B R' // EOLS (9-1/23)
F' U' L' U L F2 R U R' U' F' // 2GLL (11/34)

(Fun fact: I also encountered this same pi 2GLL case in the attempt of my 32 former NR single… although I didn't know the optimal alg at the time, only the 2-gen alg (13 moves), so I did some stuff differently to force a different 11-move 2GLL alg.) Also noticed you can do a 3-move insert for the last pair (cancelling one move) and get an 11-move antiZBLL… Edge control doesn't always pay off.

... B2 // F2L-1
B' U2 B // F2L (3-1/17)
(L' B' U2 B2 U L U' L' B' U2 L) // 1LLL (11/28)

Spoiler: #3: 27 moves

scramble: R' U' F L2 F' U2 L2 U2 R2 F2 D2 B D2 B' U L' U' F D' B2 L F' U' R2 D R' U' F

L' B' R2 F' U' F' R D R' B'
U2 L U R2 U L' U' R2 L U'
L' B2 U2 L' B' L R2

L' B' R2 F' U' F' R D // 222 + square + two pairs (8/8)
R' B' U // join stuff (3/11)
(R2 L' B L U2 B2) // F2L-corner (6/17)
(L U L' U L U2 L' U') // ab3c (8-1/24)
Skeleton: L' B' R2 F' U' F' R D R' B' U2 L U2 @ L' U' L U' L' B2 U2 L' B' L R2
@ = U' R2 U L' U' R2 U L // 5 cancel (8-5/27)

Mediocre skeleton but very lucky insertion. Found an 11-move 4c3e skeleton really late; ran out of time trying to find insertions. (Looks like Tommy Kiprillis found the same 4c3e skeleton, lol.)

(D B' D2 R' U R2) U2 // 222 + square + three pairs (7/7)
(B2 L' B' L2) // more blocks (4/11)

All three solutions were found relatively early (25 minutes, 29 minutes, 15 minutes) so that took a lot of pressure off these attempts. Getting lucky isn't a crime.