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3. Some of the are easy to understand (for example commutators), but some others are hard to understand. There are many 2e2e cycles that I don't understand and I have just memorized (for example F2 L2 U R2 B2 L2 D R2), but sometimes I forget them

Instead of memorising these algs as separate cases I memorised them as a sequence of transformations from some "base" algs.

Here's an example, take this 3e alg:

R2 F2 L2 U B2 L2 F2 D

We can get another alg for the same case by doing:

R2 F2 L2 Uw B2 L2 F2 Dw

We can generate a 2e2e alg from here by doing:

R2 F2 L2 (U y2) B2 L2 F2 (D y2)

From here we can generate more algs by cyclic shifting (moving moves from the front to the end)

F2 L2 (U y2) B2 L2 F2 (D y2) R2
L2 (U y2) B2 L2 F2 (D y2) R2 F2

Of course after using these algs for a while I've gradually learnt how to do them directly instead of going through the transformation process, but it helped with learning.

Is there any new FMC tech in the works at the moment, do you guys think? DR + slicey was a game changer, and so I can't imagine what could possibly come next. If I had to guess, I think that there could be something to do with Rniss and blockbuilding. Like maybe when you're halfway through blockbuilding and don't see what to do next, you could use Rniss to insert random moves to help. I know that you can already do that, but maybe there'd be some better version of doing that. Idk. What do you guys reckon?

Is there any new FMC tech in the works at the moment, do you guys think? DR + slicey was a game changer, and so I can't imagine what could possibly come next. If I had to guess, I think that there could be something to do with Rniss and blockbuilding. Like maybe when you're halfway through blockbuilding and don't see what to do next, you could use Rniss to insert random moves to help. I know that you can already do that, but maybe there'd be some better version of doing that. Idk. What do you guys reckon?

Hmmm... Maybe by attempting to analyze optimal solutions we can discover some patterns or something.? I really don't know what I'm saying tbh
No one knows what the next "new FMC tech" will be. We will just have to wait and see what the future holds!

1. There are different approaches, it depends on the situation. I think what is usually the best is to solve all corners and as many edges as possible, and finish with edge insertion. But this is not always easy.
Another common option is to do "blockbuilding" and try to finish directly or leave a few pieces unsolve, like in a normal solve.
I have tried your first scramble:

R' U' F D' R2 F2 D' B2 D2 U B2 F2 U' L' D F D L2 B2 U R B2 F2 U' R' U' F
（F L' D' R2 B' R）//EO（6/6）
D2 F U F //DR（4/10)

R2 U' F2 //One square and many pairs (3/13)
R2 [2] //2 other squares (1/14)

Up to here it was promising, but then I had to break some blocks to go on:

F2 L2 D' L2 [1] U B2 U2 //2e4e (7/21)

The skeleton is not incredibly good. But, as often happens with DR, the insertions are very nice:

[1] = L2 D2 L2 U2 R2 U2 (6-4/23)
[2] = R2 B2 U B2 R2 F2 D F2 (8-4/27)

Maybe later I will try the other two. If I do I will edit this post.

2. I assume you are referring to what they also call "slicey shenanigans" or "free slices". The way I see it is this: a move like M2 solves a 2e2e (double swap of edges) case (ignoring centers). Just like you solve 5c (5 corners) using 2 commutators, you can solve different cycles of edges (for example 2e4e etc) using this special "2e2e" cycles. When I insert a slice move like this, I try to always solve at least one more edge. If you do more than one insertion, the first ones tend to be easy and you can even cancel moves (you have more freedom), but for the last ones sometimes you are not lucky and you need setup moves. This is a solve I did last night:
R' U' F D' F2 L2 R2 U' R2 D2 L2 U2 F' R' U B' L' D' F' U' L2 U2 F R' U' F

B' R' L2 F U //EO (5/5)
(F2 L F2 L B' L2 B) //DR (7/12)
(R F2 R F2 R' B2) //7e (6/18)

Skeleton: B' R' L2 F U B2 R F2 [2] R' F2 R' B' L2 B [3] L' F2 L' [1] F2 [4]

Solution: B' R' L2 F U B2 R B2 L' F2 L' B' R2 B' F2 L' F2 L' B2 R2 D2 L' F2 B2 R U2 L2 (27)

3. Some of the are easy to understand (for example commutators), but some others are hard to understand. There are many 2e2e cycles that I don't understand and I have just memorized (for example F2 L2 U R2 B2 L2 D R2), but sometimes I forget them
I hope someone else has a better answer for this.

Thank you for your reply
I feel "solve all corners" it's not easy for me.I'm ready to strengthen it through the 222 cube.Although I don't know if it's useful, haha.
So most of the time, I do "blockbuilding" after DR.
This is a solve I did
R' U' F U R2 D' B2 R2 U2 R2 D2 R' B' R2 B D2 L2 D' R2 D R F2 D' R' U' F
（U' L2 F'）//EO （3/3）
D R U R' D' //DR （5/8）
L' F2 //123 （2/10）
（D2 L D2 L' U2 R D2 R2 D2）//（AB3E）（9/19）
Skeleton：D R U R' D' L' F2 D2 R2 D2 R' # U2 L D2 L' D2 F L2 U
#：F2 L D2 F2 U2 R B2 U2 (8-2)
That's lucky, because most of the time I can't make an ideal skeleton

According to cube20.org, this scramble is the hardest one out there- F U' F2 D' B U R' F' L D' R' U' L U B' D2 R' F U2 D2

What's the best result you can get on this?

Spoiler: My Attempt

Scramble: F U' F2 D' B U R' F' L D' R' U' L U B' D2 R' F U2 D2

B L (R) // EO-4e (3/3)
(U B' D' L') // EO (4/7)
(U2 F') // Two Pairs (2/9)
F2 U' R2 U L2 U' F // DR (7/16)
L2 F2 D' L2 U' // HTR (5/21)
(F2 D2 L2 D2 L2 F2 * U2 L2) // AB2e2e (7/28)
*= (F2 L2 B2 L2 F2 R2) (6-4=2/30)

Solution: B L F2 U' R2 U L2 U' F L2 F2 D' L2 U' L2 U2 R2 F2 L2 B2 D2 L2 D2 F' U2 L D B U' R' (30)

Woah, only 30 moves? I was expecting a WAY worse result than that due to it being the hardest scramble ever! Maybe 34 or something??
At the beginning it was just daunting, but after the 7-move EO things were more or less normal. I'm really happy with this solve!

I do have to warn you, it can be frustrating. Have fun!

Darn, that sucks. I think we all have our fair share of crappy 3c :/. For example in my pb mo3, I found a 14 TO 3C on the 2nd scramble, but I couldn’t find anything better than 8-1, and I just barely checked IF and 9 out of the 15 spots couldn’t cancel anything

Spoiler: If you’re curious, here it is

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

* D' // SQ
R F' L2 // p222 + 2P
R' B2 R2 B // EO
D L' // 223
R D' R' D2 // AB3c (14!!!)
*= B2 D F' D' B2 D F D' (7/21)

I also vaguely recall a solve where I had 21ish or so moves to 3c, and I couldn’t cancel any at all, optimal was 8-0 throughout the entire skeleton!! Although I don’t have proof of it, so I can’t confirm it.

PB single in the weekly comp (wew late night FMCing).

Spoiler

Scramble 1. R' U' F D F2 R2 U2 F D2 U2 L2 B R2 D2 F' D' F U F2 L' B R D U B2 R' U' F
Solution (22): R' D2 R2 U2 F U' R U2 R' U F' U2 L' B D2 R U' R' D' R U R'

skel: R' D2 R2 @ L' B D #
@ = U2 F U' R U2 R' U F' U2 // edges; ab3c (9/15)
# = D R U' R' D' R U R' // finish (8-1/22)

lolwut

A few other people found the same 6-move skeleton, lol. The edge thingy is a ZBLS alg (but not used as such here) that I learnt a few months ago and I probably should start using in speedsolves, but I can never quite distinguish that case from its mirror…

New AfR single set last weekend at OSU Blind Weekend:

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

EO F/B: @ F U' R B [4/4]
2x2x2: (R2 D2 L') [3/7]
2x2x3: (F D F') [3/10] - breaks EO
EO U/D: (U R U') [3/13]
AB5C: (B' # R2 B) [0/13]
Insert corners at @: U' B' U F U' B U F' [4/17]
Insert corners at #: (D2 R U2 R' D2 R U2 R') [6/23]

Solution: U' B' U F U' B U2 R' D2 R U2 R' D2 B U R' U' F D' F' L D2 R2 (23 moves)

24.67 PR mean, second at FMC Americas, first sub 25 and first pure DR mean

1. R' U' F U R2 F2 U F2 D' U2 R2 B2 D2 B D2 L2 R' U B2 U' L' D2 B R' U' F

Spoiler

(F' L') U D' L // EO
F' D' B' D // DR lol
(F L2 U2) // 2 sqs
B' U2 L2 D2 // solve stuff
F D2 F D2 F' D2 F D2 F2 // finish
final solution: U D' L F' D' B' D B' U2 L2 D2 F D2 F D2 F' D2 F D2 F2 U2 L2 F' L F (25)

Thoughts: this scramble sucked and I got lucky finding this 9 move DR and the stupid finish after

2. R' U' F U' L2 U B2 U F2 D' B2 U R F2 L' B' D L2 B2 U2 L U' R U' R' U' F

Spoiler

L' (R U' R) // EO
D' B2 U2 R2 D U2 F' // DR
U' D L2 // 222
(U' R2 U R2 U2 R2 U F2 U) // L3C
(U' F2 U B2 U' F2 U B2) // 5 cancel (should've seen this as a direct finish) (26)
Insert E and E' somewhere to give 24

Thoughts: If I had spent more time on the DR Cale used for his 22 on this scramble I probably would've seen the solution as well, but a 24 is fine too Wasn't focused for the first 40 mins of this attempt for some reason

3. R' U' F D2 U2 R2 F' D2 B' F R2 D2 B' D L' R U2 R' D R B' D' U' R' U' F

Spoiler

(B') B2 D2 B // EO
U R' (L2 F2 R2 U' L) // DR+sq
U2 * L2 U2 F2 U L2 U2 D2 * // solve corners
*: E2
B2 D2 B U R' ^ D2 R2 % U2 B2 U # R2 L' U R2 F2 L2 B
^: R U2 R' L F2 L' // 6-3 to 2e2e
#: U2 R2 L2 D2 R2 L2 // 6-4 to 3e
%: R2 B2 L2 D' B2 R2 F2 U' // 8-3
B2 D2 B U' R' L ~ F2 L' D2 B2 @ L2 D' B2 R2 F2 U B2 U' R2 L2 D2 L U R2 F2 L2 B
~: R L' x' // 2-5 bc U' x' F2
@: L Lw'
final solution: B2 D2 B U Rw' D2 B2 L' Lw' D' B2 R2 F2 U B2 U' R2 L2 D2 L U R2 F2 L2 B (25)
These insertions definitely could've been done more efficiently lol

Found this skeleton near the end with no time to insert:
(B') B2 D2 B // EO
U R (L2 F2 R2 U' L) // DR+sq
(F2 R2 U B2 U2) // 2e4e
IF gives pretty easy 24

Thoughts: Going into this solve I really wanted PR mean so that definitely affected my mindset, kind of annoyed I didn't see the 2e4e skeleton until so late but whatever

So, I stumbled across a DR for this week's scramble on fewest-moves.info. I DNF'd, because a) I made some notation mistakes that took time to hunt down, and b) I'm not used to this style.

D L (F' D R) //EO (5)
(U2 F2 U') //Oriented F2L (8)
(U F U' F U F2 U') //DR/OLL (12)
(F D2 B D2 F U2 B2 D2 B D2 F') //Leaving four edges (23)

D L F D2 B'.D2 B2 U2 F' D2 B* D2 F' U F2 U' F' U F U2 R' D' F

I didn't feel like doing two insertions, so I just did .=R D2 R2 D2 R2 D2 R for a 30 move total, IE finds *=F2 D2 F' B' L2 F B D2 for 27 moves and lastly CE finds a 13 move domino finish for a 25 moves.

Lastly two questions: How many 8 move 2e2e are there and how often do you manage to find optimal domino finishes?

Final: F B R L' B R' L' D2 B2 D2 L2 D2 R' D' R' L' B2 U2 B2 U2 L R2

I found this skeleton in the last 10 minutes so this was kind of stressful to insert

2)27 moves

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

Spoiler

(L' D F2 R)//EO (4/4)
D2 F D' U B2 R2 D' F//DR (8/12)
B2 L2 U * F2 U L2 R2 D R2 D' F2//2e2e (11/23)

*=U2 R2 F2 U2 F2 R2 U2 F2 (8-4/27)

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

Last 10 minutes skeleton again. There were too many potential DR setups to check, Cale and Keng Foo showed me a 23 and 22 respectively after the attempt. Oh well

3)21 moves

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

Spoiler

D' B//EO (2/2)
D' L2 D R2 B2 U' R'//DR (7/9)
(L2 D2 B2)//222 (3/12)
(U2 L2 U * F2 L2 U')//2e2e (6/18)

*=(U2 L2 F2 L2 U2 F2 L2 F2) (8-5/21)

Final: D' B D' L2 D R2 B2 U' R' U F2 U2 L2 F2 L2 U L2 U2 B2 D2 L2

Lucky insertion on an easy scramble, I believe anyone who's comfortable with DR would be able to find this solution.

This is kinda off topic, but should I do FMC at an upcoming comp? I've never done it successfully before (I did one for 20 mins, another for 30 mins, both were DNFs)

This is kinda off topic, but should I do FMC at an upcoming comp? I've never done it successfully before (I did one for 20 mins, another for 30 mins, both were DNFs)

U2 F R2 U2 L2 B D2 L2
replace the F/B moves with wide moves (this brings the moves in the first half and the second half to the same axes):
U2 b U2 L2 D2 f D2 L2
replace the L2 moves with wide moves (this brings the moves in the first half and the second half to the same faces):
U2 b U2 r2 U2 b U2 r2 = (U2 b U2 r2)2

Essentially the same type of 3-cycle as (R2 U' R2 f2)2 and (R2 u' R2 f2)2.

Protip: Check your solution! Don't look at the cube when applying your solution; look only after you're done to check that your written solution really works.

Spending just a bit of time to check your solution drastically reduces DNF rates; it'd be kind of silly to spend an hour in an FMC attempt just to DNF it.