The FMC thread

[cubeshepherd]

Sebastiano mentioned most useful algs for Edge insertions, especially the M' U2 M U2 as they are 6 movers and can lead to the better solutions when you find those positions.

Other cool things to keep in mind on Edge insertions. (Some of these might be pretty advanced but just want to post all edge insertions I know)

1. [6 Moves] M' U2 M U2 rewritten to R' L F2 R L' U2. Keep in mind that R' L do not effect the edges so you can shift either of them to the front or back to possibly cancel more. (Ex. R' F2 R L' U2 L, F2 R L' U2 L R', and R' L F2 R L' U2 are all same)
(#2, 3, and 4 all do the exact same case. Also keep in mind inverse cases for these)
2. [8 Moves] Sebastiano's R2 Fw2 R2 U R2 Fw2 R2 U can be rewritten as R2 B2 L2 D L2 B2 R2 U. Same cyclic shift for moves can be applied since R2 B2 don't effect the edges yet. (Ex. R2 B2 L2 D L2 B2 R2 U same as L2 D L2 B2 R2 U R2 B2 and as B2 L2 D L2 B2 R2 U R2)
3. [8 Moves] Another similar one is R2 B2 L2 U B2 R2 F2 D. Same shifts can be done for first 2 moves. (Ex. R2 B2 L2 U B2 R2 F2 D same as B2 L2 U B2 R2 F2 D R2 and as L2 U B2 R2 F2 D R2 B2)
4. [8 Moves] Similar still is L2 B2 R2 D R2 B2 L2 U although this time no shifts are possible since the edges are changed with the first move of L2.
5. [10 Moves] R' U' R' U' R' U R U R U swaps UR-FR-UB. I initially learned this as an F2L case (Shout out to Brest) but later as a type of 2gen edge insertions to look out for.
6. [10 Moves] U L D R F R' D' L' U' F' changes UR-FR-FU. This one is very strange but just think of it as doing all the moves around a face, then moving that face, then inverse of everything.
7. [10 Moves] U' R U M2 U' R' U M2, finally just the normal 10 movers where a Slice move (M2) is the 1 move interchange. Keep in mind other normal 10 movers where the slice move is a part of the swap (Ex. R' E R U' R' E' R U)

For Multiple Edges
Make sure you know R2 U2 R2 U2 R2 U2 and D2 L2 U2 L2 D2 R2 (plus variations and shifts of the 2nd one).

@cubeshepherd Question 2. Sebastiano mentioned the best way which is doing a 3 corner commutator involving all twisted corners. If it is only 2 twisted corners then just involve any other corner for the 3rd corner of the commutator. Because you have so much flexibility on these insertions and corners, usually you can cancel a lot on the first insertion (5 or 6 cancellation) then it leads to a normal Last 3 Corners case.

Wow! Thank you very much for the info. This will really help me (and other) out, and I sincerely appreciate you taking the time to explain that all. Thanks again.

 

[TheDubDubJr]

Wow! Thank you very much for the info. This will really help me (and other) out, and I sincerely appreciate you taking the time to explain that all. Thanks again.

No problem! Always happy to help. But if you are starting to get into FMC as a Beginner/Intermediate, just learning 1, 3, and 7 would be a good start to know. Those will be able to handle most cases that you come across.

 

[guysensei1]

Sebastiano mentioned most useful algs for Edge insertions, especially the M' U2 M U2 as they are 6 movers and can lead to the better solutions when you find those positions.

Other cool things to keep in mind on Edge insertions. (Some of these might be pretty advanced but just want to post all edge insertions I know)

1. [6 Moves] M' U2 M U2 rewritten to R' L F2 R L' U2. Keep in mind that R' L do not effect the edges so you can shift either of them to the front or back to possibly cancel more. (Ex. R' F2 R L' U2 L, F2 R L' U2 L R', and R' L F2 R L' U2 are all same)
(#2, 3, and 4 all do the exact same case. Also keep in mind inverse cases for these)
2. [8 Moves] Sebastiano's R2 Fw2 R2 U R2 Fw2 R2 U can be rewritten as R2 B2 L2 D L2 B2 R2 U. Same cyclic shift for moves can be applied since R2 B2 don't effect the edges yet. (Ex. R2 B2 L2 D L2 B2 R2 U same as L2 D L2 B2 R2 U R2 B2 and as B2 L2 D L2 B2 R2 U R2)
3. [8 Moves] Another similar one is R2 B2 L2 U B2 R2 F2 D. Same shifts can be done for first 2 moves. (Ex. R2 B2 L2 U B2 R2 F2 D same as B2 L2 U B2 R2 F2 D R2 and as L2 U B2 R2 F2 D R2 B2)
4. [8 Moves] Similar still is L2 B2 R2 D R2 B2 L2 U although this time no shifts are possible since the edges are changed with the first move of L2.
5. [10 Moves] R' U' R' U' R' U R U R U swaps UR-FR-UB. I initially learned this as an F2L case (Shout out to Brest) but later as a type of 2gen edge insertions to look out for.
6. [10 Moves] U L D R F R' D' L' U' F' changes UR-FR-FU. This one is very strange but just think of it as doing all the moves around a face, then moving that face, then inverse of everything.
7. [10 Moves] U' R U M2 U' R' U M2, finally just the normal 10 movers where a Slice move (M2) is the 1 move interchange. Keep in mind other normal 10 movers where the slice move is a part of the swap (Ex. R' E R U' R' E' R U)

For Multiple Edges
Make sure you know R2 U2 R2 U2 R2 U2 and D2 L2 U2 L2 D2 R2 (plus variations and shifts of the 2nd one).

@cubeshepherd Question 2. Sebastiano mentioned the best way which is doing a 3 corner commutator involving all twisted corners. If it is only 2 twisted corners then just involve any other corner for the 3rd corner of the commutator. Because you have so much flexibility on these insertions and corners, usually you can cancel a lot on the first insertion (5 or 6 cancellation) then it leads to a normal Last 3 Corners case.

To add a few more cases,

1) "wide move" insertions:
Things like Uw R Uw' M2 Uw R' Uw' M2, Uw R2 Uw' M Uw R2 Uw' M', etc
2) cyclic shifts of some 10 movers, these are 10 movers conjugated with a move that cancels into the slice move interchange

R2 U R2 U' M2 U R2 U' Rw2
You can even combine the wide move insertions with the cyclic shifts
L Uw R' Uw' M Uw R Uw' Lw'

 

[Shymon]

Last solve of official 30 average (30, 35, 25) done at GLS Cup II 2018
The most ridiculous solve I've ever had

Spoiler

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

Looking at this scramble I couldn't see any worthy block building start so I started looking for the EO.

Because I only do EO like once in 15 solves I'm still not good at it and check this out:

I wanted to do UD EO and stupidly, I thought UL and DL ware only misoriented edges and just playing with the cube I checked 4 frurufs to see if any would do something decent to the cube (doing frurufs is not time-consuming at all so why not)

It went like this:

U B L B' L' U' // "pseudo EO" with a pair (6/6)

L2 B' L D2 R2 L' D2 L2 D2 // F2L-2 with two pairs and one other F2L edge in place (9/15)

(At this point, I saw yellow-blue edge and realized my EO was actually "EO-2" lol)

L D L2 D' L' B D' B' D L // AB3C (10/25)

Got 30 from this skeleton, but since I had some time left I came up with an almost identical 25 move skeleton, but with R2 AUF at the end

New Skeleton: U B L B' L' U' L2 B' L D2 L U2 L2 @ U2 L' D L2 D' L' B D' B' D L R2 (25)

@ - L' D L U2 L' D' L U2 (8-8=0) what the actual fridge

Solution: U B L B' L' U' L2 B' L D2 L U2 L D L U2 L D' L' B D' B' D L R2 (25)

Btw: Marcin Stachura got 25 out of 22 moves 2 twisted corners skeleton (-8, -5) in the previous solve so I wasn't the only one with more than enough luck (though I'm sure his solution wasn't as stupid as mine)

I am more than delighted for both single and average I got. FMC really got me into it recently and I hope that won't change

 

[guysensei1]

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

one of the coolest/luckiest things I've ever done

Spoiler

D2 F' R' F2 R' F//2x2x2 (6/6)
R B ** U' B//2x2x3 (4/10)
B U2 B'//EO (3-1/13-1)
* U2 R U2 R' U2//4 twisted corners (5/17)

*=B U B' U' B U B' U'//reduce to 3E (8-4/25-4)
**=B' R2 L2 F D' F' R2 L2 B U (10-6/31-6)

Final: D2 F' R' F2 R' F R' L2 F D' F' R2 L2 B' U' B' U' B U B' U R U2 R' U2 (25)

Who said 4 twisted is a bad case?

 

[guysensei1]

Why can't insertion finder find optimal for this?

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

Spoilers for the facebook weekly comp btw

Spoiler

*L* R' D' L2 *D* B U2//2x2x2 with 2 inserted moves (7/7)
B2 L D2 L B' D//F2L-1 (6/13)
L2 F L' F' L D' L' D//3E (8/21)

L R' D' L2 D B U2 B2 L * D2 L B' D L2 F L' F' L D' L' D

*=L D' L' U2 D2 R D R' U2 D2 (10-3/31-3)

Final: L R' D' L2 D B U2 B2 L2 D' L' U2 D2 R D R' U2 L B' D L2 F L' F' L D' L' D (28)

IF says 29 for some reason.

 

[Daniel Lin]

semi hard scramble. How would you guys approach it?

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

R2 // pair
(L' B D' U L D' R' F2 D' F D F' R F D2 R D' R' D R' B R B' F' D' F D' F' D2 F) // cfop

solution: R2 F' D2 F D F' D F B R' B' R D' R D R' D2 F' R' F D' F' D F2 R D L' U' D B' L (31)

 

[Duncan Bannon]

Interesting 2x2x3

R2 L' B' U' R2 U R' B F' U' B' R2 B2 R2 - 2X2X3 14/14

OR

L' U D' F' U2 B' R - 2X2X2 7/7

L' F L2 F B' L B F' - Diag 2X2X3? 8/15

R F D F' D' R' - EO 6/21

L D L' D L D2 L' D2 - EP 8/29

ab5c

Spoiler: IF

L' D' [@1] U F' U2 B' R L' F L2 F B' L B F' R F D F' D' R' L D L' D L D2 L' D2
Insert at @1: B' U F' U' B U F U'
After the 1st insertion: L' D' B' U [@2] F' U' B U' B' R L' F L2 F B' L B F' R F D F' D' R' L D L' D L D2 L' D2
Insert at @2: U F' D' F U' F' D F
After the 2nd insertion: L' D' B' U2 F' D' F U' F' D U' B U' B' [@3] R L' F L2 F B' L B F' R F D F' D' R' L D L' D L D2 L' D2
Insert at @3: B U B' D2 B U' B' D2
Fewest moves: 38. 15 moves cancelled
The final solution: L' D' B' U2 F' D' F U' F' D' U' B U' B' D2 R L' F L2 F B' L B F' R F D F' D' R' L D L' D L D2 L' D2

None of these are great. But hey practice for me.

 

[ch_ts]

Why can't insertion finder find optimal for this?

Because insertion finder only uses the algs that its creator provided to it.

Some time ago, I found a corner insertion using sledgehammer something like [R' F R F', D] which was shorter than any of the ones IF found. I wonder if this type of commutator ever got added since then. So it's not always optimal, the insertions are not guaranteed to be optimal... but on the other hand, sometimes it will use algs which i would never use as insertions.

 

[xyzzy]

Sebastiano mentioned most useful algs for Edge insertions, especially the M' U2 M U2 as they are 6 movers and can lead to the better solutions when you find those positions.

Other cool things to keep in mind on Edge insertions. (Some of these might be pretty advanced but just want to post all edge insertions I know)

[…]

For Multiple Edges
Make sure you know R2 U2 R2 U2 R2 U2 and D2 L2 U2 L2 D2 R2 (plus variations and shifts of the 2nd one).

To add a few more cases…

[10 moves] There's this 2+2-cycle ELL alg: F R U R' U' F2 L' U' L U F; doing a cyclic shift will cancel one move and give R U R' U' F2 L' U' L U F2.

[6 moves] M2 U2 M2 U2 and shifts like R2 U2 M2 U2 r2.

[8 moves] M E2 M E2 and shifts and other variations (e.g. F2 M2 U2 M2 U2 F2, which is just a conjugation of the above case).

[10 moves] Optimal H perms: [R2 S2 R2, U/U'] and L R U2 L' R' F' B' U2 F B and the mirrors/inverses/rotations of these. You can always cancel at least two moves by choosing the correct alg, so it's really effectively 8 moves long. Also note that R2 S2 R2 = L2 S2 L2, so these are really thirty-six algs for the price of two.

 

[guysensei1]

2. R' U' F U2 B D L U2 D R F L2 F2 L' F2 R' F2 L2 D2 L' B R' U' F

Super cool solution with some hax

Spoiler

U *L'* D//square (3/3)
U2 R B//pseudo222 (3/6)
U2 L' B'//pseudo223 (3/9)
F' R U R'//pseudo F2L-1 (4/13)
U B'//4c4e (2/15)

Hax 1: Remove the move in **, leaves 3E4C in 13

Skeleton: U' D R B U2 L' B' F' * R U R' U B' (13)

Hax2: use niss (ok fine its just inverse scramble) within an insertion

*=
(R' U L' U' R)//complete F2L (5-1/18-1)
(B' L' B L' B' L2 B L')//LL (8/25)

Final: U' D R B U2 L' B' F' L B' L2 B L B' L B R' U L U' R2 U R' U B' (25)

 

[guysensei1]

To add a few more cases…

[10 moves] There's this 2+2-cycle ELL alg: F R U R' U' F2 L' U' L U F; doing a cyclic shift will cancel one move and give R U R' U' F2 L' U' L U F2.

[6 moves] M2 U2 M2 U2 and shifts like R2 U2 M2 U2 r2.

[8 moves] M E2 M E2 and shifts and other variations (e.g. F2 M2 U2 M2 U2 F2, which is just a conjugation of the above case).

[10 moves] Optimal H perms: [R2 S2 R2, U/U'] and L R U2 L' R' F' B' U2 F B and the mirrors/inverses/rotations of these. You can always cancel at least two moves by choosing the correct alg, so it's really effectively 8 moves long. Also note that R2 S2 R2 = L2 S2 L2, so these are really thirty-six algs for the price of two.

Double post but

Just wanna add another 8 move alg:

R2 B2 L2 U R2 F2 L2 D which is a 2-2 swap cancelled into the weird 8 move edge comm.

 

[Duncan Bannon]

This is from this weeks weekly FMC comp!

I'm happy with this as of now. After this I tried lots of different EO's and was able to find some okay EO's. Some let ab5c but with 2 twisted

How would you continue? Thanks.

Spoiler

(L' D2 F U' R B2 R' D2 R D' F' D') -Phesdo 2X2X3 13/13 Premove D2
(U' L' U L2) - F2L-1 4/17 Premove L2

 

[G2013]

I just had an optimal insertion of 1 cancellation. That's frustrating

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

Spoiler

R2 B2 F' R //2x2x1
F U2 R' //2x2x1 x2 + edge
D2 B D' //Pseudo 2x2x3 + many pairs
(U2 R2 F2 R2) //F2L-1 pseudo
R U //premoves
F U F' U' R' F' R F2 //L3C in 24

Skeleton: R2 B2 F' R F U2 R' D2 B D' R U F U F' U' R' F' R (U' L' U R2 U' L U R2 for 32 backup) F2 R2 F2 R2 U2

R2 B2 F' R F U2 R' D2 B D' R U F U (R B' R' F2 R B R' F2) F' U' R' F' R F2 R2 F2 R2 U2 (24+8-1 = 31)

 

[Daniel Lin]

(FB weekly comp spoiler)

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

R' B' R D F2 // 2x2x2
U' L' U B' L' B' // 2x2x3

I found a continuation to F sexy F' pll skip but I lost it. If anyone can find it I will be super happy.

 

[Duncan Bannon]

Did you continue with red or white? Or do you know?

 

[Daniel Lin]

Did you continue with red or white? Or do you know?

I don't remember

 

[Duncan Bannon]

I don't remember

Sorry for questions. I'm determined to find this out. Did you count moves? About how many?

 

[guysensei1]

(FB weekly comp spoiler)

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

R' B' R D F2 // 2x2x2
U' L' U B' L' B' // 2x2x3

I found a continuation to F sexy F' pll skip but I lost it. If anyone can find it I will be super happy.

If you remember the exact AUF and orientation of the pll skip you can do the inverse of that on a solved cube, then do the scramble and then do your block. Now you just need to solve for a LL skip which should be easier to spot than a FsexyF'.

 

[Daniel Lin]

If you remember the exact AUF and orientation of the pll skip you can do the inverse of that on a solved cube, then do the scramble and then do your block. Now you just need to solve for a LL skip which should be easier to spot than a FsexyF'.

shouldn't i just do the alg+AUF before the scramble rather than the inverse?

And i think it was F sexy F' U2 but I don't remember the orientation