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With domino solutions, you can make any combination of U and D moves wide and it will affect the E slice pieces without adding moves, and this is the same as inserting slices that cancel 2. Here I found a combination of inserted slices that solved the 3e case

This is the most important FMC solve in the world!

I'm doing the speedsolving logo lolbz xD

It's in a half-turn-only state which is pretty cool, here's my solution:
R2 B2 R2 B2 D2 F2 D2 F2 R' L D2 R L' D U' B2 D' U R2 F2 (20 moves....)

This state is basically the superflip of HTO states, it's symmetrical and most importantly is extremely difficult to solve efficiently! This is by far the hardest HTO state I've encountered. The Speedsolving logo really is interesting!
Better solution I got: F2 L2 U' D R2 F2 D' U' R2 U2 R2 U2 F B' R2 F' B - 17 moves

Right now my PB for the logo is 17 HTM / 14 STM, but if I tried some more it would probably go down. You guys should give it a shot and see what you get!

Edit-
With a 3edges insertion you could probably get a 15 move solution but rn I’m lazy lol
Edit 2-
F2 L2 U' D R2 * F2 // Block n’ stuff {6}
U2 B2 U2 B2 U D' // AllBut3Edges {6}
*= R' Rw D2 Rw' R D2 {6-1=5}
17 HTM
Can anyone else find a better insertion?

(y')
D U F2 L2 U' F2 // Square-Pair-Line Layer (can sometimes be very useful)
D2 U L2 // 2x2x3/Combine
U R2 U R2 // 2-Gen Finish
Kociemba Phase 2 Total: 13 moves

I wanted to share this great solve, not quite real personal best but it is STM PB!

Scr: R' U' F D2 B2 F U2 B' D2 L2 B' L2 F' D2 L U' B R' U' B2 R' B L2 R' D R' U' F

Spoiler: Solution, from current Weekly Comp

Solution: x2
L' B' R' F R' U' R
F2 M2 D' B2 M2 D
B2 R2 S2 U2
(17s, 20h)

Spoiler: Long talk (mostly) about HTO Reduction

The Phase 1 was the easiest I’ve ever seen, only 7 moves, and I got to use it because it led to a not-bad Phase 2, Half-Turn-Only phase was better than what I was trying to go for which is of course a plus too

Now Half-Turn-Only Reduction can be amazing. It really can, it’s even gotten me my current PB (19 moves). Anything to take away from this entire post is that HTO Redux is awesome.
The biggest thing to learn from this is the Half-Turn-Only Reduction in Phase 2:
F2 M2 D' B2 M2 D
F2 D’ B2 D would make the corner quadruplets that reduces corners to half turn only state, leaving 4 edges unsolved (unsolved as in not in their correct slices) able to be fixed using 2 “inserted” slice turns. If the top/bottom layer is misaligned by a quarter turn relative to the other then doing M2 (or S2) changes 4 edges, HTO good <-> HTO bad, similarly to doing a quarter F move changes edges, oriented <-> disoriented.
For corners to be in a half-turn-only state, look at a 2x2 and you will see what patterns are “allowed”. Basically to tell you, it has to be opposite colors on each side, and also “quadruplets”, it’s difficult to explain sorry, I’ll do my best, if you have two adj. corners then there will be three other duplicates of that pattern, the four pairs of corners are always the same.

Wanted to share this very good solve, not quite real personal best but it is STM PB!

Scr: R' U' F D2 B2 F U2 B' D2 L2 B' L2 F' D2 L U' B R' U' B2 R' B L2 R' D R' U' F
Solution: x2
L' B' R' F R' U' R
F2 M2 D' B2 M2 D
B2 R2 S2 U2
(17s, 20h)

The Phase 1 was the easiest I’ve ever seen, only 7 moves, and I got to use it because it led to a not-bad Phase 2, Half-Turn-Only phase was better than what I was trying to go for which is of course a plus too

Now Half-Turn-Only Reduction can be amazing. It really can, it’s even gotten me my current PB (19 moves). Anything to take away from this entire post is that HTO Redux is awesome.
The biggest thing to learn from this is the Half-Turn-Only Reduction in Phase 2:
F2 M2 D' B2 M2 D
F2 D’ B2 D would make the corner quadruplets that reduces corners to half turn only state, leaving 4 edges unsolved (unsolved as in not in their correct slices) able to be fixed using 2 “inserted” slice turns. If the top/bottom layer is misaligned by a quarter turn relative to the other then doing M2 (or S2) changes 4 edges, HTO good <-> HTO bad, similarly to doing a quarter F move changes edges, oriented <-> disoriented.
For corners to be in a half-turn-only state, look at a 2x2 and you will see what patterns are “allowed”. Basically to tell you, it has to be opposite colors on each side, and also “quadruplets”, it’s difficult to explain sorry, I’ll do my best, if you have two adj. corners then there will be three other duplicates of that pattern, the four pairs of corners are always the same.

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

(L' U' R)//EO
U//Kociemban 222
F/Kociemban Diamond
D' B' D2 B//Kociemban F2L-1
D F' D F//DR

It looks slightly crappy and I couldn't find anything myself, so i gave it to ruwix's solver(which uses 2phase btw)
And believe it or not, the 2nd phase is 17 moves!!!
Can anyone find anything better? I don't think the solver is optimal...
What is the superflip of phase 2 states?

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

(L' U' R)//EO
U//Kociemban 222
F/Kociemban Diamond
D' B' D2 B//Kociemban F2L-1
D F' D F//DR

It looks slightly crappy and I couldn't find anything myself, so i gave it to ruwix's solver(which uses 2phase btw)
And believe it or not, the 2nd phase is 17 moves!!!
Can anyone find anything better? I don't think the solver is optimal...

13 moves for Phase 1, not bad. For Phase 2, I believe the god's number is 16, so I'm pretty certain that program didn't solve it optimally.

Though I looked through this Phase 2, and it's not very good, if this was a real FMC attempt I might find a different Phase 1.
This is all I can find (maybe I could find a better solution if I looked harder but eh)-
Setup: R' U L R' U' F D B2 R2 B2 U2 L2 U B2 F2 D2 R' U2 B2 R B2 R' B' L D R2 B' U2 R' U' F U F D' B' D2 B D F' D F
[F2 cancels] U R2 U R2 U R2 U D F2 U' L2 U' // Half-Turn-Only Reduction (12)
B2 R2 U2 B2 R2 B2 L2 // Half-Turn-Only Finish (7)
Phase 2 Total: 19 HTM (found a different HTOR but that HTOF was hard so I looked for a second one)
13 + 19 = 32 move FMC, not bad.
By the way, if you ever struggle with Phase 2 just do HTO Reduction

What is the superflip of Phase 2 states? Who knows! I can't help here :/

13 moves for Phase 1, not bad. For Phase 2, I believe the god's number is 16, so I'm pretty certain that program didn't solve it optimally.

Though I looked through this Phase 2, and it's not very good, if this was a real FMC attempt I might find a different Phase 1.
This is all I can find (maybe I could find a better solution if I looked harder but eh)-
Setup: R' U L R' U' F D B2 R2 B2 U2 L2 U B2 F2 D2 R' U2 B2 R B2 R' B' L D R2 B' U2 R' U' F U F D' B' D2 B D F' D F
[F2 cancels] U R2 U R2 U R2 U D F2 U' L2 U' // Half-Turn-Only Reduction (12)
B2 R2 U2 B2 R2 B2 L2 // Half-Turn-Only Finish (7)
Phase 2 Total: 19 HTM (found a different HTOR but that HTOF was hard so I looked for a second one)
13 + 19 = 32 move FMC, not bad.
By the way, if you ever struggle with Phase 2 just do HTO Reduction

What is the superflip of Phase 2 states? Who knows! I can't help here :/

Thanks a lot! HTO reduction seems very cool, especially if corners are already reduced (and 4 edges have to be placed ) i might try it when i find a domino.
Coming to FMC '19?

In other news, I beat IF and did slice style edge insertions for the first time and it worked like a dream

(spoiler alert for the russian weekly)

Spoiler

R' U' F D2 L2 D R2 F2 D F2 L2 D B2 R U L F D L' R F2 R' D B2 R' U' F //Scramble

(L')//pair
(U2)//sq
(F' R F)//222
(D B2 L D B' L2 B2)D2//F2L-1
L D L' D' B D' B2 L' B L D//AB3E in 24

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

*= D2 Dw2 (2-1=1)
$= L B U2 Uw2 B' L' (6-2=4) Would've been easier to spot during the next move

Final: D2 L B U2 D2 F' D R' D' F D U2 B2 L' B L D B2 L2 B D' L' B2 D' F' R' F U2 L//29

I got 2 skeletons for a scramble, a 2e3c (one twisted corner, 2 edges need to swap, 2 corners need to swap) in 18 and 3c in 26. Which would be better to work on (say, if you couldn’t try both). On average how many moves is 2e3c?

Also I’m not sure about other ways, do tell me if there are, but I would guess in order to solve 2e3c I do a 2e2c alg to get the edges correct and get the twisted corner out of its position - hence reducing into a 3c skeleton.

TLDR: average move count for 2e3c insertion + best/good ways to do 2e3c insertion.
Also: what about 3e2c? (One flipped edge and 2e2c)

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

Example-
D F2 R' // Edge Orientation {3}
(B) // Kociemba Phase 1 minus 4C4E {1/4}
()=Inverse ofc

Now the rest of the cube can be solved with [R2,L2,U,D,F2,B2] moveset (aka Kociemba Phase 2 moveset) plus 1 other move.

So it’s basically Domino Reduction in 4 moves.

Once you have DR-4C4E (that's what I'm going to name it, DR-4C4E) then you start doing Phase 2 blocks/stuff and somewhere along the line in your solution you do a single move to correct DR. If used correctly it can easily save moves overall because the moves to correct later is always going to be lower than finishing DR right then.

I’m not sure if this has already been discovered or even named, I just discovered it myself today.
I haven’t done a lot testing with this so I don’t know everything about this, so you might be able to explore and find more about this.
This is definitely not as cool as something like NISS, Guus Schultz is just a genius (I wish I could think of something that revolutionary!) so this won't change much about FMC as a whole.

Spoiler: Edit- Example!

Online Weekly Comp Scramble- R' U' F U2 L2 R2 F D2 B' U2 F' L2 B2 L2 U' R U F2 L D B U L U' R' U' F
U2 R // Square {2}
F L F // 2x2x2 Block {3/5}
R2 B R' // Edge Orientation {3/8}
B' // Kociemba Phase 1 minus 4C4E {1/9}
~~In this it took just 1 extra move to get to DR-4c4e~~
U B2 D2 L2 U' F // Setup to Single Move Phase 1 and Form Square (+keep sqr from start) {5/14}
R2 U R2 U' Lw2 L2 U2 // Skeleton, AllBut 3C {6/20}