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My 27 move solution from German Nationals 2014 (making me national champion :)).

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

Pre: B'
F2L-1: U2 F' D2 B U' B R B2 U' B2 U'
L4C: L2 D L' D'

Skeleton: U2 F' # D2 B U' B R B2 U' B2 U' L2 D L' D' * B'

* = D B' U' B D' B' U B
# = B U' B' D' B U B' D

Solution: U2 F' B U' B' D' B U B' D' B U' B R B2 U' B2 U' L2 D L' B' U' B D' B' U - 27 moves
 
Thanks dbax0999!!

By the way, I have found this amazing lucky solve to the weekly challenge. From F2L-1 to F2L in only one move, and PLL skip!! But I'm too bad, being THAT lucky only gave me a 30 moves solution, but it is my PB!

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

U' B F L2 F' L2 R2 U L2 R //2x2x3, Premove R
R D2 R' D2 R D' R' //F2L-1
L' //Last pair in 1 move, premove L
F D L D2 L' D F' R' D R D //Optimal OLL and PLL skip
L R //Correction

Final solution: U' B F L2 F' L2 R2 U L2 R2 D2 R' D2 R D' R' L' F D L D2 L' D F' R' D R D L R (30 HTM)
 
This is my first ever FMC solve!!!
I need a continuation for this.

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

On Inverse Scramble:

F R' F' R U F R2 F' R2 F' L D2 //2x2x2 (10)
U R B U' B' // 2x2x3 (15)
R' U F2 U' F' R F2 R' F2 // F2L-1 (24)
 
This is my first ever FMC solve!!!
I need a continuation for this.

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

On Inverse Scramble:

F R' F' R U F R2 F' R2 F' L D2 //2x2x2 (10)
U R B U' B' // 2x2x3 (15)
R' U F2 U' F' R F2 R' F2 // F2L-1 (24)

You must have a typo somewhere. This is your solve so far, and there's no F2L-1.
 
I know, but I don't understand how did he came up with each substep, for example the "modifying the corner solution to solve some edges" substep.

For that step, I think he adds slice moves (that don't affect corners) to pair up one or more edges to the matching corner; slice moves should preferably cancel 1 or even two moves (in the last case, you are just using a wide move instead of a regular one).
For example, if you have a corner solution like:
U R F2 L'
you can transform it to:
U [E2] R F2 [M'] L'
and without slice moves it becomes:
U' D2 L B2 L'
That's how I understand that step and how I do it, but we should wait for Attila's reply to be sure :)
 
There is an F2L minus 1. Do a Z'.

No...

Edit: ftfy

This is my first ever FMC solve!!!
I need a continuation for this.

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

On Inverse Scramble:

F R' F' R U F R2 F' L D2 //2x2x2 (10)
U R B U' B' // 2x2x3 (15)
R' U F2 U' F' R F2 R' F2 // F2L-1 (24)
 
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Here is an example about corner-edge pairing, during solve corners.

Scramble: F2 U2 B2 R U2 B2 U2 F2 U B D R2 U' R' B U2 B L2 F (German Nationals)


F R D’ R2 D orient (5)
F2 L F2 L F2 L all corners (11 moves),
modifying:
F R D’ R2 d, orient but not lose the 1st pair,
F f, 2nd pair,
L f2, not lose the 2nd pair,
L F’ f’, all corners( - 1 move), 3rd and 4th pairs,
2nd modifying:
F R D’ R2 d F f l f2 L F’ f’ (F R D’ R2 U R L U F2 U F’ B’ - L) solve 2 centres,
3rd modifying:
F R D’ r2 U R L U F2 U F’ B’ L (F R D’ L2 D R L D B2 D F’ B’ L) 13 moves, 5 edges.
I always leave an unsolved slice(here: M), and try to solve the edges on two opposite sides, then I try to find the easiest LSE case.
 
scramble: B2 D2 B2 D' U2 F2 D F2 L2 U F L2 B2 U' L' U B' L D2 R2

B F' L U2 R2 U' L . U2 // 2x2x3 (8/19)
D' B2 L B L' B D // all but 5 edges (7/19)

insert at . F B' L' B F' D // 5 cycle, cancels 2 moves (6-2/19)

challenge: find where is the lie in the solution. (it is not a prepared scramble and i didn't use any kind of solver software and the movecount should be fine too, don't worry ;D)
B F’ z U,
R2 D2 l’ B (last 4 of the scramble: B’ L D2 R2),
I write down without rotation: B F' L U2 R2 U' L (which will be pretty good start :) )

Here's an interesting question: Under the current regulations, should this be considered a valid official Fewest Moves solve? (E2e)
 
Here's an interesting question: Under the current regulations, should this be considered a valid official Fewest Moves solve? (E2e)

Good question actually :D And another question: If not then how could the person checking the solution possibly notice something like that... And how could we prevent this from happening.

EDIT: Also where is the limit? Here he does 3 moves and then practically inverts 4 last moves of the scramble. What if he did Y moves and would then invert X last moves of the scramble then? What numbers would be OK for X and Y and what should be forbidden?
 
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Here's an interesting question: Under the current regulations, should this be considered a valid official Fewest Moves solve? (E2e)
I'm not sure that my conclusion is correct, just a sudden thought.
I do not know what meant Benyó when he said “lie”(Maybe other thing)
Seeing this solution and explanation, I accept it as completely regular.
But his note made me think, if not prepared solve or computer, where is the lie?
 
Good question actually :D And another question: If not then how could the person checking the solution possibly notice something like that... And how could we prevent this from happening.

EDIT: Also where is the limit? Here he does 3 moves and then practically inverts 4 last moves of the scramble. What if he did Y moves and would then invert X last moves of the scramble then? What numbers would be OK for X and Y and what should be forbidden?

I'm not sure that my conclusion is correct, just a sudden thought.
I do not know what meant Benyó when he said “lie”(Maybe other thing)
Seeing this solution and explanation, I accept it as completely regular.
But his note made me think, if not prepared solve or computer, where is the lie?

I guess my personal inclination at the moment is to say that it's okay. It's not an exact inversion of the scramble; there are some pieces that are not affected by the trick. And of course, it's very hard to see; I would imagine that Attila is one of only a few that would be able to spot such a thing - and probably none of us would have seen it if we hadn't been given a reason to look for something like it.

And yes, I also wonder if this is even what Benyó meant, or if he had something else in mind.

But if it is valid, it brings up another interesting perspective as to how one might go about looking for a solution: Apply some portion of the scramble and see if you get something that looks nice, and if so, figure out how to manipulate the rest of the scramble so that the important parts get canceled. Kind of scary, actually.
 
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