The Hardest Scramble

Scramble: F U’ F2 D’ B U R’ F’ L D’ R’ U’ L U B’ D2 R’ F U2 D2
According to cube20.org, this particular position was the hardest to solve for the computer. Is it also hard for human FMC solvers? According to most of the cubers who tried it, yes!
The first to try the scramble was Conrad Rider, who found a 35 HTM solution. Quoting from his original post on speedslving.com:

“After seeing no 1-move blocks on both regular and inverse scramble I decided to go for a ZZ-based start, and managed this 35-mover (not great):

EO: F R L B’ U’ D’ F (7)
Line+Pair: U’ R’ U’ (3/10)
RH Side: D2 R2 L D2 * R (5/15)
F2L-1 + 1x2x2: D’ L D L’ D2 (5/20)
3-corners: L2 D L’ D’ L D L’ D’ L (9/29)
Insert at *: B’ L’ B R B’ L B R’ (8/37)
2 moves cancel

I also found this mediocre blockbuilding start, but no good finish:
2 pairs: L’ B2 (2)
2 1x2x2’s + pair: F R L B U2 B2 (6/8)
F2L-1, no EO: D B’ R B U D’ F D R’ U2 (10/18)”

Later, Tomoaki Okayama found a 34 HTM solution in one hour and Improved Conrad’s solution to 32 HTM. From his original post:

“Solution: L F D2 U’ B L U’ R2 U2 R’ U D2 L’ B U’ L’ U B D’ L U’ L’ D L U B L’ B’ L’ B2 L’ B L2 D’ (34 HTM)

Pre-scramble: D’

2x2x1 block: L F D2 U’ B L
2x2x3 block: U’ R2 U2 R’ U D2
Orient edges: L’ B U’ L’ U
All but 3 corners: B * L B L’ B’ L’ B2 L’ B L2
Correction: D’
Insert at *: D’ L U’ L’ D L U L’

Hard scramble for me, too. Any 1-move makes no c/e pair (as you pointed out), all edges are wrongly oriented, so I have no clue where to start.

Another try, the same start as above:

Pre-scramble: B2 D’

1st 2x2x1 block: L F D2 U’ B L
2nd 2x2x1 block: U’ R’ U2 R2
Expand to 3x2x1: F’
F2L minus 1 slot: U’ R U2 D2

but I couldn’t find a good continuation.

@Conrad
I found that your first solution could be shortened to 32 HTM.

EO: F R L B’ U’ D’ F (7)
Line+Pair: * U’ R’ U’ (3/10)
RH Side: D2 R2 L D2 R (5/15)
F2L-1 + 1x2x2: D’ L D L’ D2 (5/20)
4-corners: L D + L D’ (4/24)

Insert at *: R’ D2 R U’ R’ D2 R U (6 moves cancel)
Insert at +: B R’ B’ L B R B’ L’ (2 moves cancel)”

And he later found another 32 HTM solution using a start by Palash Dubey. From his post:

“R’ F2 U’ L’ B2 D(2x2x1)
F L F U’ B(2x2x2)
F(2x2x1)
L2 F R’ D’ R2 F’ R’ L(F2L minus 1 slot)
D’ B D B'(Orient edges)
D2 R’ D L’ D’ L R(All but 3 corners)

Hmm. 31 HTM skeleton is also not so good…

Next try:

Scramble: F U’ F2 D’ B U R’ F’ L D’ R’ U’ L U B’ D2 R’ F U2 D2
Solution: R’ F2 R’ D2 R U R’ D2 R2 B L D F U’ B U F2 U’ R’ U R2 F2 D’ F D2 L D’ L’ F D’ F’ D (32 HTM)

Two c/e pairs: R’ F2 (same as yours)
1st 2x2x1 block: U + R B L
2nd 2x2x1 block: D F’ U’
Make 2x2x3 block: B * R’ U R2
F2L minus 1 slot: F2 D’ F D2 L D’ L’
All but 4 corners: F D’ F’ D

Insert at *: B’ U F2 U’ B U F2 U’
Insert at +: U’ R’ D2 R U R’ D2 R

32 moves again, still not Sub 30. Hard scramble!”

Then Guus Razoux Schultz found a 31 HTM solution in one hour:

“pre-moves [D2 U’ F’]
2x2x3: U’ L R’ F D2 R’ B R2 D’ L B U’ (12+3)
F2L: L’ B D2 B’ D2 (17+3)
LL: D’ L’ B’ L D2 R2 U2 F’ U2 R2 D’ L’ (28+3)
pre-move correction: D2 U’ F’ (31)”

The first 30 HTM solution (still not sub-30) is from Tomoaki Okayama:

“NISS solve.

(Normal)

Two c/e pairs: F’ R D2
2x2x1 block: R2 B’
2x2x2 block: U D F’ D2
2x2x3 block: U2 L

(Inverse)
Pre-scramble: U L’ U2 D2 F D’ U’ B R2 D2 R’ F

Orient edges: R’ U’ R
F2L minus 1 slot: B’ U2
All but 5 corners: R B’ R’ B
All but 3 corners: B’ L’ B R B’ L B R’
Correction: U L’ U2 D2 * F D’ U’ B R2 D2 R’ F

Insert at *: U’ B U F U’ B’ U F’ ”

Then Attila Horváth found another 30 HTM solution in about 2 hours using his corners-first method:

“L2BU2B2R2L2U’L2B2 (9) all corners +2 edges,
RU’F’RL’UB (7/16) more 2 edges,
R2BRL’D’ (5/21) more 2 edges,
RL’F2URL’B’U2L (9/30) 6E4C.”

David Woner also tried the scramble and got a 32 HTM NISS solution:

“B D2 L’ F’ U’ R L D
L B L’ B’ F’ U L2 F
(F2
U B’ U R’ U’ R U’ B
L’ U’ L U’ L’ U2 L)’ ”

But the first human sub-30 is from Sébastien Auroux who found a 29 HTM solution in less than one hour!

“Pseudo 2x2x3 on Inverse: F’ R B D B L’ B’ U’ F D F’
switch and L5C: D2 R’ B’ R D R2 B’ R D

Skeleton: D2 R’ B’ R D R2 B’ R D F D’ F’ . U B L B’ D’ * B’ R’ F

. = F2 U’ B2 U F2 U’ B2 U
* = D B U’ B’ D’ B U B’

Solution: D2 R’ B’ R D R2 B’ R D F D’ F U’ B2 U F2 U’ B2 U2 B L U’ B’ D’ B U B2 R’ F ”

Later Sebastiano Tronto (me) tried the scramble and first got 33 HTM (no time limit):

“With my NISS notation (moves in brackets are done on inverse scramble)
L’ B2 //2 ce pairs (2/2)
(L B R’ L’ F’) //2 squares (5/7)
D U’ R + U2 B //2x2x1 + other blocks (5/12)
(D’ F’ D’ F) //Pseudo F2L-1 + pair ready (4/16)
D2 L’ U’ L U //All but 3 edges and 3 corners (5/21)

Final skeleton and insertions:
L’ B2 D U’ R + U2 B D2 L’ U’ L U F’ D F D F * L R B’ L’
+ = D2 F’ D F U2 D2 B’ D’ B U2 //3e, 3 moves cancel
* = F2 L B L’ F2 L B’ L’ //3c, 3 moves cancel out

Final solution: L’ B2 D U’ R D2 F’ D F U2 D2 B’ D’ B2 D2 L’ U’ L U F’ D F D F’ L B L’ F2 L B’ R B’ L’ (33 HTM)

IF cancels one more move, but its first insertion cancels only one move and the second one is inserted inside the first (= I would have never looked for it):
L’ B2 D U’ R U2 B [@1] D2 L’ U’ L U F’ D F D F L R B’ L’
Insert at @1: F2 D B D’ F2 D B’ D’
After the 1st insertion: L’ B2 D U’ R U2 B F2 D B D’ F2 D [@2] B’ D L’ U’ L U F’ D F D F L R B’ L’
Insert at @2: D’ B2 U’ D L2 U
Fewest moves: 32. 3 moves cancelled
The final solution: L’ B2 D U’ R U2 B F2 D B D’ F2 B2 U’ D L2 U B’ D L’ U’ L U F’ D F D F L R B’ L’ ”

Found a 31 HTM solution using Conrad’s start:

“Scramble: F U’ F2 D’ B U R’ F’ L D’ R’ U’ L U B’ D2 R’ F U2 D2
F R L * B’ + U’ D’ F //Conrad’s EO (7/7)
U’ R’ D2 U L’ U2 R’ //A more efficient 2x2x3 EO (7/14)
D’ L D’ L’ D L’ //All but 2 corners 3-cycles (6/20)
* = L’ F L B’ L’ F’ L B //3c (4/24)
+ = R’ U L’ U’ R U L U’ //3c (7/31)

Insertions are optimal according to IF

And found a 30 HTM solution:

“Scramble: F U’ F2 D’ B U R’ F’ L D’ R’ U’ L U B’ D2 R’ F U2 D2
Premoves B’ D B, on inverse:
F’ D’ R L
F R2 D’
B R2 B’ D’ F R //Pseudo F2L-1 (13/13)
F’ U L’ U2 L F //Pseudo F2L (6/19)
B U L U’ L’ B’ U F2 //LL + adjust (8/27)
B’ D B //Undo premoves (3/30) ”

But the best known human solve is the astonishing 25 HTM solution by Attila Horváth, with his corners-first approach:

“F2 B U B2 L R’ U2 F’ U L2 D’ F2 L’ D2 U2 L B F’ D’ U’ L2 D2 U2 B’ L2 25 HTM.

on inverse:
L2 B orient corners,
U2 D2 L2 U2 more 4 edges,
L R’ @ F’ L2 R2 B D2 more 2 edges,
R B2 L’ D L2 F B’ U2 L’ U’ D2 all but 6 centres,
insert at @: M S M’ S’ 7 moves cancel.
final (inverse) solution:
L2 B U2 D2 L2 U D F B’ L’ U2 D2 L F2 D L2 U’ F U2 R L’ B2 U’ B’ F2″

2014-07-19 Update:
Robert Yau and Daniel Sheppard found a 28 HTM solution (original post); Daniel found the 2x2x3 and Robert completed the skeleton:

Premove D (to help with the end of F2L after 2x2x3)
2x2x3: R’ F2 U R2 F L2 D2 L U’ D B’ (11) This is based on the 2x2x2 R’ F2 U R2 F L’ U’, with some extra moves to get 2x2x3 and to help with the continuation.
F2L-1 + EO: D’ F L F’ D’ L’ D’
F2L leaving 3 corners: L B’ L2 B
Skeleton: R’ F2 U R2 F L2 * D2 L U’ D B’ D’ F L F’ D’ L’ D’ L B’ L2 B D (23)
Insert L2 D’ R’ D L2 D’ R D at * to cancel 3 moves

Fun fact: (at the moment) on the speedsolving forum, Okayama’s signature is “God’s number is 20. My number is 30. (FMC/classic #266 – ongoing…)” referring to his best solution for this scramble.

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