https://cube20.org/how many scrambles are even 16 optimal?
Ahah, I also thought the same until todayI thought FMC single was dead after the 17, well done for proving me wrong!
I just noticed the numbers for 16-19 add up to 43.6 *10^18, greater than the 43.25 total positions - so there's clearly some rounding up going on .https://cube20.org/
If that site's numbers are accurate
Solutions for my 22.00 WR mean (16, 26, 24) at FMC 2019:
1.
Scramble: R' U' F D2 L2 F R2 U2 R2 B D2 L B2 D' B2 L' R' B D2 B U2 L U2 R' U' F
Solution: D2 F' D2 U2 F' L2 D R2 D B2 F L2 R' F' D U' (16 - optimal!)
I have found a couple of interesting EOs on normal scramble, which looked like they could lead to some nice domino solves. But I decided to switch immediately to check the inverse as well. DR + easy corners = insert right away!
(U D' F R) //EO (4/4)
(L2 F' B2 U' B2 U' * ) //DR (6/10)
(R2 B + F D2) //5e (4/14)
* = U D' F2 D U' # R2 //2e2e (6-2/16)
+ = E2 //Leaves 4x (x = "centers") (2/18)
# = E M2 E' M2 (2)
First solution: D2 F' D2 U2 F' L2 R2 {U' D B2 D B2 U} B2 F L2 R' F' D U' (20)
Replace {U' D B2 D B2 U} with R2 D R2 D, which also cancels 2 with the previous move (-6+4-2)
I don't what to say about this... a really advanced solve with lot of luck involved. I was shaking so much after finding the 16 that I had troubles writing down the first move.
2.
Scramble: R' U' F D2 L2 B F L2 B D2 F L D R2 U2 B L R2 U' R2 U B U2 R' U' F
Solution: U2 R' L B' R2 B L2 B' R2 B U L2 R' D2 R' D' L' D2 L D B2 F2 R' F' L' R (26)
(R' L F) //EO (3/3)
(R F2) U2 //2 squares (3/6)
R' L' * U R2 L2 //223 + pairs (5/11)
R D2 R' //Pseudo F2L-1 (3-1/13)
D' L' D2 L D B2 //3C (6/19)
* = L2 B' R2 B L2 B' R2 B (7)
Kinda unlucky insertion, but this evens out with the kinda lucky insertion on the last solve
3.
Scramble: R' U' F U2 R2 D B2 D' R2 B2 L2 F' D R2 B D' R D2 F U2 B' U' R' U' F
Solution: F2 R' D R D2 L2 F2 B2 L F L' B2 L F L' U' R2 B2 L' B' R U R L (24)
(L' R' U' R' B) //EO (6/6)
(L B2) F2 //2 squares (3/9)
(R2 U) //222 (2/11)
(L F2 L' F2 L2) //F2L-1 (5/16)
(D2 R' D' R) //3C (4/19)
Skeleton (on normal): F2 R' D R D2 L2 F2 * L F2 L' U' R2 B2 L' B' R U R L
* = B2 L F L' B2 L F' L' (5)
I have found this quite quickly, but it looks like there should be something better.. I had another 24 as well with a very similar skeleton (same 3 corners left):
(L' R' U' R' B) //EO (6/6)
(L B2) F2 //2 squares (3/9)
(R2 U) //222 (2/11)
(L F2 R F2 R2 D2 L D' R)
A few thoughts.
* I am obviously very happy. I have put a lot of effort in FMC lately (practicing almost every day after hours of math research/classes/teaching is really tiring!). it's nice to see hard work paying of.
* I totally was not expecting this. I thought that it was possible we could never see an official 16, and the mo3 is very low too.
* I am sorry for Mark, he only got to keep his records for a couple of weeks...
Are you sure? How did you determine that? Note that recent scrambles have the 3 extra moves at the beginning and end, so it requires processing each scramble to see what its optimal length is. Did you use software to process every scramble in the WCA database?Apparently there has never been a sub 16 move optimal scramble in any official FMC competition.
Apparently there has never been a sub 16 move optimal scramble in any official FMC competition.
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