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WRs! Sebastiano Tronto 22 mean and 16 single at FMC 2019!

Mike Hughey

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#4
how many scrambles are even 16 optimal?
https://cube20.org/
If that site's numbers are accurate, there are about 3 18 move scrambles for every 17 move scramble, and 12 17 move scrambles for every 16 move scramble. So 16 or fewer move optimal scrambles should come along about once every 36 scrambles or so - not all that rare. (Note that's a very rough calculation using what are themselves very rough estimates from that website - the actual number seems like it's somewhere between 40 and 60 scrambles, actually).

I suspect we'll see a 15 move solution someday, and I wouldn't be surprised if we actually get a 14.

Still, it either takes really good skill combined with some good luck, or really really good luck, to find an optimal solution. I know in Sebastiano's case, it's the former - an amazing achievement!

Edit: I find it fascinating that there are apparently more than twice as many 8-move-optimal scrambles as there are 20-move-optimal scrambles. I never would have guessed that!
 
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#5
Wow! I thought that almost all scrambles were 18 optimal, because every time I get a pb or sometimes just for fun I put a scramble into cube explorer, and I seem to always get 18 optimal. I only think I have even seen a 17 optimal once, but maybe that is just my luck.
 

pjk

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#13
Reposted from here:
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...
 

Mike Hughey

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#15
Apparently there has never been a sub 16 move optimal scramble in any official FMC competition.
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?

If the numbers from the website I quoted are somewhat correct, it seems really unlikely for there to have never been one. With 1835 competitions in the past that have held FMC, and many of them having more than one scramble per competition (most recently having at least 3), you'd think the odds would be pretty overwhelming we'd have at least one 15 move scramble. Seems the odds for a 15-move optimal scramble should be less than 1 in 1000.

Edit: This actually seems like it might be a fun project - if you haven't done it already, someone with lots of computing power available should process every FMC scramble in the WCA database and list the number of scrambles with each optimum length. It would be really interesting to know what that's like.
 

Kit Clement

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#16
Apparently there has never been a sub 16 move optimal scramble in any official FMC competition.
That is an incredibly false statement. There have been at least nine 15-move optimal scrambles since scrambles were tracked:

Thailand Championship 2015: L2 B2 U2 B2 R2 U2 B' R2 U2 B2 F' L F' L2 F U' F2 L' R2 U' F
Dutch Open 2015: U2 R2 F' U2 D' L' D2 F' U F' R F' R2 F' L2 F' L2 B2 D2
Plentzia Open 2016 Scramble 2: R2 D2 F2 R' U R2 D' B U' F2 L F' D B F2
Brasileiro 2016 Scramble 1: R' U' F R2 U' B2 R2 U B2 D U2 B2 U R U2 R D L B D R' D U' R' U' F
Joao Camara 2016: R' U' F L' U2 L D2 F2 R2 D2 R2 D' L B2 D' L2 B' U R' D' B' U2 R' U' F
Sydney Championship 2016 Scramble 1: R' U' F D U2 B2 D F2 R2 U R2 B2 F2 U' B' D2 L F' U' R' B' U' L2 D' R' U' F
Cobb Cubes 2017: R' U' F R2 U' R2 D B2 D U R2 U' F2 L' U' F' D2 L' D' L2 B R2 B' R' U' F
Silent Swap Open 2017 R2 Scramble 3: R' U' F R2 D2 F2 L' F2 U2 B2 L' B2 F2 U' B R' B' D2 B' L U' R2 F2 U' R' U' F
PSKubing 2017: R' U' F D2 F2 L2 F2 U2 R' B2 F2 R' B' R B' F' D U B2 R' F D R' U' F

Source: https://docs.google.com/spreadsheet...ck7pxSSvfnxHM3buyKvBQ0DmM_8YvKynlIxnDD0#gid=0

Likely more than this since this was analyzed by Baiqiang a year ago.
 

Mike Hughey

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#17
Ah, so someone HAS already done it. although as you say that's old.

Interesting: 59 16-move optimal scrambles, at that time.

Also interesting: considering this was done a year ago, I wonder if there have been any 14-move optimal scrambles yet. If not, we're due.
 
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