Round 1 Attempt 1 - 20

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

Solution: D B' U' F L D F2 R2 F2 B' R2 F' U B2 U B2 R2 U2 D2 F2 (20)

D B' U' F L //EO (5/5)
D //JZP (1/6)
(F2 L2 F2 U' F2 U) //DR (6/12)
B2 L2 F D2 B //HTR (5/17)
F2 D2 //Leave double slice (2/19 but actually 18)

Rewrite
D B' U' F L D
(F2 L2 F2 U' F2 U D2)
{B2 L2 F D2 B F2}

{} = F2 R2 F2 B' R2 F' (0/18)

For the part on inverse at first I rewrote it as
(F2 L2 D U' R2 D2 U L2 D') (3/21)

But then I found this non-obvious equivalent
(F2 D2 U2 R2 B2 U' B2 U') (-1/20)

Optimal from EO :)

Now if you look at the solution linearly on normal, it looks like a DR solve:

D B' U' F L //EO (5/5)
D //RZP (1/6)
F2 R2 F2 B' R2 F' //Sub-optimal DR, I would never look at this (6/12)
U B2 U //HTR (3/15)
B2 R2 U2 D2 F2 //Finish (5/20)

Adding a slice to turn the 11 move DR into a 12 mover is something I
would never consider, but in this case it make the HTR much easier.


The scramble had 14 EOs in 4, only 1 of which requiring NISS. I missed
some of the linear ones and I don't know why, maybe I felt some comp
pressure.

That turned out not to be a problem because the 4 move EOs all sucked.
I had a few short DRs from the, but they were all 5qt.  From 4 move EOs,
mallard finds a 23 with RZP in 6 and DR in 12. With EO in 4 and RZP in
5 the best it finds is a 25.

Good time management on my part, I started rushing through 5 move EOs
at the right moment and found a bunch of direct RZPs, but did not try
to switch after each of them immediately. The EO I used was the 20th,
and it immediately stood out. Found the double slice quite early and I
have not worked on anything else after that.

-------------------------------------------------------------------------------
Round 1 Attempt 2 - DNF (but I could have written down a 26, I'm stupid)

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

The most promising thing I had was this:

R2 U' R2 D' //EO (4/4)
L R2 D2 B L2 B L' //DR (7/11)
F' L2 F' R2 U2 B [1] //HTR (6/17)
U2 R2 F2 R2 U2 R2 //Leave slice (6/23)

I found it at 48 minute, plenty of time to complete the solve, right?
RIGHT?
Apparently not. The best I could find was a 26 and I did not bother
writing it down because FOR SURE I one can find at least a 24 on this,
right? Checking it now I see that [1] = B' F R2 B F' U2 gives 25, so why
did I not see it? I guess I'll never know.

Optimal from this DR is 22 with just one extra move for HTR:

D2 F U2 B [s1] U2 L2 F' //HTR with extra D2 at the start (7/18)
U2 L2 B2 [s2] //Leave slice (3/21)
[s1] = [s2] = S2

Had I found a good slicing on my leave slice in 23 I would probably looked
for more HTRs, and this is quite an obvious one. But I needed more time,
I am not that fast at checking HTRs (yet).

With a 22 on this scramble it would have been 21.33 ER mean. I am not quite
there yet, but this shows that I am not as far as I thought either :)

I should have written down the 26 and I would have been happy
with a sub23 mean. But It was not an easy call to make, a couple of minutes
at the end can make the different when finding difficult slices (and they did
in attempt 3!).

I also had this decent DR:

(D R' D2 B) //EO (4/4)
R U F2 B2 D R //DR (6/10)
U L2 D' B2 R2 D' B2 D' //Possible HTR

Optimal is 23 but it requires HTR in 20.

Again missed a couple of linear EOs in 4, not of a kind that I usually forget
to check. I just need to focus more in the EO phase. I also misse U R (U R)
but that can happen.
-------------------------------------------------------------------------------
Round 1 Attempt 3 - 22

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

Solution: L2 B U2 R2 F' B R2 F L2 F' L2 U2 F' U B2 U' F2 B D' L U L' (22)

(L U' L') //EO (3/3)
(D B' F2 U B2 U') //DR 2qt (6/9)
L2 F (F U2 L2 B D2 B') //HTR +2qt (8/17)
(R2 U2 L2) //Leave slice, the dreaded 4x (3/20)

DR part all on inverse:
(F U2 L2 B D2 B' R2 U2 L2 F' R2)

The 4x slice can be solved by inserting two single slice moves in the same
direction separated by a (D)-sequence (see my slice theory page at
https://sebastiano.tronto.net/speedcubing/slice-theory). If you look at
this scramble, every three consecutive floppy moves are an I-sequence!
This is normally very good for simplifying a solution, but not for solving
a 4x. Indeed it took me around 20 minutes to finish my solve.

At first I found a 24 by inserting a 4x somewhere.
Then I found this, I don't remember how (my notes are very chaotic):

(B L2 D2 F D2 F' U2 B' F U2 L2 F B2 L2) (+3/23)

And with less than two minutes left I found this:

(F U2 L2 F L2 F' R2 B' F R2 U2 B' L2) (+2/22)

I wrote it down and finished checking at 59:30. If I had a good solve
(or just a non-DNF) on the second attempt, I would have freaked out. What
is going on with these hard slices?!

It turns out 22 is optimal from this DR, and there is no way to get it
in 2qt.  Cool!

About the scramble: it was very good, there were many short DRs and I
did not even have time to check all the 4 move EOs - the one time where
I found all of them. Stupid 20 minutes slice from Hell.

Other interesting DRs:
B' R2 D F
U2 L2 U2 L' U' L' //3qt in 10, 24 optimal with 5qt bleh

B' R2 D F
(U2 R2 L U L) //3qt in 9 but it's fake HTR corners, 24 optimal

Pretty satisfied with this attempt :)

-------------------------------------------------------------------------------
Round 2 Attempt 1 - 22
R' U' F L D' R2 D2 U2 B F2 D2 L2 U2 L2 B' L2 D' F R2 D' U B D2 R' U' F
-------------------------------------------------------------------------------
Round 2 Attempt 2 - 27
R' U' F R F' L' B2 L' F B L' D B' D' B2 U D2 L2 B2 D F2 R' U' F
-------------------------------------------------------------------------------
Round 2 Attempt 3 - 25
R' U' F R' L' D' L U' R2 D2 F' D R2 B R2 U2 F L2 F' L2 U2 R' B R' U' F