# <r2,U>



## Stefan (Nov 29, 2010)

From CubeCast Episode 10: scramble and solve the 3x3x3 in <r2,U> (only r2, U, U' and U2 are allowed).

http://mzrg.com/qqtimer/
=> 3x3x3 subsets
=> 2-Generator <R,U> (Scramble length:25)
=> treat all R-moves as r2

44.56, 28.86, 42.38, 1:04.74, 16.56, 38.84, 34.56, 25.57, 10.78, 1:04.72, 20.15, 16.51
best time: 10.78
best avg5: 20.74 (σ = 3.72)
best avg12: 33.27 (σ = 14.29)


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## Toad (Nov 29, 2010)

o_o

I can't do it.


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## trying-to-speedcube... (Nov 29, 2010)

Solve corners, then conjugate loads of 3-cycles with [r2 U r2 U' r2 U r2 U' r2, U2]

That's how I solved it =D
EDIT: first timed solve 59.66


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## Stefan (Nov 29, 2010)

You need to solve the centers, too.

best avg12: 23.69 (σ = 5.37)


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## ben1996123 (Nov 29, 2010)

I managed to get it all solved apart from a U perm on bottom and I can't figure out how to do it...


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## krnballerzzz (Nov 29, 2010)

Freaking sweet! I'm gonna give it a shot when I get home from work.


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## Stefan (Nov 29, 2010)

Average of 5: 12.43


Spoiler



1. 13.81 R2 U2 R' U' R U R2 U2 R' U' R U2 R2 U' R U' R U' R' U R U' R U2 R'
2. 12.80 U2 R U R' U' R2 U' R2 U R2 U2 R2 U2 R U R2 U R2 U R2 U' R U R' U2
3. 10.68 U R2 U R U R U R U R U' R' U' R2 U2 R' U2 R U2 R U2 R2 U2 R2 U2
4. (21.54) U' R' U2 R' U' R' U' R2 U2 R U2 R' U' R U2 R' U R U2 R2 U2 R2 U2 R U
5. (9.27) R U2 R U2 R' U2 R' U R' U R' U' R' U R' U R U2 R U2 R2 U2 R' U2 R



Average of 12: 14.48


Spoiler



1. 13.81 R2 U2 R' U' R U R2 U2 R' U' R U2 R2 U' R U' R U' R' U R U' R U2 R'
2. 12.80 U2 R U R' U' R2 U' R2 U R2 U2 R2 U2 R U R2 U R2 U R2 U' R U R' U2
3. 10.68 U R2 U R U R U R U R U' R' U' R2 U2 R' U2 R U2 R U2 R2 U2 R2 U2
4. 21.54 U' R' U2 R' U' R' U' R2 U2 R U2 R' U' R U2 R' U R U2 R2 U2 R2 U2 R U
5. 9.27 R U2 R U2 R' U2 R' U R' U R' U' R' U R' U R U2 R U2 R2 U2 R' U2 R
6. 21.08 R2 U' R2 U2 R U R' U R2 U2 R2 U' R U2 R' U' R2 U2 R U' R' U' R U R2
7. 13.74 U' R' U' R2 U2 R U' R2 U2 R U' R U2 R2 U' R' U R' U' R U R2 U R U2
8. (9.22) U R' U R U2 R U' R' U' R' U2 R U R U2 R2 U' R U R2 U' R' U2 R U2
9. (1:01.41) R U2 R U R' U' R' U2 R2 U2 R U2 R U R2 U R2 U' R U' R' U R2 U R (totally lost it here, messing up the algs all the time)
10. 13.65 R U2 R' U' R2 U' R2 U' R' U R' U R2 U' R2 U2 R' U' R' U' R' U R' U2 R2
11. 15.55 U' R2 U2 R' U R2 U2 R U' R2 U' R' U R' U2 R U R U' R' U' R' U R' U
12. 12.74 R2 U' R' U' R2 U R' U R' U2 R2 U R2 U2 R' U R U2 R U2 R U2 R U R'


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## trying-to-speedcube... (Nov 29, 2010)

Stefan said:


> You need to solve the centers, too.
> 
> best avg12: 23.69 (σ = 5.37)


Ah yes, forgot about that. r2 U2 r2 U2 r2, just after corners.


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## Kirjava (Nov 29, 2010)

best time: 7.41
best avg5: 14.76 (σ = 1.28)
best avg12: 16.87 (σ = 2.96)

Using a non corners first method.


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## Stefan (Nov 29, 2010)

Kirjava said:


> best time: 7.41




Whatever. Averages are what counts 



Kirjava said:


> Using a non corners first method.




You mean just not a pure one, right?


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## Kirjava (Nov 29, 2010)

Stefan said:


> Whatever. Averages are what counts



Yeah, you're miles ahead. I'm wondering what method you're using...



Stefan said:


> You mean just not a pure one, right?


 
Yeah. They're not solved first, but they're not solved last, either.


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## MTGjumper (Nov 29, 2010)

Did Thom give you this idea?


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## Stefan (Nov 29, 2010)

MTGjumper said:


> Did Thom give you this idea?


 
Yeah, on the cubecast Thom said someone called Simon Crawford gave him this challenge.

single: 5.03

Average of 5: 11.99


Spoiler



1. (5.03) U R U2 R2 U' R U R2 U2 R2 U2 R' U2 R2 U' R2 U R2 U R2 U R2 U' R U'
2. (18.46) U' R' U R2 U' R U2 R2 U R2 U' R2 U' R' U2 R' U R' U' R2 U R U R2 U'
3. 14.65 U' R U2 R2 U' R U2 R U' R' U2 R2 U' R2 U' R2 U R2 U2 R2 U' R2 U2 R' U'
4. 11.37 R2 U2 R2 U' R U2 R2 U' R U' R2 U2 R2 U2 R U R U R2 U2 R' U R2 U R'
5. 9.97 R' U R U R2 U2 R2 U R' U' R' U' R' U R U R U' R2 U' R' U R2 U' R


Average of 12: 14.14


Spoiler



1. 13.98 U2 R U' R2 U R' U2 R' U R' U2 R U2 R' U2 R' U' R' U2 R2 U R' U' R' U2
2. 17.77 R U2 R' U2 R2 U2 R U R' U2 R U' R2 U' R' U2 R' U2 R2 U' R U R' U R2
3. 17.86 U2 R2 U R U' R U' R2 U R' U2 R U R' U R2 U' R U2 R U R U R2 U2
4. 16.67 R2 U R U R' U' R2 U2 R2 U' R2 U R2 U R' U' R2 U2 R U R2 U R' U' R
5. 10.61 U R U' R U' R' U2 R' U' R2 U2 R2 U' R' U R' U2 R' U' R2 U2 R' U' R' U2
6. (5.03) U R U2 R2 U' R U R2 U2 R2 U2 R' U2 R2 U' R2 U R2 U R2 U R2 U' R U'
7. (18.46) U' R' U R2 U' R U2 R2 U R2 U' R2 U' R' U2 R' U R' U' R2 U R U R2 U'
8. 14.65 U' R U2 R2 U' R U2 R U' R' U2 R2 U' R2 U' R2 U R2 U2 R2 U' R2 U2 R' U'
9. 11.37 R2 U2 R2 U' R U2 R2 U' R U' R2 U2 R2 U2 R U R U R2 U2 R' U R2 U R'
10. 9.97 R' U R U R2 U2 R2 U R' U' R' U' R' U R U R U' R2 U' R' U R2 U' R
11. 14.84 U2 R U' R2 U R' U' R2 U R2 U R U2 R2 U' R' U2 R U R2 U2 R U2 R U2
12. 13.71 R' U R2 U R2 U2 R U2 R U2 R' U' R U' R2 U2 R' U' R U' R2 U' R2 U' R'


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## Stefan (Nov 29, 2010)

My method:


Spoiler



1. Solve D+DR+DB+DBR+DFR (usually start by building (not placing) the D+DR+DB+DBR block)

2. Solve remaining up to five edges by shooting from DF:
Shoot DF->UF-UR with (r2 U r2 U' r2 U r2 U' r2 U)2
Shoot DF->UF-UB with (r2 U r2 U' r2 U r2 U' r2 U2)2
Shoot DF->UF-UL with (r2 U r2 U' r2 U r2 U' r2 U')2



What's yours, Thom? And how about you, Simon?


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## Stefan (Nov 29, 2010)

Well, my 5.03 was of course lucky, didn't bother to keep track of the best non-lucky one (would have to think about what's lucky). Reconstruction:


Spoiler



Scramble: U r2 U2 r2 U' r2 U r2 U2 r2 U2 r2 U2 r2 U' r2 U r2 U r2 U r2 U' r2 U'
Solve:
U' r2 U2 r2 U2 r2 (build the D+DR+DB+DBR block)
U r2 U' r2 U r2 (add the DFR corner and solve the block)
U'


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## Kirjava (Nov 29, 2010)

Stefan said:


> My method:
> 
> 
> Spoiler
> ...


 


Spoiler



Haha, I wondered if you would do something similar to me.

1. Solve D+DR+DBR+DFR
2. r2Ur2U'r2U'r2U'r2Ur2U2r2U'r2U2 or (U2r2)*6 and setups for edges

I made this up at the UK Open so I've not been using a solver or anything.

I think luck plays a bigger part in my method for influencing times than in yours.

Seperation -> 1look finish might be good.


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## Stefan (Nov 29, 2010)

Spoiler



Ah yes, at some point I had your step 1 as well, and also used (U2r2)*6. Not anymore, though. Your separation idea might be fast, but sounds like many algs. I very much prefer my single simple alg method 


Try this scramble, I screwed it up completely (39.40):
U2 r2 U2 r2 U r2 U r2 U' r2 U' r2 U' r2 U r2 U2 r2 U' r2 U r2 U2 r2 U

That's it, 200 solves on qqtimer, I'm done for now. Session results:


Spoiler



number of times: 200/200
best time: 5.03
worst time: 1:01.41

current avg5: 17.87 (σ = 1.01)
best avg5: 11.99 (σ = 1.96)

current avg12: 19.57 (σ = 5.68)
best avg12: 14.14 (σ = 2.68)

current avg100: 17.74 (σ = 6.88)
best avg100: 17.13 (σ = 5.73)

session avg: 19.64 (σ = 7.99)
session mean: 19.77


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## Kirjava (Nov 29, 2010)

Stefan said:


> Spoiler
> 
> 
> 
> I very much prefer my single simple alg method





Spoiler



Of course you do, it's very pochmannesque. 

I've kinda given up trying to beat you now. If I were to attempt it again I think I'd learn your method. I think 'my' version can be more efficient but yours is nice and straight forward. Not needing to think seems to be useful for this challenge. The best direct solving method is probably to follow yours and do some freestyle u perms and stuff to take advantage of lucky cases.




I got 12.34 on the scramble you posted, kinda screwed up myself. Undoing setups in 'my method' can get confusing.


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## Cyrus C. (Nov 29, 2010)

Here's how I do it:


Spoiler



1. Solve a 2x2x2.
2. Build it to a 2x2x3.
3. Solve the EP.

Step 1 and 2 are quite intuitive.



I'm not too fast, 45ish.


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## Stefan (Nov 29, 2010)

Kirjava said:


> Spoiler
> 
> 
> 
> The best direct solving method is probably to follow yours and do some freestyle u perms and stuff to take advantage of lucky cases.


 


Spoiler



I'm still not really good with my first step, that could be improved. And one could learn algs for all last-5-edges cases. I especially hate U-perms and Z-perms, those take me way too long (about 40 and 60 moves, respectively).


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## ben1996123 (Nov 29, 2010)

R2 U' R2 U' R U' R' U' R2 U' R U' R2 U2 R2 U2 R' U' R' U R' U2 R U2 R 



I got 17.39, but my solve before was over 4 minutes...

EDIT:

"Consistency" :3



Spoiler



Average of 5: 55.30
1. (4:16.84) R' U R2 U R U R' U2 R2 U R2 U R U2 R U2 R' U R2 U R' U R2 U' R2 
2. (17.39) R2 U' R2 U' R U' R' U' R2 U' R U' R2 U2 R2 U2 R' U' R' U R' U2 R U2 R 
3. 38.20 U R' U2 R2 U R2 U' R2 U' R U' R U' R' U2 R2 U R2 U R2 U' R' U' R2 U 
4. 58.60 U' R U' R U R2 U2 R2 U R U2 R2 U2 R2 U R U R' U' R2 U R2 U' R2 U2 
5. 1:09.10 R' U' R2 U R2 U' R U2 R2 U2 R U2 R' U R' U R U R U R U2 R2 U2 R

current avg5: 55.30 (σ = 12.83)


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## Kirjava (Nov 29, 2010)

Spoiler



you could always learn r2Ur2U'r2U'r2U'r2Ur2U2r2U'r2U2 for U perm. I think someone would have to bust out ksolve if they wanted to take this much further

also L5E is like 60 algs, you'd need crazy dedication to learn it


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## ben1996123 (Nov 29, 2010)

1. 11.60 R' U2 R2 U2 R' U R U R2 U2 R2 U2 R' U' R U R U' R U2 R2 U' R2 U R'

My method:

1. Separation (intuitive plus some "algs" that are pretty much intuitive anyway)
2. PCBL (Permute corners of both layers, only 1 possibility apart from solved: r2 U2 r2 U' r2 U2 r2 U r2 U' r2 U r2 U' r2 U' r2 U r2 (U') to do a Y perm on top and a Jb on bottom.)
3. Edges ([r2 U2]*6, [r2 U2]*5 r2 U [r2 U2]*5 r2 U', and Thom's U perm with r2 U2 setup for bottom layer edges.)

Could have been faster (17.58), messed up separation. I'm only posting this because I forced an edges skip


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## Stefan (Nov 29, 2010)

Spoiler



_"L5E is like 60 algs, you'd need crazy dedication to learn it "_
No, just 60 raw cases. You can adjust U. Same way you need only 4 algs for edge PLL, not 12. I think I'd have to learn 13 more algs.

Ok, tried KSolve now (attached).

Shortest 3-cycle I found so far (and it's easy): (r U' r U' r U r U)2
Your U perm seems to be optimal.
H perm: (r U')6 (U' r)6 = (r U')5 r U2 (r U')5 r
Z perm: r U' r U2 r U2 r U r U r U' r U2 r U2 r U' r U' r U2 r

Hate that Z perm. Might be better to not let it search with single turns but with finger-friendly turn sequences. Well, U' and r2 are always ok, but U/U2 not so much.


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## qqwref (Nov 29, 2010)

Anyone want an H perm?

(r2 U')5 r2 U2 (r2 U') 5 r2

EDIT: Damn you, Stefan! PS:
best avg5: 11.22 (σ = 2.08)


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## Stefan (Nov 29, 2010)

qqwref said:


> Damn you, Stefan!



tee hee hee 



qqwref said:


> best avg5: 11.22 (σ = 2.08)


 
Noooooooooooo 
Method? Amount of practice?
Ugh... I really don't want to try harder...


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## qqwref (Nov 29, 2010)

Method is yours. Amount of practice is maybe... an hour? an hour and a half? About as long as it takes to do 100 solves (so far).

I'll post my avg5/12/100 as soon as I stop doing solves... avg100 is around 15.5 so far and going down (due to improvement since I started).


EDIT: :tu
number of times: 159/160
best time: 3.09


Spoiler



scramble: U' R' U R U2 R' U R2 U2 R' U2 R2 U2 R2 U R' U' R' U' R U R2 U2 R U' 

block: r2 U' r2 U r2 U' r2
L5E: U' :O


best avg5: 9.53 (σ = 1.38)


Spoiler



1. 7.97 R' U R' U R U2 R2 U' R U' R2 U' R' U R' U2 R2 U R U2 R U2 R' U2 R'
2. (12.36) R' U' R' U' R2 U' R U R' U' R2 U2 R' U R2 U R' U' R' U R U' R2 U2 R2
3. 11.32 U2 R2 U' R2 U R U R2 U R U2 R2 U R' U' R U R2 U2 R' U' R U' R U
4. 9.30 U' R' U' R' U' R2 U R U R2 U' R' U R U R U2 R U' R2 U' R2 U' R2 U
5. (7.55) R U R2 U' R U' R2 U R2 U R2 U2 R U' R' U R2 U' R2 U' R U R U R


best avg12: 11.40 (σ = 2.64)


Spoiler



1. 13.35 U R2 U R U' R U2 R2 U2 R U2 R2 U2 R2 U2 R' U' R' U' R' U' R' U' R2 U'
2. 9.69 R2 U' R2 U' R2 U' R2 U R2 U' R' U R U' R2 U' R' U R2 U R2 U R2 U R2
3. (3.09) U' R' U R U2 R' U R2 U2 R' U2 R2 U2 R2 U R' U' R' U' R U R2 U2 R U'
4. 13.21 U' R U R' U R2 U2 R2 U R2 U2 R2 U2 R2 U R' U2 R2 U' R' U R2 U2 R2 U
5. (16.55) R2 U' R2 U' R' U2 R' U' R U2 R' U' R' U' R2 U2 R2 U' R2 U' R2 U' R' U' R2
6. 12.75 R U' R U R U R U R2 U R2 U2 R U' R U2 R' U R' U' R2 U2 R U2 R2
7. 16.50 U2 R' U2 R2 U R2 U2 R U2 R U R U' R U R U R U2 R' U2 R' U2 R U
8. 7.97 R' U R' U R U2 R2 U' R U' R2 U' R' U R' U2 R2 U R U2 R U2 R' U2 R'
9. 12.36 R' U' R' U' R2 U' R U R' U' R2 U2 R' U R2 U R' U' R' U R U' R2 U2 R2
10. 11.32 U2 R2 U' R2 U R U R2 U R U2 R2 U R' U' R U R2 U2 R' U' R U' R U
11. 9.30 U' R' U' R' U' R2 U R U R2 U' R' U R U R U2 R U' R2 U' R2 U' R2 U
12. 7.55 R U R2 U' R U' R2 U R2 U R2 U2 R U' R' U R2 U' R2 U' R U R U R


best avg100: 13.27 (σ = 3.48)
session avg: 15.30 (σ = 6.69)


Spoiler



1:02.70, 21.75, 28.54, 23.76, 13.83, 15.24, 8.63, 21.07, 20.51, 13.78, (DNF(20.51)), 11.01, 9.83, 29.82, 11.45, 12.94, 18.20, 17.22, 15.28, 23.37, 20.23, 16.80, 20.44, 20.41, 14.78, 11.38, 8.59, 5.92, 13.68, 41.21, 18.09, 15.06+, 22.75, 24.22, 19.12, 30.32, 31.67, 20.89, 13.55, 20.27, 12.98, 11.37+, 14.14, 14.25, 10.88, 13.15, 22.35, 27.27, 25.66, 11.90, 6.44, 13.30, 11.30, 17.42, 18.56, 19.42, 14.09, 16.33, 15.03, 11.84, 14.81, 10.66, 21.12, 12.08, 12.46, 6.45, 8.46, 13.57, 13.85, 6.67, 11.29, 13.34, 12.16, 12.62, 13.75, 11.26, 13.83, 10.72, 18.49, 15.65, 20.48, 9.79, 15.68, 15.74, 12.70, 14.69, 11.61, 13.38, 8.88, 8.20, 16.41, 10.20, 19.28, 14.77, 19.34, 14.24, 15.96, 13.35, 9.69, (3.09), 13.21, 16.55, 12.75, 16.50, 7.97, 12.36, 11.32, 9.30, 7.55, 17.60, 17.51, 21.47, 9.89, 14.93, 12.34, 10.29, 9.24, 9.84, 10.75, 9.17, 34.19, 21.16, 9.86, 12.88, 9.51, 11.86, 7.57, 10.38, 18.94, 15.31, 13.66, 12.31, 13.02, 8.18, 18.29, 15.41, 14.50, 16.40, 11.13, 13.30, 10.40, 22.27, 13.26, 16.69, 14.21, 12.90, 14.04, 12.22, 10.40, 11.65, 13.14, 13.07, 12.53, 10.45, 19.63, 15.10, 17.49, 13.74, 13.34, 18.78


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## ben1996123 (Nov 30, 2010)




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## jms_gears1 (Nov 30, 2010)

Spoiler



The only alg i use to solve is: r2 U r2 U r2 U' r2 and its inverse


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## jms_gears1 (Nov 30, 2010)

26.08 U R' U R' U2 R' U2 R2 U R' U R' U' R' U R U' R' U2 R' U R' U2 R U' 



Spoiler



Basically i build the R side 1x2x3, then i attach DF to the L/R blocks. so that its F2L minus one cross piece and one corner piece (always DB and DBR)
then i use: r2 U r2 U r2 U' r2 and its inverse to pair the two and insert them.
After words i use: r2 U r2 U r2 U' r2 to do a bunch of UPerms


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## cmhardw (Nov 30, 2010)

qqwref said:


> Anyone want an H perm?
> 
> (r2 U')5 r2 U2 (r2 U') 5 r2


 
I've been using [r2 (U')2 (r')2 (U')2]2 r2 (U')2 (r')2 U' [r2 (U')2 (r')2 (U')2]2 r2 (U')2 (r')2 U
but I think I like yours better. They seem to be basically the same concept, but I use double U turns and you use singles making yours much faster.


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## Stefan (Nov 30, 2010)

Ok Michael, I give up, you win 

My best averages now:
best avg5: 11.74 (σ = 1.45)
best avg12: 13.06 (σ = 1.82)
best avg100: 15.95 (σ = 4.15)


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## jms_gears1 (Nov 30, 2010)

number of times: 12/12
best time: 17.80
worst time: 46.24

current avg5: 24.91 (σ = 3.21)
best avg5: 24.91 (σ = 3.21)

current avg12: 30.08 (σ = 6.29)
best avg12: 30.08 (σ = 6.29)

session avg: 30.08 (σ = 6.29)
session mean: 30.41


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## Stefan (Nov 30, 2010)

best time: 3.64
best avg5: 9.68 (σ = 1.85)
best avg12: 11.75 (σ = 2.76)
best avg100: 13.40 (σ = 3.51)


Spoiler



The 3.64 scramble and solution:
Scramble: r2 U r2 U' r2 U r2 U' r2 U2 r2 U' r2 U' r2 U r2 U r2 U' r2 U' r2 U r2
Solution: r2 U r2 U' r2 U r2 U' r2 U

Average of 5: 9.68
1. (6.99) U2 R2 U' R' U R' U' R U2 R' U R2 U' R' U' R2 U' R' U R2 U' R' U' R' U
2. 10.67 R2 U R' U2 R U2 R U R' U2 R U2 R2 U R2 U' R U2 R U2 R2 U R U R
3. (15.83) R U R2 U2 R U' R U2 R' U R' U2 R2 U R U R2 U R2 U R' U R' U R
4. 11.28 U2 R U2 R' U R U2 R2 U2 R2 U' R' U R2 U R U R' U' R' U R2 U R U'
5. 7.09 U2 R U R2 U' R U' R' U' R U R' U' R2 U R' U2 R' U2 R' U R2 U' R U2 

Average of 12: 11.75
1. 6.99 U2 R2 U' R' U R' U' R U2 R' U R2 U' R' U' R2 U' R' U R2 U' R' U' R' U
2. 10.67 R2 U R' U2 R U2 R U R' U2 R U2 R2 U R2 U' R U2 R U2 R2 U R U R
3. 15.83 R U R2 U2 R U' R U2 R' U R' U2 R2 U R U R2 U R2 U R' U R' U R
4. 11.28 U2 R U2 R' U R U2 R2 U2 R2 U' R' U R2 U R U R' U' R' U R2 U R U'
5. 7.09 U2 R U R2 U' R U' R' U' R U R' U' R2 U R' U2 R' U2 R' U R2 U' R U2
6. (17.23) R' U R U' R U2 R2 U' R' U R2 U' R' U2 R' U' R2 U2 R' U R' U R2 U R'
7. 11.40 R' U' R2 U2 R' U2 R2 U' R U R' U' R U2 R' U2 R2 U R2 U2 R2 U R U2 R'
8. 12.99 U' R U R U' R' U2 R2 U2 R U R U2 R' U2 R U2 R' U' R2 U' R U R' U
9. 13.83 R' U R2 U2 R2 U' R' U2 R2 U' R' U R' U' R2 U2 R2 U' R' U2 R U' R2 U' R'
10. 13.65 U' R' U' R2 U R2 U' R' U2 R U R U' R U R2 U2 R2 U R2 U2 R' U' R2 U
11. 13.81 R U R U' R U2 R2 U2 R2 U2 R2 U' R' U' R2 U2 R2 U R U2 R U' R2 U' R
12. (6.42) U' R2 U R U2 R' U2 R' U2 R U' R U R U R U R U R U R2 U2 R2 U' 

best avg100: 13.40 (σ = 3.51)
8.54, 12.81, 12.38, 12.32, 23.95, 13.75, 3.64, 13.96, 9.47, 12.05, 12.12, 12.20, 22.06+, 11.42, 18.67, 11.60, 13.31, 10.52, 17.09, 14.75, 13.37, 10.47, 11.77, 13.69, 16.13, 14.57, 10.76, 12.92, 9.43, 12.81, 15.46, 13.30, 14.23, 11.70, 8.75, 11.60, 10.03, 17.27, 15.13, 14.23, 12.81, 16.17, 8.96, 13.50, 10.06, 9.82, 17.43, 12.42, 18.55, 17.35, 14.28, 14.32, 15.09, 13.34, 25.77, 13.34, 13.45, 19.00, 12.84, 5.51, 7.82, 12.78, 13.85, 13.62, 20.00, 10.18, 16.20, 11.04, 14.66, 20.48, 23.64, 14.58, 10.97, 11.88, 15.83, 11.02, 13.59, 15.84, 13.64, 7.88, 12.52, 20.70, 15.82, 6.99, 10.67, 15.83, 11.28, 7.09, 17.23, 11.40, 12.99, 13.83, 13.65, 13.81, 6.42, 9.42, 13.62, 18.22, 14.51, 8.77


Didn't learn any new algs besides that H perm, probably mostly improved in my step 1 (which I still find interesting and it's what made me try again). Michael's still better in everything, gah. So close (0.59, 0.15, 0.35 and 0.13 seconds away).


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## Johannes91 (Nov 30, 2010)

FYI, the worst case is 30 moves:
U r2 U r2 U r2 U r2 U r2 U2 r2 U' r2 U r2 U' r2 U2 r2 U r2 U r2 U r2 U r2 U r2.


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## Stefan (Nov 30, 2010)

Ugh, that case just looks ugly. Solved it in 42 moves, though, not too bad. Wish I could solve the hardest 3x3x3 cases in 28 moves so easily (same factor, 1.4).

But hey, when I saw your name I thought _"oh sh**, Johannes is gonna beat us all"_. I still have big trouble with the first block(s), could imagine you being better at that.


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## vcuber13 (Dec 1, 2010)

Stefan said:


> Shortest 3-cycle I found so far (and it's easy): (r U' r U' r U r U)2
> Your U perm seems to be optimal.
> Z perm: r U' r U2 r U2 r U r U r U' r U2 r U2 r U' r U' r U2 r
> 
> Hate that Z perm. Might be better to not let it search with single turns but with finger-friendly turn sequences. Well, U' and r2 are always ok, but U/U2 not so much.[/spoiler]


 
wouldnt 2 u perms be shorter? and perhaps more finger trickable?


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## Stefan (Dec 1, 2010)

vcuber13 said:


> wouldnt 2 u perms be shorter? and perhaps more finger trickable?


 
I don't see how. Show us?


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## vcuber13 (Dec 1, 2010)

Stefan said:


> I don't see how. Show us?


 
i was thinking your 3 cycle was a u perm


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## qqwref (Dec 1, 2010)

Shortish similar 3-cycles:
(DF -> UL -> UB): r2 U' r2 *U'* r2 U r2 *U* r2 U' r2 *U'* r2 U r2 (U)
(DF -> UR -> UL): r2 U' r2 *U'* r2 U r2 *U2* r2 U' r2 *U2* r2 U r2 (U')
(DF -> UF -> UB): r2 U' r2 *U2* r2 U r2* U2* r2 U' r2 *U* r2 U r2 (U)
(UF -> UR -> UB): r2 U' r2 *U2* r2 U r2 *U'* r2 U' r2 *U'* r2 U r2 (U2)
(DF -> UL -> UF): r2 U' r2 *U* r2 U r2 *U'* r2 U' r2 *U* r2 U r2 (U')
(UF -> UL -> UB): r2 U' r2 *U* r2 U r2 *U* r2 U' r2 *U2* r2 U r2 (U2)


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## deepSubDiver (Dec 1, 2010)

A few optimal blocks. Note: Random-move scrambles, not random state!

```
U' r2 U2 r2 U2 r2 U r2 U' r2 U' r2 U2 r2 U2 r2 U' r2 U2 r2 U r2 U r2 U' 
[False, [1, 3, 0, 5, 2, 6, 4], [4, 2, 3, 1, 5, 0]]
solving block
SOLUTION: r2 U2 r2 U2 r2 U' r2 U2 r2 U2 r2 U' r2 U r2 

U' r2 U r2 U2 r2 U' r2 U2 r2 U2 r2 U r2 U r2 U2 r2 U r2 U2 r2 U2 r2 U' 
[False, [1, 5, 6, 2, 0, 4, 3], [1, 4, 5, 0, 2, 3]]
solving block
SOLUTION: r2 U r2 U2 r2 U' r2 U r2 U r2 U' r2 U2 r2 
SOLUTION: r2 U r2 U' r2 U' r2 U r2 U2 r2 U' r2 U2 r2 
SOLUTION: r2 U2 r2 U r2 U2 r2 U2 r2 U r2 U2 r2 U2 r2 
SOLUTION: r2 U2 r2 U' r2 U2 r2 U2 r2 U' r2 U2 r2 U2 r2 
SOLUTION: r2 U' r2 U2 r2 U' r2 U2 r2 U r2 U' r2 U' r2 

U r2 U' r2 U2 r2 U2 r2 U' r2 U' r2 U r2 U2 r2 U2 r2 U r2 U' r2 U r2 U' 
[False, [6, 5, 0, 2, 1, 4, 3], [5, 2, 0, 1, 3, 4]]
solving block
SOLUTION: r2 U' r2 U r2 U2 r2 U r2 U r2

U' r2 U r2 U2 r2 U' r2 U2 r2 U' r2 U2 r2 U r2 U2 r2 U r2 U2 r2 U2 r2 U2 
[False, [1, 0, 3, 2, 5, 6, 4], [3, 0, 2, 4, 5, 1]]
solving block
SOLUTION: U' r2 U r2  (wat?)

U r2 U r2 U2 r2 U' r2 U r2 U r2 U r2 U r2 U2 r2 U' r2 U2 r2 U r2 U 
[False, [6, 3, 0, 2, 5, 1, 4], [1, 2, 0, 4, 5, 3]]
solving block
SOLUTION: U' r2 U' r2 U2 r2 U r2 U2 r2 U2 r2 

U r2 U r2 U2 r2 U2 r2 U r2 U' r2 U' r2 U' r2 U' r2 U r2 U' r2 U' r2 U' 
[False, [3, 5, 2, 4, 0, 1, 6], [1, 5, 4, 2, 0, 3]]
solving block
SOLUTION: U' r2 U2 r2 U2 r2 U' r2 U' r2 U' r2 U r2 U' r2 

U r2 U2 r2 U2 r2 U r2 U2 r2 U2 r2 U' r2 U r2 U' r2 U2 r2 U' r2 U r2 U 
[False, [2, 0, 1, 6, 3, 5, 4], [5, 1, 2, 4, 3, 0]]
solving block
SOLUTION: U r2 U' r2 U2 r2 U2 r2 U' r2 U' r2 

U' r2 U r2 U r2 U2 r2 U' r2 U r2 U2 r2 U' r2 U r2 U2 r2 U2 r2 U' r2 U 
[False, [1, 6, 0, 2, 3, 5, 4], [1, 0, 5, 4, 3, 2]]
solving block
SOLUTION: r2 U' r2 U' r2 U r2 U r2 U r2 U' r2 U' r2
```
So, nice blocks don't mean short blocks.

Average of 1,000 for the block was around 13 moves.
Average of 100 for optimal solutions was around 22 moves.
During that average I encounterd 6 positions which were not solvable in 25 moves - thus, 25 move scrambles don't do it for us.

When I implemented a more efficient algorithm (not even using transition or pruning tables... Ugh!) I will do a more detailed analysis.


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## keemy (Dec 1, 2010)

finally had time to actually try this so I did 25 timed solve (improved by 2nd half XP)
best avg5: 14.12 (σ = 0.65)
best avg12: 16.80 (σ = 3.53)
session avg: 21.55 (σ = 5.64)

not sure about method I have been doing something very limited but reco was easy.(note i am doing <l2,U> because i'm cool like that >_>)
1. join (DF and DLF) or (DL and DLF)
2. join (D center) and edge (DF or DL) not used in step one to the block formed by step one
3. pick up last corner (DBL) onto the 2x2x1 formed and place entire block on D. 
4. put in the DB edge (algs are really fast for this, but I am bad at executing the mirror for DF so that's why I always do it this way)
5. LL (I need to work on this my reco and execution are pretty slow)

I may have some time again tomorrow so watch out qq.


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## deepSubDiver (Dec 1, 2010)

Depth distribution table for optimal solutions:
9: <0,1%
10: <0,1%
11: <0,1%
13: <0,1%
14: 0,1%
15: 1%
16: 2%
17: 4%
18: 5%
19: 11%
20: 11%
21: 18%
22: 23%
23: 13%
24: 9%
25: 2%
26: 0.4%
27: 0.2%
28: <0.1%


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## Stefan (Dec 1, 2010)

deepSubDiver said:


> A few optimal blocks.



Nice, looks like I'm not that bad at it after all. Would've done it optimally several times, near-optimally the other times. I should learn looking for the dangling corner earlier, and know solutions for some ugly special cases where I need to look and think way too much.



deepSubDiver said:


> thus, 25 move scrambles don't do it for us.



Damn... guess I'll use 30 if I try this again and there's no random-state scrambler by then (which should be easy to do, there's just a few hundred thousand states, right?).


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## Johannes91 (Dec 2, 2010)

deepSubDiver: Cool, our programs seem to agree.



Stefan said:


> Damn... guess I'll use 30 if I try this again and there's no random-state scrambler by then (which should be easy to do, there's just a few hundred thousand states, right?).


Ask and ye shall receive: http://laire.fi/t/r2U.pl.

I can easily generate any statistics if there's interest.


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## Stefan (Feb 1, 2011)

Before I forget it: A while ago I improved further (just couldn't steal Michael's single record, grrr):

best time: 3.64
best avg5: 9.43 (σ = 0.34)
best avg12: 10.78 (σ = 2.10)
best avg100: 12.27 (σ = 3.10)
Still used 30 random moves scrambling...

Details:


Spoiler



best avg5: 9.43 (σ = 0.34)
1. 9.12 R U2 R2 U' R U R U' R' U' R' U2 R U' R' U R' U' R2 U2 R2 U2 R' U R'
2. (6.38) U' R U' R2 U' R' U' R2 U R' U2 R U R2 U R2 U2 R' U2 R' U2 R U2 R2 U'
3. 9.26 R' U2 R' U R U2 R U R2 U R2 U' R2 U' R U R2 U' R2 U' R' U R2 U2 R'
4. 9.90 R U R' U R2 U2 R2 U R U' R U R' U' R' U R U2 R2 U' R2 U' R2 U R2
5. (10.04) R U R' U R U R' U R' U2 R2 U' R' U' R U' R2 U' R' U R2 U2 R U2 R' 
Followed by 9.87 and 8.34, but bad times before and after, so no good Ao12.

best avg12: 10.78 (σ = 2.10)
1. 9.30 R U R2 U' R U R2 U' R' U' R' U' R U' R U2 R' U2 R2 U2 R2 U' R2 U' R U' R U' R U2
2. 12.86 U2 R U' R' U' R' U2 R' U2 R' U R' U R' U R2 U' R2 U R2 U2 R' U R2 U R' U2 R U2 R'
3. 12.91 U2 R2 U2 R2 U' R' U2 R2 U' R' U' R2 U R2 U R' U' R' U' R' U R' U R2 U R U R' U' R2
4. 11.19 R' U R2 U2 R' U R' U' R' U2 R' U' R U2 R' U' R' U R U R' U' R' U' R U2 R2 U R2 U'
5. (7.29) U R' U2 R U2 R2 U' R2 U' R' U R2 U' R2 U' R U' R' U R U' R2 U' R' U' R U' R U R'
6. 10.81 U' R' U2 R' U' R' U R' U R U' R2 U2 R U2 R' U' R' U' R' U R U2 R' U R U R2 U' R'
7. 14.43 U' R' U R' U2 R U' R U R2 U R U R' U2 R U R U' R2 U' R U2 R' U' R' U' R U R
8. 10.34 U' R2 U2 R U' R2 U' R2 U' R U' R' U2 R U2 R' U R U' R2 U2 R U2 R2 U R' U' R U' R2
9. 7.46 R2 U2 R' U R' U2 R2 U' R U R' U R2 U2 R2 U2 R U2 R U R' U2 R U R' U' R' U2 R2 U2
10. 10.60 R' U' R' U' R' U R' U R U R2 U' R2 U R U' R2 U' R2 U R' U2 R U' R U' R' U2 R2 U2
11. (14.71) U R' U R2 U' R2 U' R' U2 R2 U' R2 U' R2 U2 R' U' R U' R2 U2 R' U' R2 U2 R' U R2 U R2
12. 7.89 U' R U2 R2 U' R2 U R U' R2 U2 R2 U2 R' U R U2 R U R2 U2 R U2 R2 U' R' U' R U2 R 

best avg100: 12.27 (σ = 3.10)
10.12, 14.49, 6.31, 13.69, 17.65, 7.91, 14.25, 22.18, 14.93, 13.78, 15.91, 11.15, 11.11, 8.44, 16.96, 14.83, 12.18, 10.39, 10.18, 11.70, 9.42, 12.97, 12.54, 13.44, 20.27, 11.62, 9.34, 12.76, 13.11, 10.22, 11.84, 17.89, 13.37, 7.19, 4.48, 15.97, 14.78, 10.25, 9.40, 10.02, 9.22, 11.78, 16.27, 12.00, 7.97, 9.56, 13.30, 13.91, 12.53, 14.60, 9.20, 13.32, 12.74, 11.30, 8.42, 12.61, 9.77, 20.05, 10.83, 16.84, 6.39, 11.61, 10.75, 8.53, 15.73, 11.37, 9.58, 9.19, 10.43, 17.29, 11.25, 17.74, 10.77, 14.18, 7.31, 10.25, 16.07, 8.79, 13.86, 12.72, 11.26, 8.46, 11.95, 23.16, 10.24, 11.39, 14.99, 9.71, 15.54, 11.74, 15.80, 15.09, 13.80, 14.19, 12.26, 9.11, 11.07, 12.71, 10.00, 8.83


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## Filipe Teixeira (Jul 12, 2014)

My method on this:

Solve DF and DB.
Make the right block.
Solve EPLL with normal algs.


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