The 3x3 Permutation Example Solve Thread

acrystal said:

Next

Click to expand...

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

x y'
R D F2 R F2 // CPFB
U2 R' U' r' R' U R // SB
M U2 M2 U E2 M E2 // LSE

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

x y'
R D F2 R F2 // CPFB
r U2 r' U r2 U' R // SB
U' M2 U B2 M B2 M2 // LSE

Renslay said:

I actually found two 19-STM solutions with the same CPFB:

First attempt:

 Twizzle link 

 Setup 

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

 Moves 

x y'
R D F2 R F2 // CPFB
U2 R' U' r' R' U R // SB
M U2 M2 U E2 M E2 // LSE

Tried to improve; this one is equal in STM, but shorter in HTM:

 Twizzle link 

 Setup 

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

 Moves 

x y'
R D F2 R F2 // CPFB
r U2 r' U r2 U' R // SB
U' M2 U B2 M B2 M2 // LSE

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

Click to expand...

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

z2 // Inspection
R D2 B2 U' B' D2 // X-Cross
U L U L' // 2nd Pair
F' L F M x U' R' F' U2 F // 3rd+4th Pairs
L2 D Lw' U2 Lw D' L' U2 L' U // LL

acrystal said:

Bruh why are my solutions getting bad

Click to expand...

acrystal said:

Next

Click to expand...

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

y
r R u R B' U' R2 B // CPFB
U' r' R' U r2 U' M2 U' R' // SB
U M U2 M U M // LSE

Renslay said:

They are not bad! I enjoy them.

 Twizzle link 

 Setup 

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

 Moves 

y
r R u R B' U' R2 B // CPFB
U' r' R' U r2 U' M2 U' R' // SB
U M U2 M U M // LSE

The CPFB felt long, the SB is okay, the LSE saved it in the end.

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

Click to expand...

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

y z' // Inspection
R' U' S // Cross
U2 M' B2 M2 F' M' // 1st+2nd Pairs
B U2 B' // 3rd Pair
U2 L' U' L2 y z R' F' R U R U' R' S' U // LS

acrystal said:

You actually mean it? Why thank you very much! There really isn't that much stuff going on in CFOP, and your Roux solutions are way better, and I can't comprehend the idea of CP, especially the short CPFB solutions.

Click to expand...

acrystal said:

Next

Click to expand...

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

y z
R U B M F // CPFB
U' M U' M2 U r U2 R U' R' // SB
U' M' U' M' U2 M2 // LSE

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

y z
R U B M F // CPFB
U' M U' M2 U r U' r U2 r R2 // SB
U' M U M U2 // LSE

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

y z
R U B M F // CPFB
U r U2 r U R r U' r // SB
U' M' U' M2 U' u2 M' u2 // LSE

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

y z
R U B M F // CPFB
R2 r U r' U R' U' r U r' // pseudo SB
U' M' U B2 M B2 r2 // LSE

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

y z
R U B M F // CPFB
R2 r U r' U r' U' r U r' // pseudo SB
U M2 U' E2 M' E2 r2 // LSE

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

y z
R U B M F // CPFB
U' M U' M2 U r U' R U2 R' // SB
U M' U F2 M' F2 M2 // LSE

Renslay said:

Yes! It's interesting to see these, it requires a differently wired brain.

As for the CP, my method is laughably stupid. I look for a decent FB with my usual colors, I usually find a 4-6 long solution fairly easy. Let's say I find this: R' F B' R' B'.
I check the CP by placing the SB's corners into their place and check it the top layer corners are well permuted. This is not part of the solution; just checking the CP. If it's incorrect, I try to modify the original FB, usually with 1 extra move. Since this one ended with a B', how about inserting these?
- insert B U B' at the end -> FB becomes R' F B' R' U B'.
- insert B U' B' at the end -> FB becomes R' F B' R' U' B'.
- insert B U2 B' at the end -> FB becomes R' F B' R' U2 B'.

I check whenever the CP is fixed in these cases (move the SB corners to their place, look at the top layer corners).

If none of these work, I look for other parts of the original FB where I can insert a random move without messing up the FB. For example, after the first R' F, nothing important is on the U side! That means I can try these:
- R' F U B' R' B'.
- R' F U' B' R' B'.
- R' F U2 B' R' B'.
And I check all the CP cases for these.

If I still can't find anything... Maybe I try a completely different FB, maybe with different colors. So far of all the scrambles I had in this thread there was only one "cursed" case where it took me an annoyingly long time until I found a decent CPFB... CP just refused to pop up!

Is this method stupid? Yes. Is there a better way to find CPFB? Probably. But I enjoy these little searches. And that's what matter to me.

(Btw After CPFB, the rest is fairly easy, and also fun to look around for short solutions.)



For this I found numerous almost-equal solutions branching from the same CPFB, all of them 21-23 STM. Here are the two shortest:

 Twizzle link 

 Setup 

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

 Moves 

y z
R U B M F // CPFB
U' M U' M2 U r U2 R U' R' // SB
U' M' U' M' U2 M2 // LSE

 Twizzle link 

 Setup 

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

 Moves 

y z
R U B M F // CPFB
U' M U' M2 U r U' r U2 r R2 // SB
U' M U M U2 // LSE

Spoiler: A couple of 22-STM alternatives

 Twizzle link 

 Setup 

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

 Moves 

y z
R U B M F // CPFB
U r U2 r U R r U' r // SB
U' M' U' M2 U' u2 M' u2 // LSE

 Twizzle link 

 Setup 

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

 Moves 

y z
R U B M F // CPFB
R2 r U r' U R' U' r U r' // pseudo SB
U' M' U B2 M B2 r2 // LSE

 Twizzle link 

 Setup 

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

 Moves 

y z
R U B M F // CPFB
R2 r U r' U r' U' r U r' // pseudo SB
U M2 U' E2 M' E2 r2 // LSE

 Twizzle link 

 Setup 

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

 Moves 

y z
R U B M F // CPFB
U' M U' M2 U r U' R U2 R' // SB
U M' U F2 M' F2 M2 // LSE

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

Click to expand...

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

z2 // Inspection
L F2 D2 // Cross
B U' B' // 1st Pair
U' S' L S // 2nd Pair
F' U2 F // 3rd Pair
L' U2 L // 4th Pair
U' R' F' M U' M' F M U Rw // LL

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

z2 // Inspection
L F2 D2 // Cross
B U' B' // 1st Pair
U' S' L S // 2nd Pair
F' U2 F // 3rd Pair
U2 L F' L' z y2 L F L' U' L' U L S U // LS

acrystal said:

Woah that actually is pretty dumb! I'm actually surprised it doesn't take you too long.

I think my solutions are pretty good, like this one with very short Cross+F2L insertions. However, my LL solutions are a bit long and I don't have any idea if they are shorter.

Click to expand...

acrystal said:

Next

Click to expand...

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

y' z'
U F' D' U' R2 U2 B' // CPFB
R' U R U' r2 U r' R2 // pseudo SB
U E2 M' E2 r R // LSE

Renslay said:

Yeah, LL is hard, because both the corners and the edges can be permuted...
Can you influence one or both at the last pair insertion?

 Twizzle link 

 Setup 

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

 Moves 

y' z'
U F' D' U' R2 U2 B' // CPFB
R' U R U' r2 U r' R2 // pseudo SB
U E2 M' E2 r R // LSE

Just for funsies, here are a bunch of FBs I found before the CP:

Spoiler

(y' z') U F' D' U' R2 B'
(x2) U R2 r u U' R r2 B'
(z) L D' F' U r B'
(z) f' R' f F U2 F2
(z) M2 B' M r' F

I eventually chose the first, with the CP fix being a U2 insertion:
(y' z') U F' D' U' R2 U2 B'

Fun fact: my CPFB is completely legit, it accidentally has the correct orientation.

Next: D F' D2 F D2 F R2 U2 R2 D2 R2 U2 F U F2 R B R D' R F

Click to expand...

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

z2 x // Inspection
M F' U R' U2 R' // X-Cross
L' U' L // 2nd Pair
E L U L' Uw B' U B // 3rd+4th Pairs
y' F R U R' U' F' U2 // LL

acrystal said:

Depends on what case I get

I got bit lucky, as I got a Y-Perm (the LL with the lowest movecount)

 Twizzle link 

 Setup 

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

 Moves 

z2 x // Inspection
M F' U R' U2 R' // X-Cross
L' U' L // 2nd Pair
E L U L' Uw B' U B // 3rd+4th Pairs
y' F R U R' U' F' U2 // LL

Next

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

y' U R F2 D // CPFB
U' r' U2 r' // SB
U M2 U D2 M' D2 U' L' // LSE

Fred said:

 Twizzle link 

 Setup 

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

 Moves 

y' U R F2 D // CPFB
U' r' U2 r' // SB
U M2 U D2 M' D2 U' L' // LSE

LSE makes my brain hurt

Click to expand...

Fred said:

 Twizzle link 

 Setup 

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

 Moves 

y' U R F2 D // CPFB
U' r' U2 r' // SB
U M2 U D2 M' D2 U' L' // LSE

LSE makes my brain hurt

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

Click to expand...

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

z2 // Inspection
L2 D R D2 // Cross
S R Bw U2 B' // 1st+2nd Pairs
L' U' L2 U' L' U' B' U' Bw L' U' L U L F' L' Fw U // 3rd+4th Pairs+LL

acrystal said:

Next

Click to expand...

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

y2 x'
r B' F' R' U F // CPFB
U r' R' U' r R U R // SB
U M2 // LSE

Renslay said:

 Twizzle link 

 Setup 

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

 Moves 

y2 x'
r B' F' R' U F // CPFB
U r' R' U' r R U R // SB
U M2 // LSE

Yeeeees! 16-STM, 17-HTM! Let's goooooo!

There was no big trick here, just pure luck with that LSE (it almost feels like an LSE-skip, at least permutation-wise).
Original FB was:
(y2 x') r B' F' R' F, inserted a U to fix CP.

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

Click to expand...

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

z2 // Inspection
L2 D' L R D2 L2 F2 L F // X-Cross
U F U F' // 2nd Pair
U2 B' U' B // 3rd Pair
R U' M' x' U2 L' U' L U' L' U // LS