The 3x3 Example Solve Game with only half turns

[Renslay]

That's superb right there

I need help again cuz idk how to solve this case

 Twizzle link 

 Setup 

B2 L2 B2 L2 B2 L2 B2 R2 F2 D2 B2 U2 L2

 Moves 

L2 U2 L2 F2 U2

Next

I looked at your proposal. I don't know a direct solution, I'd do an L-pattern and then a 3-perm. If you chose the right algorithms, the cancellation is insane here!

 Twizzle link 

 Setup 

B2 L2 B2 L2 B2 L2 B2 R2 F2 D2 B2 U2 L2

 Moves 

L2 U2 L2 F2 U2 L2 B2 L2 (y x') B2 R2 U2 R2 B2

// original:
// L2 U2 L2 F2 U2 // your first part
// (L2 B2)3 // L-pattern
// yx' (R2 U2 R2 B2)2 // 3-perm

I originally inserted this as 3-perm:
yx' (L2 U2 L2 B2)2
But I realized I can use the mirrored version for a LOT of cancellation!

Is L2 B2 L2 (y x') B2 R2 U2 R2 B2 the shortest solution to this case? Honestly, I don't know. But I keep this in mind if I run into this exact pattern again!

 

[acrystal]

I looked at your proposal. I don't know a direct solution, I'd do an L-pattern and then a 3-perm. If you chose the right algorithms, the cancellation is insane here!

 Twizzle link 

 Setup 

B2 L2 B2 L2 B2 L2 B2 R2 F2 D2 B2 U2 L2

 Moves 

L2 U2 L2 F2 U2 L2 B2 L2 (y x') B2 R2 U2 R2 B2

// original:
// L2 U2 L2 F2 U2 // your first part
// (L2 B2)3 // L-pattern
// yx' (R2 U2 R2 B2)2 // 3-perm

I originally inserted this as 3-perm:
yx' (L2 U2 L2 B2)2
But I realized I can use the mirrored version for a LOT of cancellation!

Is L2 B2 L2 (y x') B2 R2 U2 R2 B2 the shortest solution to this case? Honestly, I don't know. But I keep this in mind if I run into this exact pattern again!

Oh, I thought you knew some alg but this works I guess as it is 8 moves. How could R2 U2 R2 F2 U2 be useful though?

 

[Renslay]

Oh, I thought you knew some alg but this works I guess as it is 8 moves. How could R2 U2 R2 F2 U2 be useful though?

Uhm, I don't understand. What does R2 U2 R2 F2 U2 do and where?

 

[acrystal]

Uhm, I don't understand. What does R2 U2 R2 F2 U2 do and where?

But I realized I can use the mirrored version for a LOT of cancellation!

 

[Renslay]

By mirrored version, I mean mirrored version of the 3-perm:
(L2 U2 L2 B2)2
versus:
(R2 U2 R2 B2)2
(mirrored across the yz plane)

Both do the same, but if the previous patterned ended up with R2, or even better, U2 R2, or even more... (considering the y x' move here), then the second is much better than the first.

 

[Renslay]

Next

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 F2 L2 U2 B2 R2 D2 R2

 Moves 

d2 L2 d2 L2 D2 L2 D2 B2 L2 B2 L2 D2 B2 D2 B2 D2

// original:
// d2 L2 E2 // corners
// (D2 L2)3 // L-pattern
// (L2 B2)3 // L-pattern
// (B2 D2)3 // L-pattern

Couldn't find any better.

Next: B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

 

[acrystal]

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 F2 L2 U2 B2 R2 D2 R2

 Moves 

d2 L2 d2 L2 D2 L2 D2 B2 L2 B2 L2 D2 B2 D2 B2 D2

// original:
// d2 L2 E2 // corners
// (D2 L2)3 // L-pattern
// (L2 B2)3 // L-pattern
// (B2 D2)3 // L-pattern

Couldn't find any better.

Next: B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

OMG I JUST FOUND A 11-MOVE SOLUTION WITH LEGENDARY CANCELLATION

 Twizzle link 

 Setup 

B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

 Moves 

Rw2 x y D2 L2 D2 F2 L2 F2 D2 L2 F2 R2

Next

 

[Renslay]

OMG I JUST FOUND A 11-MOVE SOLUTION WITH LEGENDARY CANCELLATION

 Twizzle link 

 Setup 

B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

 Moves 

Rw2 x y D2 L2 D2 F2 L2 F2 D2 L2 F2 R2

Next

Hoooaaah, nice! Congrats! Care to explain / insert the non-cancelled solution?

 

[Renslay]

Next

Woaaaaah, I just found a 9-STM solution to this!

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 D2 L2 F2 D2 L2 F2 L2 F2

 Moves 

B2 E2 R2 B2 R2 U2 R2 B2 E2

I'm gonna put into spoiler how I did it, because it contains a trick I haven't used so far!

Spoiler: explanation

Original:

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 D2 L2 F2 D2 L2 F2 L2 F2

 Moves 

// original:
B2 U2 R2 // corners
(R2 E2)2 // H-pattern
(R2 U2 R2 B2)2 // 3-perm

Now with cancellation, but watch the E2 in the middle!

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 D2 L2 F2 D2 L2 F2 L2 F2

 Moves 

// original cancellation, but then I noticed I can remove the (E2) and put it at the end...
B2 u2 R2 (E2) R2 U2 R2 B2 R2 U2 R2 B2

// original:
// B2 U2 R2 // corners
// (R2 E2)2 // H-pattern
// (R2 U2 R2 B2)2 // 3-perm

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 D2 L2 F2 D2 L2 F2 L2 F2

 Moves 

// This is just moved the (E2) to the end:
B2 u2 R2 R2 U2 R2 B2 R2 U2 R2 B2 (E2)

This gives us the final cancellation...

Next: B2 L2 D2 B2 U2 L2 F2 R2 B2 D2 L2 D2 L2

 

[acrystal]

Hoooaaah, nice! Congrats! Care to explain / insert the non-cancelled solution?

 Twizzle link 

 Setup 

B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

 Moves 

M2 B2 R2 B2 // 223
x y D2 F2 D2 F2 D2 L2 D2 F2 L2 F2 D2 L2 F2 R2 // H-Perm

This uses your trick; M2 x y F2 -> Rw2 x y

 

[Renslay]

Next: B2 L2 D2 B2 U2 L2 F2 R2 B2 D2 L2 D2 L2

 Twizzle link 

 Setup 

B2 L2 D2 B2 U2 L2 F2 R2 B2 D2 L2 D2 L2

 Moves 

R2 F2 R2 b2 D2 B2 D2 B2 L2 D2 L2 D2 L2

// original:
// R2 F2 R2 S2 // corners
// (B2 D2)3 // L-pattern
// (D2 L2)3 // L-pattern

Next: B2 L2 B2 R2 B2 L2 B2 U2 F2 L2 U2 B2 L2

 

[acrystal]

 Twizzle link 

 Setup 

B2 L2 D2 B2 U2 L2 F2 R2 B2 D2 L2 D2 L2

 Moves 

R2 F2 R2 b2 D2 B2 D2 B2 L2 D2 L2 D2 L2

// original:
// R2 F2 R2 S2 // corners
// (B2 D2)3 // L-pattern
// (D2 L2)3 // L-pattern

Next: B2 L2 B2 R2 B2 L2 B2 U2 F2 L2 U2 B2 L2

 Twizzle link 

 Setup 

B2 L2 B2 R2 B2 L2 B2 U2 F2 L2 U2 B2 L2

 Moves 

R2 U2 R2 U2 B2 D2 B2 D2 // 223
z y U2 R2 U2 R2 U2 y' (B2 L2 U2 L2)2 // Remaining pieces

Next

 

[Renslay]

Next

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 L2 D2 R2 F2 R2

HOLY SxxT 8-MOVE SOLUTION! NEW RECORD FOR ME!

It was a crazy journey!

Spoiler: How I found it

I did a couple of tries, and this looked promising:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 U2 // corners
E2 S2 M2 // checkerboard pattern
(R2 S2)2 // H-pattern
z2 (L2 U2 L2 B2)2 // 3-perm

Naturally there are some neat cancellations between the patterns:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 S2 r2 S2 R2 (S2) (z2) L2 U2 L2 B2 L2 U2 L2 B2

Normally I would stop here. But I recently started to look into mid-pattern turns, and look at that: you can place the second S2 (the one in parentheses) to the end of the solve, because it does not affect the pattern solving itself:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 S2 r2 S2 R2 (z2) L2 U2 L2 B2 L2 U2 L2 B2 (S2)

This results the following collapse:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 S2 r2 S2 (z2) U2 L2 B2 L2 U2 L2 b2

It's a good stopping point, ya? But that S2 r2 S2 bothered me in the middle. Can it also be put elsewhere? What if I leave it out completely?

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 L2 b2

Oh, the end is interesting, it's almost a full H-pattern... But that syncs with the last moves! IF YOU LEAVE OUT THE LAST TWO STEPS:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 // L2 b2

That is just 3 moves!

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 R2 B2 R2

But now there are a whole new set of cancellations!
F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 R2 B2 R2 // u2 (z2) U2 becomes (x2)
F2 L2 U2 F2 L2 (x2) L2 B2 L2 U2 R2 B2 R2 // L2 (x2) L2 becomes (x2)
F2 L2 U2 F2 (x2) B2 L2 U2 R2 B2 R2 // F2 (x2) B2 becomes (x2)
F2 L2 U2 (x2) L2 U2 R2 B2 R2

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

// FINAL:
F2 L2 U2 (x2) L2 U2 R2 B2 R2

// cancellation chain:
// F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 R2 B2 R2 // u2 (z2) U2 becomes (x2)
// F2 L2 U2 F2 L2 (x2) L2 B2 L2 U2 R2 B2 R2 // L2 (x2) L2 becomes (x2)
// F2 L2 U2 F2 (x2) B2 L2 U2 R2 B2 R2 // F2 (x2) B2 becomes (x2)
// F2 L2 U2 (x2) L2 U2 R2 B2 R2

I am still puzzled by this.

Edit: I checked with an Optimal Solver what would have been its suggestion, and the optimal is indeed 8 moves! Although it suggested a different one:

Spoiler: Optimal Solver solution

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

R2 D2 R2 F2 L2 B2 L2 D2

Next: B2 L2 B2 R2 B2 U2 L2 F2 U2 F2 R2 F2 R2

 

[acrystal]

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 L2 D2 R2 F2 R2

HOLY SxxT 8-MOVE SOLUTION! NEW RECORD FOR ME!

It was a crazy journey!

Spoiler: How I found it

I did a couple of tries, and this looked promising:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 U2 // corners
E2 S2 M2 // checkerboard pattern
(R2 S2)2 // H-pattern
z2 (L2 U2 L2 B2)2 // 3-perm

Naturally there are some neat cancellations between the patterns:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 S2 r2 S2 R2 (S2) (z2) L2 U2 L2 B2 L2 U2 L2 B2

Normally I would stop here. But I recently started to look into mid-pattern turns, and look at that: you can place the second S2 (the one in parentheses) to the end of the solve, because it does not affect the pattern solving itself:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 S2 r2 S2 R2 (z2) L2 U2 L2 B2 L2 U2 L2 B2 (S2)

This results the following collapse:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 S2 r2 S2 (z2) U2 L2 B2 L2 U2 L2 b2

It's a good stopping point, ya? But that S2 r2 S2 bothered me in the middle. Can it also be put elsewhere? What if I leave it out completely?

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 L2 b2

Oh, the end is interesting, it's almost a full H-pattern... But that syncs with the last moves! IF YOU LEAVE OUT THE LAST TWO STEPS:

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 // L2 b2

That is just 3 moves!

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 R2 B2 R2

But now there are a whole new set of cancellations!
F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 R2 B2 R2 // u2 (z2) U2 becomes (x2)
F2 L2 U2 F2 L2 (x2) L2 B2 L2 U2 R2 B2 R2 // L2 (x2) L2 becomes (x2)
F2 L2 U2 F2 (x2) B2 L2 U2 R2 B2 R2 // F2 (x2) B2 becomes (x2)
F2 L2 U2 (x2) L2 U2 R2 B2 R2

 Twizzle link 

 Setup 

B2 R2 L2 F2 R2 B2 L2 D2 L2 U2 L2 F2

 Moves 

// FINAL:
F2 L2 U2 (x2) L2 U2 R2 B2 R2

// cancellation chain:
// F2 L2 U2 F2 L2 u2 (z2) U2 L2 B2 L2 U2 R2 B2 R2 // u2 (z2) U2 becomes (x2)
// F2 L2 U2 F2 L2 (x2) L2 B2 L2 U2 R2 B2 R2 // L2 (x2) L2 becomes (x2)
// F2 L2 U2 F2 (x2) B2 L2 U2 R2 B2 R2 // F2 (x2) B2 becomes (x2)
// F2 L2 U2 (x2) L2 U2 R2 B2 R2

I am still puzzled by this.

Next: B2 L2 B2 R2 B2 U2 L2 F2 U2 F2 R2 F2 R2

8 moves is insane! And yeah, it sure looks confusing on how you did it.

 Twizzle link 

 Setup 

B2 L2 B2 R2 B2 U2 L2 F2 U2 F2 R2 F2 R2

 Moves 

(U2 F2)3 R2 B2 D2 // 223
R2 B2 R2 z' L2 U2 L2 B2 L2 U2 L2 // Remaining pieces

Spoiler: Edit

I also found this solution after looking at what i did

 Twizzle link 

 Setup 

B2 L2 B2 R2 B2 U2 L2 F2 U2 F2 R2 F2 R2

 Moves 

U2 F2 U2 F2 L2 F2 R2 U2 B2 U2 B2 // 223
x' z F2 D2 L2 D2 F2 L2 F2 D2 L2 F2 // Remaining pieces

Next

 

[Renslay]

8 moves is insane! And yeah, it sure looks confusing on how you did it.

Thank you! I started to discover these neat tricks I can use to shorten down the solution!

Next

 Twizzle link 

 Setup 

B2 L2 D2 L2 D2 F2 L2 D2 F2 L2 D2 L2

 Moves 

R2 d2 b2 D2 L2 D2 L2 D2 B2 R2 F2 L2

// original:
// R2 D2 // corners
// E2 M2 S2 // checkerboard pattern
// B2 (L2 D2)3 B2 // conj. L-pattern
// (B2 L2)3 // L-pattern

// original with cancels:
// R2 d2 (M2) b2 L2 D2 L2 D2 L2 D2 L2 B2 L2 B2 L2

// moving (M2) to the end shorts down the ending:
// R2 d2           b2 L2 D2 L2 D2 L2 D2 L2 B2 L2 B2 L2 (L2 B2 L2 R2 F2 L2) -> 
// R2 d2 b2 L2 D2 L2 D2 L2 D2 L2 B2 R2 F2 L2

// you can reverse (L2 D2)3 into (D2 L2)3 in the middle:
// R2 d2 b2 (L2 D2 L2 D2 L2 D2) L2 B2 R2 F2 L2  ->
// R2 d2 b2 (D2 L2 D2 L2 D2 L2) L2 B2 R2 F2 L2

This is another nice example of some neat tricks. I enjoy looking for ways to rearrange the middle of a solve in order to find more cancellations.

Next: B2 L2 B2 L2 B2 D2 B2 D2 R2 U2 L2 F2 L2

 

[acrystal]

 Twizzle link 

 Setup 

B2 L2 B2 L2 B2 D2 B2 D2 R2 U2 L2 F2 L2

 Moves 

D2 L2 D2 R2 B2 U2 R2 U2 R2 // 223
x' z2 D2 F2 D2 L2 D2 F2 L2 F2 D2 L2 // Remaining Pieces

Next

 

[Renslay]

Next

 Twizzle link 

 Setup 

B2 L2 B2 D2 B2 R2 B2 L2 U2 R2 B2 U2 D2

 Moves 

B2 L2 D2 L2 D2 (y) L2 U2 R2 B2 R2 U2 R2 B2

// B2 L2 D2 L2 D2 // corners
// y L2 R2 (R2 U2 R2 B2)2 // M2 + 3-perm

EDIT: one STM-move shorter!

 Twizzle link 

 Setup 

B2 L2 B2 D2 B2 R2 B2 L2 U2 R2 B2 U2 D2

 Moves 

B2 L2 D2 L2 E2 (y x) R2 U2 R2 B2 R2 U2 r2

// B2 L2 D2 L2 D2 // corners
// y' x (B2 R2 U2 R2)2 // 3-perm

Next: B2 D2 F2 D2 B2 D2 R2 F2 U2 R2 D2 R2 F2

 

[acrystal]

 Twizzle link 

 Setup 

B2 L2 B2 D2 B2 R2 B2 L2 U2 R2 B2 U2 D2

 Moves 

B2 L2 D2 L2 D2 (y) L2 U2 R2 B2 R2 U2 R2 B2

// B2 L2 D2 L2 D2 // corners
// y L2 R2 (R2 U2 R2 B2)2 // M2 + 3-perm

EDIT: one STM-move shorter!

 Twizzle link 

 Setup 

B2 L2 B2 D2 B2 R2 B2 L2 U2 R2 B2 U2 D2

 Moves 

B2 L2 D2 L2 E2 (y x) R2 U2 R2 B2 R2 U2 r2

// B2 L2 D2 L2 D2 // corners
// y' x (B2 R2 U2 R2)2 // 3-perm

Next: B2 D2 F2 D2 B2 D2 R2 F2 U2 R2 D2 R2 F2

Crazy solutions!

 Twizzle link 

 Setup 

B2 D2 F2 D2 B2 D2 R2 F2 U2 R2 D2 R2 F2

 Moves 

D2 B2 E2 R2 x Bw2 D2 F2 D2 L2 D2 F2 L2 F2 D2 L2 F2 R2 F2

Next

 

[Silky]

Crazy solutions!

 Twizzle link 

 Setup 

B2 D2 F2 D2 B2 D2 R2 F2 U2 R2 D2 R2 F2

 Moves 

D2 B2 E2 R2 x Bw2 D2 F2 D2 L2 D2 F2 L2 F2 D2 L2 F2 R2 F2

Next

Scramble: B2 R2 L2 B2 D2 B2 U2 B2 R2 D2 F2 L2

L2 F2 L2 R2 U2 R2 // 123 (6)
B2 U2 F2 D2 // Cancellation into 2e2e (4/10)

Pretty sure this is optimal, lol. It there a thread of this for 4x4? Still got to watch the tutorial for this. Definitely interested in seeing the strats for 4x4

Next: B2 D2 B2 L2 F2 D2 F2 D2 R2 U2 D2 B2

 

[Renslay]

Scramble: B2 R2 L2 B2 D2 B2 U2 B2 R2 D2 F2 L2

L2 F2 L2 R2 U2 R2 // 123 (6)
B2 U2 F2 L2 // Cancellation into 2e2e (4/10)

Pretty sure this is optimal, lol. It there a thread of this for 4x4? Still got to watch the tutorial for this. Definitely interested in seeing the strats for 4x4

The last turn should be a D2 not an L2, but otherwise, it looks good! Congrats!

Next: B2 D2 B2 L2 F2 D2 F2 D2 R2 U2 D2 B2

 Twizzle link 

 Setup 

B2 D2 B2 L2 F2 D2 F2 D2 R2 U2 D2 B2

 Moves 

F2 R2 U2 y R2 U2 R2 B2 R2 u2 R2 E2

// original:
// F2 R2 U2 L2 // corners
// y (B2 R2 U2 R2)2 // 3-perm
// (R2 E2)2 // H-pattern

Next: B2 L2 B2 L2 U2 L2 F2 U2 L2 B2 L2 F2 L2