CFOP Quick-witted Princess Leia (Solve completion guessing)

[Tito_H]

Episode XX+3

Princess Leia
was in trouble again.
She was in the commander’s
room in the Death Star, surrounded
by Darth Sidious, Darth Vader, Commander Tarkin, etc…

The Superlaser of the Death Star was aiming at the Earth.

Death Sidious said to Leia, “You could scarcely won the challenges 1, 2, and 3. But this time I prepared the tougher one, so I am pretty sure you will fail this time.”

He pulled out a Rubik's Cube from his long, flowing sleeve and said, "Can you solve this T type OLL using the T perm PLL? I would save the Earth if you could. Do you accept the challenge? No calling in Superman or popping out any pieces!"

OLL style



Princess Leia replied, "I'll accept!" and added, "You're probably going to add another condition right before the start, aren't you? Just tell me what that hidden condition is!"

He replied, "As expected of Princess Leia. You know how mean I am. Yes, that's right. The additional condition is to complete OLL+PLL, that is, Solve, in 20 moves or less (in QSTM basis)."

Princess Leia was a little stumped, and said in her mind, “A T-perm requires a minimum of 15 moves(Note #1), so I had to turn this OLL into a T-perm in five moves or less. If I permuted the two twisted corners at that position, it would become a T-perm, but it didn't look like I could do it in five moves. It was also forbidden to let the pieces popped out...”

Can anyone kindly help her to save the Earth?

Note #1 on 27-Dec-2025:
bcube gave me several T perm algs of 14 moves!

 

[Fred]

Spoiler: Solution

F B' T perm F' B
Or do a z rotation first and it looks like a case from the Classic Pochmann blindsolving method: S' T perm S. (D2 L2 T perm L2 D2 would exceed 20 quarter turns.)

 

[bcube]

A T-perm requires a minimum of 15 moves (in QSTM basis)

 

[Tito_H]

Fred, thank you so much for your quick response and amazing solution. The Earth has been saved.

I wasn't familiar with the Classic Pochmann blindsolving method, but it seems like it was an easy problem for someone who has studied BLD.

The algorithm z S' T perm S didn't occur to me, but that makes good use of the fact that PLL doesn't affect the F2L part, so it was Eureka for me!

The procedure Princess Leia came up with was shown in the simulation below, but that was 21 moves, not meeting the condition!


(21 moves in QSTM basis, although the counter shows 19. The z S' U2 S completes OLL, and the rest is left hand T perm.)

bcube, thank you for your information on the 14-moves algorithms of T perm. Those could reduce hers by one move, which also made possible to meet the condition.

To be honest, I made a mistake. I forgot to consider the last AUF's two moves when I made this guessing. She couldn't have solved the case without your posts!

 

[bcube]

21 moves in QSTM basis, although the counter shows 19

Please see the metric parameter to understand why your simulator is showing 19 moves by default.

QSTM is not supported but there are 2 workarounds I can think of: use STM and replace each half-turn by 2 quarter-turns like this:



Alternatively, you can hide the move counter using the counter parameter, and say somehting like "this move sequence is 21 moves long in QSTM" directly in your forum post.

 

[Tito_H]

Thanks, bcube.
I will “use STM and replace each half-turn by 2 quarter-turns” of your good idea next time.

 

[BVCuber13]

Fred, thank you so much for your quick response and amazing solution. The Earth has been saved.

I wasn't familiar with the Classic Pochmann blindsolving method, but it seems like it was an easy problem for someone who has studied BLD.

The algorithm z S' T perm S didn't occur to me, but that makes good use of the fact that PLL doesn't affect the F2L part, so it was Eureka for me!

The procedure Princess Leia came up with was shown in the simulation below, but that was 21 moves, not meeting the condition!


(21 moves in QSTM basis, although the counter shows 19. The z S' U2 S completes OLL, and the rest is left hand T perm.)

bcube, thank you for your information on the 14-moves algorithms of T perm. Those could reduce hers by one move, which also made possible to meet the condition.

To be honest, I made a mistake. I forgot to consider the last AUF's two moves when I made this guessing.

She couldn't have solved the case without your posts!

There is also a T perm from that angle that skips AUF (saves one move) entirely due to the fact that the state is a U2 off from the normal T perm. It goes like this:
L’ U’ L U L F’ L2 U L U’ F R U’ R’
I’m not sure if this would have helped Princess Leia complete the challenge but I hope this helped!

 

[Tito_H]

There is also a T perm from that angle that skips AUF (saves one move) entirely due to the fact that the state is a U2 off from the normal T perm. It goes like this:
L’ U’ L U L F’ L2 U L U’ F R U’ R’
I’m not sure if this would have helped Princess Leia complete the challenge but I hope this helped!

Oh la la!



You also saved her & the Earth!
Thanks, BVCuber13.