CFOP Quick-witted Princess Leia (Solving competition)

Tito_H

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May 23, 2024
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Japan
Episode XX+5
The Imperial Army
was building a second
Death Star above the moon Endor.
Princess Leia and R2D2 successfully
completed their mission to destroy the shielding
radio wave generator protecting the Death Star…

After the mission, Princess Leia and R2D2 were walking through the forest to return to their spaceship when suddenly, several small native tribesmen emerged from the bushes, pointing their long spears at them. Princess Leia gave up resistance and was taken to their tribe.

When they arrived, the chief appeared and said, "You, the woman, will spend the rest of your life here weeding. You, the machine, will be bought by the junkyard that comes by periodically." He continued, "However, I will give you a chance to avoid this. Rubik's Cube solving is currently popular on this planet, and the competition for the championship is fierce. If you can beat the current champion candidate, I will let you go."

Then, a small but unusually large-faced man emerged from a tent. His eyes were about 20 cm apart. The chief introduced him, "This man named Head is currently ranked second in the tribe, and is a master of Look-ahead."

"Let's get started. First, Head," said the chief, handing him the scrambled cube. It was a small cube, 5cm wide, just large enough to fit his small hand. He picked up the cube, positioned his head about 10cm above it, and held it at an angle. Princess Leia wondered if he was nearsighted, but upon closer observation, she noticed that both of his eyes were moving independently, like a chameleon.

"I see, he's holding his head directly above the cube, looking at the F and R faces with his right eye and the L and B faces with his left eye! His eyes are far apart, and the cube is small, so from that angle, he should be able to easily see all five faces except the bottom D face. That is the reason why he's good at looking ahead! He must have trained hard to prevent the information coming in from one eye from interfering with the information coming in from the other," she muttered to herself, impressed in a way.

He solved the cube in 15 seconds.

The chief said, "Now it's your turn," and handed her a cube that had been scrambled according to the simulation below.


(Scramble: L' F2 R2 U2 F2 R' U2 R' D2 U2 F2 U B F' D' B2 U' F2 L)

Princess Leia's abilities are at the Sub-17 level, so it seems unlikely that she will be able to win. Will Princess Leia be able to overcome this difficult situation?

Readers, please think about what measures Princess Leia might take.
 
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Let's see what Princess Leia did.

She asked R2D2, "Please use theoretical reasoning and calculate my chances of winning this scrambled cube."

R2D2 replied, "Your chances of completing it in 15 seconds are less than 20%."

She expressed her impatience, saying, "I guess I won't make it if I just solve it normally." She then asked R2D2 again, "The chief seems to respect fairness, so this scramble should be the same as the cube he gave to Head. What if I reversed the scramble and solved it?"

He replied, "In that case, your chances of completing it in 15 seconds are 75%."

She pondered, "Okay! Now all that's left is how to reverse the scramble without being noticed..." and an idea came to her. She said to R2D2, "You project the cube in the air, turning it a little bit slowly, in the reverse scramble sequence," and held up the cube.

R2D2 projected the cube into the air and began the reverse scramble, and she began moving it in the same way as the projected cube.



The chief and his tribesmen were under the illusion that the cube she was turning was being projected.

She somehow managed to solve the cube. The chief looked at his watch and said, "The time it took you to solve it was... 14.1 seconds!"

She was delighted, "Yes, I won!" but was surprised when the chief added, "Therefore, this game is a draw!" The chief explained, "In this country, decimals are rounded up, so both of the records will be 15 seconds," and said, "I'll have you try again with a different opponent. Please wait a moment."

Princess Leia seemed confused, but at any rate, she was able to breathe a sigh of relief as she had overcome the immediate challenge.
 
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