Escape the Library

【Endless Staircase-03】

The reason why the Möbius ring has become an infinite path that can never go out is because after the strip of paper is rotated, the end and the end are connected together. As long as this connection point is disconnected, the strip of paper will return to normal, and the same is true of the Penrose Staircase. .

At this time, all seven people were standing on the stairs marked with "4". After getting Xingwen's consent, Zhang Xiaonian simply used an excavator to cut the connection point between the stairs "4" and "1".

As soon as the orange-yellow excavator shoveled down, there was a crisp sound of "pop" in everyone's ears, as if the building blocks were broken. Immediately following, there was another sound of "Boom", and the stairs under their feet actually began to rotate!

Yue Xingwen immediately reminded: "Everyone stand firm!"

Everyone was swayed to and fro, and hurriedly held on to the handrail on the right side of the stairs. The entire staircase took them 180 degrees counterclockwise before they stopped steadily.

Everyone looked at each other.

Ke Shaobin whispered, "Harry Potter's Magic Castle?"

Qin Lu was stunned, and said, "This staircase actually moves. It seems that there is a hidden mechanism?"

There was another staircase in front of them, which was connected to the staircase marked "4" where they were located, and there was no "1" mark on the front staircase. That is to say, the original four flights of stairs with 1, 2, 3, and 4 connected end to end and infinitely looped, because the connection point was disconnected, the distorted space returned to normal, and the top of 4 was no longer connected to 1, but a new section. steps.

Yue Xingwen looked overhead and could still see the familiar glass ceiling. The scene around him didn't seem to have changed at all, and all the stairs looked exactly the same as before.

Unconsciously, they have actually followed the rotation of the stairs and came to another space.

Jiang Pingce frowned and said, "Xiao Nian, measure the distance."

Zhang Xiaonian immediately took out the laser rangefinder, measured the distance between the current staircase and the roof, and said in surprise, "The distance has changed, it's 27.5 meters!"

Just now, they were 30 meters away from the roof.

From the 1st floor to the 2nd, 3rd, 4th floor, and then to the 1st floor, no matter where you are, the distance from the roof is 30 meters. This shows that they have been climbing up on the surface, but in fact, they are constantly circling on a strange level.

That's the weird thing about Penrose Stairs - what the eyes see doesn't match the space the body is in.

Now 27.5 meters from the ceiling, apparently they went up 2.5 meters!

Jiang Pingce said: "It seems that we finally left the first floor."

Zhang Xiaonian said excitedly: "Each floor is 2.5 meters high. Just now, it was 30 meters from the roof. Suppose we were on the 1st floor; now the distance is 27.5 meters, and this is the real 2nd floor!"

Jiang Pingce closed his eyes and quickly drew a three-dimensional geometric model in his mind.

After clarifying his thoughts, he looked at Yue Xingwen and said: "We can understand this building as a tower-like structure. The total height is 30 meters, the floor height is 2.5 meters, and there are a total of 12 floors of towers. Each floor tower , is an independent space, and the interior of the space is a four-story circulation staircase connected to each other. Between the towers on each floor, hidden organs are connected to each other.”

While listening, Ke Shaobin drew a model diagram on the computer, and soon he drew a structure of a 12-story tower, each of which consisted of 4 flights of stairs. Ke Shaobin rotated the laptop screen and asked Jiang Pingce, "Is that what you mean?"

Jiang Pingce nodded: "Almost."

Zhang Xiaonian looked at the model diagram and said excitedly: "It's very clear from this look. The space inside each tower is calculated independently. We are now from the first tower to the second tower. The mechanism between the two towers, It's the connection between the 4th staircase and the 1st staircase." He looked at Jiang Pingce with admiration, "Senior brother, do you know architectural design too?"

Jiang Pingce said lightly: "Using solid geometric reasoning, the principle is the same."

Everyone leaned over to take a closer look, and as soon as the picture was drawn, everyone immediately felt that the three-dimensional maze in front of them became more intuitive. Just now, the circular staircase they couldn't climb out was actually "the first floor space of the 12-story tower", and Zhang Xiaonian used an excavator to dig out the connection point of the 4th and 1st stairs, triggering the mechanism, and the stairs rotated, making the first floor The space is connected to the second floor space.

So, where is the mechanism connecting the second floor space to the third floor space?

Yue Xingwen thought about it carefully and said, "Well, Brother Zhuo also marked it according to the tower-like structure. Now it is a 2-story tower, which is written as 2-1, 2-2, 2-3, 2-4, and when it reaches 3 For the tower, just write 3-1, 3-2 so that there will be no confusion later."

All the stairs look exactly the same, and it's hard to tell them apart without labels. The way of labeling that Yue Xingwen said is really intuitive, and everyone knows what level of plane they are on when they look at the label.

Yue Xingwen said: "Senior brother, please change your position with me. You go ahead so that it is convenient to mark."

Zhuo Feng nodded, summoned a golden electric current, and burned a [2-1] mark on the front steps.

Everyone continued to climb up. The stairs here are the same as before. It is also a section of stairs divided into 13 steps, inclined upwards at an angle of 45 degrees, with a total vertical height of 2.5 meters, and an angle of 90 degrees with the connected stairs.

After climbing 2-1, 2-2, and 2-3, they returned to the level marked "4" just now.

Encounter the Penrose Cycle Ladder again!

Zhuo Feng burned a "1-4" and "2-4" on the "4" layer.

Jiang Pingce said: "It seems that the fourth step is the connection point between the first floor space and the second floor space. In order to verify the conclusion, Xiao Nian, you can dig it out and take a look."

Zhang Xiaonian nodded and dug up the connection point between 2-4 and 2-1. The familiar rumbling sounded, the steps they were on began to rotate 180 degrees counterclockwise again, and then, the familiar "1" appeared in front of them!

Yue Xingwen said: "Turn 180 degrees counterclockwise, turn 180 degrees again, and we turn back again?"

Zhang Xiaonian took a measurement with a laser rangefinder and said excitedly, "30 meters from the roof, we have indeed returned to the first floor!"

It seems that Jiang Pingce's inference is completely correct.

Yue Xingwen patted Jiang Pingce's shoulder with a smile: "Tower-like structure, each tower is calculated independently, thank you for thinking of it."

Jiang Pingce's three-dimensional geometry is very powerful. Yue Xingwen has always known that his spatial imagination is not comparable to that of ordinary people. Even if he is not an architecture major, he can analyze the core design of this maze through data reasoning and geometric modeling. Ding, Yue Xingwen admired very much in his heart, and couldn't help but look at Jiang Pingce and said, "Next, you lead the team, and I will follow you."

The corners of Jiang Pingce's lips lifted lightly: "Well."

He looked at Zhuo Feng and said, "Brother Zhuo, please remark the stairs on the first floor."

Zhuo Feng changed the 2, 3, and 4 marks that were originally burned into 1-2, 1-3, and 1-4, indicating that this is a first-floor space. Among them, 1-4 and 2-4 are the same step, which is the connection of the organ.

Jiang Pingce said: "Disconnect the organ and go to the second floor."

Zhang Xiaonian disconnected the connection point again and returned to the second-floor space just now.

After everyone took a few steps up, Jiang Pingce said, "Disconnect 2-2 and 2-3."

Zhang Xiaonian operated quickly. After disconnecting 2-2 and 2-3, the 2-2 stairs where they were located also began to rotate. This time, it was rotated 90 degrees clockwise and connected to the next floor. Everyone saw the familiar " 1-2".

Lin Manluo was stunned: "Have we returned to the first floor?"

Jiang Pingce said: "Disconnect 1-4 and 1-1, go to the 2nd floor, and then disconnect 2-3 and 2-4."

Zhang Xiaonian obediently followed Jiang Pingce's instructions. Everyone returned to the second floor. Zhang Xiaonian opened the connection point between 2-3 and 2-4. After the 2-3 staircase was rotated, a new unmarked staircase appeared in front of him.

Without Jiang Pingce's reminder this time, Zhang Xiaonian consciously took out the laser rangefinder, measured the distance between the current position and the roof glass skylight, and said excitedly: "The distance from the roof is 25 meters, and we came to the third floor tower. !"

Everyone looked at each other with a hint of joy in their eyes.

Jiang Pingce calmly concluded: "Each tower is composed of four Penrose staircases that are connected end to end, and the connection points between the steps are the hidden organs, two of which lead to the upper floor and two to the next floor. If the space in the back also follows this rule, every time we go to a new floor, we exclude the steps we are on, and we only need to do 3-to-2 multiple-choice questions. Walk through it once, and the maze will become very easy."

Ke Shaobin couldn't help complaining: "Others will probably faint when they come in, but you said it's very simple."

Jiang Pingce: "..."

Yue Xingwen said with a smile: "It's very simple for us Pingce, he has done geometric modeling in his mind."

Jiang Pingce looked indifferent: "Keep walking. I don't think the maze created by designer Zhao should always follow the same pattern and repeat it 12 times in a row."

Zhang Xiaonian agreed: "I also think that it took us 10 minutes to go to the third floor space. If the following rules are the same, we can go out in less than half an hour."

Yue Xingwen said: "Hurry up and keep going."

Everyone continued to move up. Zhang Xiaonian dug up the connection point between 3-2 and 3-3. After the stairs were rotated, a new step was connected in front of him. After walking to the new step, the distance was measured. It was 22.5 meters. Zhang Xiaonian said: " Fourth floor!"

Jiang Pingce: "Continue."

According to distance reasoning, the 30-meter-high building has 2.5 meters on the first floor, and the whole building has 12 floors. At present, they have reached the 4th floor, and the rules of the first 4 floors are the same, so it's not like they have all the same rules until they reach the 12th floor, right?

Zhuo Feng marked the [4-1] mark on the steps ahead.

Everyone continued to go up, and just after a few steps, a strange "boom" sound came from their ears, and the steps they were on suddenly broke from the middle!

Jiang Pingce and Zhang Xiaonian walked at the forefront for distance measurement, Zhuo Feng had to mark and walked side by side with them, and the rest of Yue Xingwen, Ke Shaobin, Qin Lu and Lin Manluo walked behind. Everyone followed closely with each other, no more than one step forward and backward.

However, the stairs snapped off at their feet!

Yue Xingwen almost stepped on the air, when Jiang Pingce heard the sound, he turned around almost like a conditioned reflex, and grabbed Yue Xingwen's arm suddenly: "Be careful!"

The broken steps made the four of Yue Xingwen empty, and they fell rapidly!

Zhuo Feng shouted: "Manluo!"

Lin Manluo reacted very quickly, her right hand suddenly stretched out, and the green vines climbed upwards like a snake in an instant, directly wrapping around Zhuo Feng's waist, Zhuo Feng grabbed the other end of the vine and pulled her up, Lin Manluo hung in the air, His face turned pale: "Qin Lu and Xiao Ke fell off!"

Yue Xingwen's entire body was also suspended in the air at this time. He turned his head and looked behind him. He could no longer see the figures of Ke Shaobin and Qin Lu. Under his feet were densely packed staircases, like an abyss... Will they fall into Bolognese?

Yue Xingwen's heart trembled, and he hurriedly grabbed Jiang Pingce's hand.

Jiang Pingce's back was tense, and the veins on the back of his hands burst out. He held Yue Xingwen tightly, and said solemnly, "I'll pull you up."

Yue Xingwen nodded: "Yes."

Jiang Pingce squatted down halfway, grabbed Yue Xingwen's hand with his right hand, and held Yue Xingwen's shoulder with the other hand and pulled up hard. With his strength, Yue Xingwen climbed up with both hands and feet, and sat on the stairs. Beside him, he gasped in fright.

Lin Manluo was also pulled up by Zhuo Feng with vines.

Yue Xingwen glanced down, Ke Shaobin and Qin Lu disappeared, only the screams when they fell, Yue Xingwen hurriedly typed on the research group channel: "Ke Shaobin, Qin Lu? Are you still there? ?"

After a while, Ke Shaobin replied: "We fell back to the 1st floor. I saw the 1-2 mark drawn by Senior Brother Zhuo."

Yue Xingwen said: "It's fine if you're okay!"

Qin Lu and Ke Shaobin were also very frightened. When they fell directly, they thought they would fall to their death, but they fell back into a layer of space. Ke Shaobin was falsely alarmed and typed: "Fortunately, it is not a survival course, otherwise we are now It's a meatloaf."

Qin Lu also calmed down and said, "I located the position of 4-1 on the globe just now. Do you want to send it over?"

Yue Xingwen said, "Come back."

Qin Lu turned on the plate swap, and the two of them appeared at the stairs. Lin Manluo's face softened a little: "The stairs were broken too suddenly just now, I didn't have time to hold you, you two didn't fall hurt!"

Ke Shaobin smiled and said, "It's okay, senior sister."

This floor of stairs has been completely broken, and the distance between the breaks is more than 2 meters, and they can't jump over it.

Qin Lu asked, "Should I move again?"

Lin Manluo said, "I'll come, save your skills."

After she finished speaking, she raised her right hand, and five green vines rushed out of her hands, and built a green "vine bridge" between the broken stairs. At the same time, the other end of the vine was tied to Ke Shaobin and Qin. The waist is exposed, so that the two will not fall off.

Lin Manluo said, "Come over here, be careful."

Ke Shaobin and Qin Lu took a few steps forward, and Zhuo Feng and Lin Manluo immediately grabbed their hands and pulled them over in one breath. The crowd gathered again. Seeing that neither of them were injured, Yue Xingwen finally breathed a sigh of relief and said, "Scare me, this staircase was really broken by surprise."

Jiang Pingce looked down at him: "Are you all right?"

Yue Xingwen sat on the steps next to him, smiled and shook his head: "It's alright, just a false alarm. Fortunately, I'm not a big fat man, otherwise, you might not be able to pull me, and I'll pull you down instead."

Just kidding, it seems to be fine. Jiang Pingce stretched out his hand to Yue Xingwen who was sitting next to him, Yue Xingwen handed it to him naturally, Jiang Pingce pulled him and made Yue Xingwen stand firm, then he looked at his teammates and said, "Fourth floor In the beginning, the rules of the stairs are different from before, it is very likely that it will suddenly break when you reach the middle, everyone be careful with your feet!"