Escape From the Library

【Endless Stairway-02】

At 8 o'clock in the morning, the course examination of "Endless Staircase" officially started.

Yue Xingwen only felt that his eyes went dark, and when he regained his vision again, he found that everyone was inside a building.

There is a slanting staircase at a 45-degree angle in front of it, and at the end of the staircase is connected to the next staircase. All the stairs form a "back"-shaped hollow structure. Looking up, you can see the transparent glass skylight at the top of the entire building.

The floating frame brushed over the course prompt: "The exam begins, please walk to the roof of the building within one hour."

In other words, this maze is composed of countless stairs, as long as you climb the stairs to the top floor, you will complete the exam.It sounds very simple, can't you get out if you climb all the way up?However, this course is a maze class in the School of Architecture, and it will certainly not be easier than the prime number maze in the School of Mathematics!

The complexity of the maze in the School of Mathematics lies in the calculation of prime numbers. Just looking at the internal structure of the maze, there are only three floors: upper, middle, and lower. As long as you draw pictures while walking, you can always get out.

However, the building of the School of Architecture does not yet know how many floors it has.Yue Xingwen didn't dare to be careless. He looked at his teammates and said, "I don't know how many stairs there are in the three-dimensional maze. Don't disperse. If the maze changes dynamically, you won't be able to find it if you get separated."

Zhang Xiaonian looked up at the glass ceiling, and took out a laser range finder to measure it. The floor height of this building reached 30 meters. According to the calculation of a building with a floor height of 2 to 5 meters, the whole building should be 3 meters high. Between ~10 layers.

The internal structure of the building is very similar to a common shopping mall. When people are on the first floor, they can look up and see the glass shed on the roof. The hollow part of the "Hui" character is often used to hang festival balloons and various activities. The escalator circles diagonally upwards, from the first floor to the top floor, which is very intuitive at first glance.

From where they are now, they can directly see the roof of the building.

However, the 3-credit course of the School of Architecture cannot allow them to climb a few floors just like walking in a shopping mall. There must be some mystery inside.

Yue Xingwen looked back at Zhang Xiaonian: "Xiaonian, can you see what's wrong with this staircase?"

Zhang Xiaonian shook his head: "I can't see it yet. The interior design of this building is nothing special. It is exactly the same as the usual shopping malls. We have to go to the second floor to see if there is a mechanism?"

Yue Xingwen said bluntly: "Let's go, try to climb one floor first, Ke Shao pays attention to modeling, and Xiaonian measures the distance."

Ke Shaobin immediately took out his laptop, created a new document, and asked Xiaotu to take pictures and draw the stairs.

Yue Xingwen reminded: "Everyone follow closely, I, Ping Ce, and Xiaonian are in a group of 3 people, and the rest are in a group of 4 people. The distance between each other should not exceed 1 step, so as not to suddenly break the stairs or change direction. "

Suddenly the stairs change direction?This is impossible in reality.

But the library is a magical university. Who knows if this building will suddenly become Harry Potter's castle, and the stairs will be broken in the middle, or change directions?There is nothing wrong with Yue Xingwen being cautious.

The seven people were divided into two groups according to Yue Xingwen's instructions, and they climbed up with their front feet followed by their back feet.

They quickly climbed up one floor, Jiang Pingce said: "A floor has 13 steps."

Zhang Xiaonian said: "The height of the floor is 2 meters, and the inclination angle is 5 degrees."

Ke Shaobin quickly entered the data into the computer, built the model, and said, "There are 1 steps on the first floor. Where are we now, on the second floor?"

Zhuo Feng said: "Do you want to make a mark on the stairs, so as not to be confused later?"

Yue Xingwen said: "Brother, can you make a mark?"

Zhuo Feng raised his right hand slightly, a golden electric current suddenly appeared in his hand, and the electric current shot out with a "sizzling" sound. He controlled the golden electric current, as if he was holding a golden leather whip in his hand.When the electric current touched the stairs, Zhuo Feng wrote a "1" with his fingers, and the golden current followed his fingers, burning a charred "1" on the stairs.

Then, he burned a "2" on the stairs on the next floor.

Everyone: "..."

The marks burned out by electric current cannot be erased by rubbing.

Yue Xingwen couldn't laugh or cry: "Your electricity can still be used like this?"

Zhuo Feng withdrew his hand and coughed lightly: "The enhanced electricity can burn anything."

Yue Xingwen praised: "With the mark of the senior brother, we won't be in a mess, everyone keep up."

After walking up the second floor, Jiang Pingce reported the data: "The second floor also has 13 steps."

Zhang Xiaonian said: "The data is the same as before."

Yue Xingwen said: "Continue."

Everyone followed Yue Xingwen and walked quickly through the third floor.

Jiang Pingce frowned slightly: "It's still the same as before."

Zhuo Feng burned a black "3" character on the steps with electricity, representing the third floor.

Yue Xingwen was puzzled: "The same stairs, keep going up? The School of Architecture can't be so boring, right? Let's continue to climb up."

After everyone walked up to the fourth floor, Jiang Pingce said: "13 steps."

Ke Shaobin entered the data, and then, everyone followed Yue Xingwen through the corner, and when they continued to go up, they were shocked to find that there was a charred "1" on the stairs ahead.

Everyone looked at each other in blank dismay: "What's the situation?"

Lin Manluo looked at Zhuo Feng suspiciously: "Isn't this the mark you burned on the first floor just now?"

Zhuo Feng was also a little confused: "We obviously climbed up to the 4th floor, how could we return to the 1st floor?!"

Yue Xingwen couldn't figure it out either. They had been climbing up the stairs just now, and they climbed up 4 floors in a row, but the number "1" appeared in front of them. Never mistaken.

Obviously walking up, how come back to the first floor?

Jiang Pingce looked up at the glass window on the roof, and frowned slightly: "After climbing 4 floors, we returned to the 1st floor. If we continue to climb, we will still return to the 1st floor, and we will never get out."

Yue Xingwen said: "Just to verify, Senior Brother Zhuo, you wait here. Qin Lu, you come with me and get a seat here. If it's not right, Qin Lu can still come back from the plate movement."

Qin Lu nodded and followed Yue Xingwen.

The two quickly climbed up, and after climbing four floors in a row...

Sure enough, he joined up with a few teammates.

Seeing Yue Xingwen and Qin Lu who obviously climbed up the stairs from the front and appeared behind them not long after, everyone looked at each other in blank dismay.Qin Lu whispered: "Turn around and return to the original place, isn't this the same as a ghost hitting a wall in a horror movie?"

Ke Shaobin adjusted his glasses, and said: "In horror movies, it often happens that the main character is trapped in the stairs at night, desperately running up or down, and ends up running several floors in a row before returning to the original point..." He was nervous Looking at Yue Xingwen calmly, "Could it be that we also met a ghost hitting the wall? Will we never get out?"

Yue Xingwen looked back at Zhang Xiaonian, who was staring at Ke Shaobin's laptop in deep thought.Following his gaze, it happened to be a three-dimensional figure modeled by Ke Shaobin in the computer.

Because when everyone was climbing up just now, Zhang Xiaonian measured the data, and the three-dimensional map Ke Shaobin drew was very similar to the stairs that everyone saw with their eyes, and it was almost an equal-scale restoration.It can be found from the perspective view that the angle between the first floor and the second floor is 90 degrees; the angle between the second floor and the third floor, and the third floor and the fourth floor is also a vertical 90-degree angle.

Yue Xingwen saw that his younger brother looked serious, so he couldn't help asking softly, "Xiao Nian, did you find anything?"

Zhang Xiaonian came back to his senses, pointed to the modeling graphics and said: "Assuming that the front is north, the direction of the stairs on the first floor is from west to east, the second floor is from east to south, the third floor is from south to west, and the fourth floor is from west to north." , just forming a ring structure.”

Jiang Pingce took a closer look, and it was true.

The direction of the stairs they walked was →, ↓, ←, ↑, forming a ring structure.

Zhang Xiaonian confirmed: "This should be the Penrose ladder."

Zhuo Feng raised his eyebrows suspiciously: "Penrose Stairs? What do you mean?"

Zhang Xiaonian stretched out a hand and made a simple gesture in the air: "In the three-dimensional space, we are always going up. It is impossible to go up four floors in a row and return to the first floor. But if this is not the three-dimensional space , the distorted space connects the tail of the fourth floor with the starting point of the first floor, which will form a closed, three-dimensional "back"-shaped staircase passage. No matter how many times we walk, we will always be in this back-shaped staircase. Spin inside."

Jiang Pingce suddenly asked, "Similar to the 'Mobius strip'?"

The others looked at them blankly, these technical terms were really incomprehensible to liberal arts students.

Jiang Pingce simply explained: "The Möbius strip is to twist a piece of paper 180 degrees and connect it end to end. The original two-sided paper will become only one curved surface. Assuming that the Mobius The tape has been magnified into a building, and we walk forward on this paper tape, no matter how long we walk, we will never get out, which is very similar to the Penrose ladder that the younger brother said."

Zhang Xiaonian nodded: "Yes, the key to the 'Möbius Strip' is to twist the paper strips by 180 degrees, but the buildings in the three-dimensional world cannot twist the stairs, so the 'Penrose Staircase' has always been an unachievable building Hypothesis. But the space of the library can be distorted, the first floor and the fourth floor are connected end to end, and there is a closed circular staircase that cannot be walked out.”

No wonder this course is called "Endless Staircase". It turned out to be a circular staircase design similar to "Ghosts Hitting the Wall". Let alone walking out of the maze in an hour, even if they climb here for 1 hours, they will continue to climb from the 10th floor back to the 4st floor. Floor, never ending.

Yue Xingwen rubbed his temples: "How do we get out of the building whose space is distorted?"

Zhang Xiaonian's expression was tangled: "Climbing the stairs won't work, it will only go around repeatedly on the 4th floor and the 1st floor. To crack the Penrose ladder, we must find out where the distorted part is and return the space there. "

Jiang Pingce said lightly: "Break the connection point that connects end to end, and you can break the closed loop."

Zhuo Feng said: "That is, the connection point between the first floor and the fourth floor?"

Zhang Xiaonian hurriedly shook his head: "Not necessarily, it may be the connection point between the 2nd floor and the 3rd floor, and the 3rd floor and the 4th floor is the distorted part. The four-story staircase is like four independent building blocks. Originally, the four building blocks They all go up, but one piece is twisted and connected to the other. Since we cannot see the model outside the three-dimensional space from the perspective of God, which piece is distorted, we cannot make hasty judge."

Zhuo Feng understood: "You mean, the '1' I marked is not necessarily the 1st floor? It is possible that the place where we first appeared was the 2nd or 3rd floor? Anyway, the four floors of stairs are exactly the same, keep going up , and connected to each other, where is the 1st floor and where is the 4th floor, in fact, we can't confirm, right?"

Zhang Xiaonian said: "That's what it means."

Everyone looked at each other and fell into a daze for a while.

Ke Shaobin carefully looked at the modeling graphics, scratched his head and said: "The four stairs are indeed exactly the same, including the angle, the number of steps, and the length data. After the ring connection, it looks like a distorted square."

Yue Xingwen looked at Jiang Pingce: "I really don't understand these things, tell me, how do you find the exit?"

Jiang Pingce said decisively: "Xiao Nian, measure the data on each floor of the stairs to see if there is any difference in the height of the stairs from the ceiling."

Zhang Xiaonian quickly reported the result: "The height of the ceiling is exactly the same for the four floors of stairs."

Yue Xingwen had a headache and said: "That is to say, we seem to be climbing up all the time, but in fact, we have always been on the same plane, and the height has not changed?"

Zhang Xiaonian nodded: "This is the strangeness of the 'Penrose Staircase'. It seems to be going up all the time, but it is actually spinning around on the same plane. Three-dimensional space cannot explain this phenomenon, and it is possible only in higher dimensions. Appear."

Jiang Pingce said: "The four floors are all the same, so we can only try one by one."

Zhang Xiaonian summoned the excavator.

Everyone: "..."

So, is this maze going to be done with an excavator?

Zhang Xiaonian looked at the team leader inquiringly: "Brother, did I cut off the connection?"

Yue Xingwen helped his forehead helplessly: "Okay, let's dig."