【Endless Staircase-02】

At 8:00 in the morning, the course examination of "Endless Staircase" officially started.

Yue Xingwen only felt that it was dark in front of him. When he regained his vision again, he found that everyone was inside a building.

In front of you is a 45-degree slanted upward staircase. The end of the stairs is connected to the next flight of stairs. All the stairs form a "back"-shaped hollow structure. See the clear glass skylight at the very top of the entire building.

Brushing the course prompt in front of you: "The exam starts, please get out of the rooftop of the building within an hour."

That is to say, this maze consists of countless stairs, as long as you climb the stairs to the roof on the top floor, you will complete the exam. It sounds very simple, can't you get out when you climb all the way up?

However, this class is a maze class in the School of Architecture, and certainly no easier than the maze of prime numbers in the School of Mathematics!

The maze of the Mathematical Institute is complicated by the operation of prime numbers. Just looking at the internal structure of the maze, there are only three floors: the upper, middle, and lower floors, which are connected by elevators. As long as you walk and draw a plan, you can always go out.

But the building of the School of Architecture does not yet know how many floors there are. Yue Xingwen did not dare to be careless. He looked at his teammates and said, "The three-dimensional maze, I don't know how many floors there are. Don't spread out, Wan Wan. One? The maze will change dynamically, and if you get lost, you can’t find it.”

Zhang Xiaonian raised his head? He looked at the hollow glass ceiling in the center of the "hui" shape.

The internal structure of this building is very similar to a common shopping mall. When people look up on the first floor, they can see the glass shed on the roof. The hollow part of the "back" shape is often used to hang holiday balloons. , as well as advertisements of various activities, the escalator is inclined upward, from the first floor to the top floor, it is very intuitive at a glance.

Where they are now, they can directly see the rooftop of the building.

However, for the 3-credit course of the School of Architecture, it is impossible for them to climb a few floors and go out like a shopping mall. There must be some mystery inside. Yuexingwen's approach of telling everyone not to scatter is right.

Yue Xingwen turned back? Looking at Zhang Xiaonian: "Xiao Nian, you? Can you see what's wrong with this staircase?"

Zhang Xiaonian shook his head: "At present, the interior design of this building is very conventional, exactly the same as the usual shopping malls, we have to walk two floors to see the difference before we can see the difference. ."

Yue Xingwen said simply: "Let's go, try climbing a floor first, Ke Shao pays attention to modeling."

Ke Shaobin immediately took out his laptop, created a new three-dimensional document, and let Xiaotu take pictures and draw the stairs.

Yue Xingwen said: "Everyone follow closely, I, Ping Ce and Xiao Nian will form a group of 3 people, and the remaining 4 people will form a group, and the distance between each other should not be more than 1 step, so as to avoid the stairs suddenly breaking and going away. "

Stairs suddenly broken? This is not possible in reality.

But the library is a magical university, who knows if this building will suddenly become Harry Potter's castle, walking, and the stairs are broken in the middle, or change direction? Yue Xingwen is more cautious? It's not wrong.

The 7 people immediately divided into two groups according to the instructions of Yue Xingwen, and climbed up with the front foot and the back foot.

They quickly climbed the first floor, and Jiang Pingce said, "A floor is 13 steps."

Ke Shaobin quickly entered the data into the computer: "The first floor, 13 steps, where are we now? The second floor?"

Zhuo Feng said, "Would you like to make a mark on the stairs?"

Yue Xingwen said: "Senior brother, is there a way to mark it?"

Zhuo Feng's right hand was slightly raised, and the golden electric current in his hand flowed out with a "Zizi" sound. He controlled the golden electric current like a golden leather whip in his hand. When the current touched the stairs, Zhuo Feng wrote a "2" with his finger, and the golden current followed his finger movement, burning a black "1" on the stairs.

Then, he burned out a "2" on the next flight of stairs.

Everyone: "..."

The marks burned by electricity cannot be wiped off!

Yue Xingwen didn't know whether to laugh or cry: "Can your electricity 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 senior brother, we will not be in chaos, everyone will continue to go up."

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

Yue Xingwen said: "Continue."

Everyone followed Xingwen closely and walked quickly to the third floor.

Jiang Pingce frowned slightly: "The 13 steps are the same as before."

Zhuo Feng used electricity to burn a black "3" on the steps, representing the third floor.

Yue Xingwen was a little confused: "The same steps, keep going up? The School of Architecture won't be so boring, let's continue."

After everyone finished the fourth floor, Jiang Pingce said, "13 steps, with an angle of 90 degrees."

Then, when everyone walked around the corner and continued to go up, they were shocked to find that——

On the stairs in front, a charred "1" appeared.

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

Lin Manluo looked at Zhuo Feng suspiciously: "Isn't this? You? Just now? Is it the burn marks on the first floor?"

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

Yue Xingwen couldn't figure it out either. They just kept going up and climbed up 4 floors in a row. As a result, the number "1" appeared in front of them. This is the trace that Brother Zhuo just burned. Everyone Can never be wrong.

Jiang Pingce raised his head and glanced at the glass ceiling that seemed to be close at hand, frowning slightly: "After climbing the 4th floor and returning to the 1st floor, we will continue to climb up, or will we return to the 1st floor, in a cycle, and never get out. "

Qin Lu said in a low voice, "Isn't this the same as the ghost in a horror movie?"

Ke Shaobin adjusted his glasses and said, "In horror movies, the protagonist is often trapped in the stairs at night, desperately running up or down. "..." He looked at Yue Xingwen nervously, "Did we also encounter ghosts hitting the wall? Can't get out forever?"

Yue Xingwen turned back and looked at Zhang Xiaonian, who was staring at Ke Shaobin's laptop and pondering.

Following his gaze, it happened to be a three-dimensional figure modeled by Ke Shaobin in the computer.

Because Jiang Pingce has been reporting data and angles, the three-dimensional picture drawn by Ke Shaobin is very similar to the stairs that everyone sees, almost a photo restoration. It can be found from the three-dimensional diagram that the angle between the first floor and the second floor is 90 degrees; between the second floor and the third floor, the third floor and the fourth floor is also a vertical angle of 90 degrees. .

When Yue Xingwen saw his younger brother's serious expression, he couldn't help but ask softly, "Xiao Nian, did you find anything?"

Zhang Xiaonian returned to his senses, pointed to the modeling graphics and explained: "Assuming that the front is the north side, 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 south to west. The building runs 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 exactly ?→, ↓, ←, ↑, forming a ring structure.

Zhang Xiaonian said, "This is the Penrose Staircase."

He stretched out a hand, made a simple gesture in the air, and said: "In the three-dimensional space, we have been walking up, it is impossible to go up four floors in a row, and then return to the first floor. However, if this is not a three-dimensional space, and the twisted space connects the tail of the fourth floor with the starting point of the first floor, it will form a closed, three-dimensional 'back'-shaped staircase The passage, no matter how many times we walk, we will always be spinning in this return staircase."

Jiang Pingce suddenly said: "Similar to, Mobius belt?"

The others looked at them blankly. These professional terms, liberal arts students do not really understand.

Jiang Pingce briefly explained: "Möbius strip is to twist a piece of paper 180 degrees and connect it end to end. The original paper strip with two sides will become only one curved surface. Suppose, the Mobius strip is enlarged into a building, and we walk forward on this paper strip, no matter how long we go, we will never get out.”

Zhang Xiaonian nodded: "Yes, the key to the Mobius belt is to twist the note 180 degrees, but ordinary three-dimensional buildings cannot distort space, so the Penrose Staircase has always been? The architectural hypothesis that cannot be realized. But the space of the library can be distorted, and the first floor and the fourth floor are connected end to end, and there is a closed circular staircase that can’t go out.”

No wonder? This course is called "Endless Staircase". It turned out to be a circular ladder design similar to "Ghosts Beating the Wall". They don't say it is? It takes 1 hour to walk out of the maze. Even if you climb here for 10 hours, you will continue to climb from the 4th floor. Climb back to the 1st floor, never ending.

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

Zhang Xiaonian looked tangled: "One? Climbing the stairs all the time, it will definitely not work, that will only turn around on the 4th and 1st floors. To crack the Penrose Staircase, we must find where the distorted part is and find the space there. Giving back."

Jiang Pingce said lightly: "Xiao Nian right? That's right, you can break the closed loop by disconnecting the end-to-end connection point."

Zhuo Feng said: "That is, the connection point between the 1st floor and the 4th floor?"

Zhang Xiaonian hurriedly shook his head: "Not sure, it may be the connection point between the 2nd and 3rd floors, and the 3rd and 4th floors is the distorted part. The four-story stairs are like four independent blocks. The building blocks, originally, the four building blocks were all going up, but one of them was twisted and connected with the other one. Because we can't see it from God's perspective The model outside the three-dimensional space, which piece is distorted, cannot be judged hastily."

Zhuo Feng understood: "What do you mean? The '1' I marked may not necessarily be the 1st floor? Maybe the place where we first appeared was the 2nd floor or the 3rd floor? Anyway The four floors of stairs are exactly the same, go straight up, and are connected to each other, where is the first floor, in fact, we can't confirm it?"

Zhang Xiaonian said: "Yes? What does this mean?"

Everyone stopped in place, and fell into a daze for a while.

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

Jiang Pingce said decisively: "Choose one of the four, let's try it one by one."

Zhang Xiaonian nodded, then summoned the excavator.

Everyone: "..."

So, this time the maze, is it? Have you ever used an excavator?

Zhang Xiaonian asked questioningly and looked at the team leader, Yue Xingwen helped his forehead helplessly: "Okay, let's dig." w, please keep in mind:,