I Just Want to Be a Quiet Top Student

On the morning of July 3, the second teaching building of Shuimu University.

Erjiao is an old building, built before 1949.

It is rumored that supernatural events often occur in the Second Sect, commonly known as haunted.

The Second Teaching is never open at night, the school said it is to save water and electricity.

The highest scientific research and academic institutions like Shuimu University naturally advocate science. Ghosts and snakes have only the fate of being crushed in the face of powerful scientific forces. After the founding of the People's Republic, they are not allowed to become fine.

In this season, more than half of the college students have completed the final exam, and the second teacher is free. This is the venue for the national preliminaries and national finals of this year's high school mathematics league.

At 9 o'clock this morning, the national preliminaries will be held.

With half an hour to go, a total of 192 contestants from 32 provinces and cities are all on standby at 201 and 202. Ten teams with a total of 60 players will qualify for the national final.

"Actually, I am very satisfied to be able to participate in the national competition, really." said Qi Jianhong, the youngest member of the Nanyue Provincial Mathematical Team.

Shen Qi scolded: "Qi Jianhong, you know what a shit, if you can't enter the national finals, we'll just come to Shuimu University for nothing. You think you are a member of the five tyrants of Hubei, Hunan, Zhejiang, Beijing, and Shanghai, and you can be selected for the provincial team. Get the contract of Mizuki University and Yenching University?"

Qi Jianhong was unconvinced: "I don't rely on recommended admissions, can I pass Shuimu and Yanda in the college entrance examination?"

Shen Qi asked, "Your grades in other subjects are good?"

Qi Jianhong said triumphantly: "That is, in our high school, my total score was always the first in the whole grade, and if I couldn't beat the second place with more than 50 points, I would lose. Mathematics is just my hobby. I can dominate the whole grade by relying on it." It is an invincible comprehensive strength.”

"You're a pretty good young lady, but I don't care how good you are in your high school, you must give me your highest level in the national preliminaries, otherwise I will beat you." Shen Qi resolutely said arrive.

"You, you... so barbaric!" Qi Jianhong was only around 1.5 meters tall and had no strength to restrain a chicken. He would definitely not be able to beat Shen Qi who was around 1.7 meters tall.

"In fact, it doesn't matter if you beat you up. From the beginning of the training camp, I repeatedly emphasized that we are a team, come from the same place, and share a common dream. I can't beat you five alone, but I have a champion Heart. And you are all hot chickens." After Shen Qi finished speaking, he took his stationery set and left classroom 202 without looking back.

"Shen Qi, you... you actually said we are hot chickens!" Qi Jianhong was ashamed and annoyed, and he said to the other four teammates: "Shen Qi said we are hot chickens, so hateful!"

"Hmph, Shen Qi is a pretentious thing."

"We are not spicy chickens, we are strong!"

"Shen Qi, Hun Dan, I must defeat you!"

"I will definitely score higher than you in the national preliminaries!"

"+1!"

Qi Jianhong and other five people shared the same hatred, and an unprecedented atmosphere of unity appeared in this team for the first time.

Shen Qi, Qi Jianhong and other six people were arranged in six different classrooms. At 5 minutes to 9 o'clock, the invigilator began to read the rules of the competition: "The rules are very simple. You have 3 hours to complete the national pre-examination papers, and you are not allowed to look around during the answering process. , please raise your hand if you have anything to do. After the competition rules have been read out, the examination papers and draft papers will be distributed."

Shen Qi took the exam in classroom 101. He got the national pre-examination paper and quickly scanned through the three exam questions. Each question scored seven points, and the paper score was 21 points.

From the provincial preliminaries to the provincial semi-finals, and then to the national preliminaries, the scores on the paper are getting lower and lower, but the difficulty is getting higher and higher.

For the first question, a pattern was drawn on the scroll.

There are two small islands floating in a river, the islands are connected by bridges, and the islands are connected by bridges to the river bank.

There are one river, two islands and eight bridges.

Question: How can a walker walk through eight bridges at a time without repeating or missing, and finally return to the starting point.

"Hey, who came up with this question, does Euler allow you to do this?"

Shen Qi can see through everything at a glance. This question is a variant of "Euler's Seven Bridges", Mizuki Eight Bridges?

Euler, the god-level master in the history of mathematics, was energetic when he was young. He liked mathematics and girls.

When Euler was in her twenties, she fell in love with a girl, a beautiful and gentle art teacher. He crazily pursued this art teacher and finally succeeded. The two got married and had 13 children... It can be seen that Euler is not only academically top-notch, but also in good health.

On a bright spring day in 1736, Euler was waiting for his art teacher girlfriend to arrive in a park in Königsberg.

Being late is a woman's innate attribute, waiting left and right, an hour has passed, and the girl who teaches art has not yet attended the appointment.

Euler was bored, so he started to study mathematics. He found two small islands suspended in a river in Königsberg Park, and there were seven bridges connecting the small islands and the river bank. Shuttle between two small islands.

Euler suddenly came to inspiration, and he proposed an idea, whether there is a path that can pass through seven bridges without omission or repetition from any point, and finally return to the starting point.

Later, Euler wrote this idea into a paper and submitted it to the St. Petersburg Academy of Sciences. The title of the paper was "Seven Bridges of Königsberg". Later generations also called it "Euler's Seven Bridges Problem".

Later, Euler himself overturned this assumption, proving that such a path cannot exist.

In order to slap himself in the face, Euler invented a new proof method, and he created a new branch of mathematics-geometric topology.

This is the pattern of top mathematicians, I am invincible, I have no opponent, my only opponent is myself, in order to defeat myself, I create a new branch of mathematics.

Two or three hundred years have passed, and Shen Qi is facing a new problem, the Eight Bridges problem.

The original version of Euler's Seven Bridges couldn't get the answer. As for whether there is such a path in Eight Bridges, we have to do some calculations to know.

Shen Qi counted up and down, left and right, half an hour passed, and he couldn't figure it out!

Whether the Eighth Bridge is the same as the Seventh Bridge, there is no so-called path at all, which can pass through each bridge without omission or repetition, and finally return to the starting point.

"The national competition is a national competition after all. Topology is very difficult to do. I have no way to find out this path, nor can I prove that it does not exist."

Shen Qi put down the pen ruler and pressed his temples vigorously, it was a bad start, a bad start.

As the time passed by, Shen Qi couldn't write. He was a little obsessive-compulsive. He had to solve the first question and then solve the next two questions.

"Euler, Seventh Bridge, Eighth Bridge... By the way, why do I have to use Euler's theory to solve the variant problem based on Euler's Seventh Bridge? This is a trap, an endless loop!"

Shen Qi suddenly realized, I thought of it, I thought of it, Poincaré's network theory!

This is an admissible topological operation if the two stub connections are exactly the same as before.

Otherwise it is not allowed!

That's right, the singularity of the Eight Bridges diagram is at both ends, so there is no such connection at all, and each bridge can be passed without omission or repetition.

The answer to this question is: no! live! exist!

Shen Qi frantically wrote down the proof process. It took him only 3 minutes to complete the proof, while the thinking process lasted for 1 hour.

"Phew... 7 points, next question." Shen Qi let out a long breath, burning to death a lot of brain cells, so tired. But the battle has just begun, he can't relax, he must complete all the answers within the specified time, and guarantee to be absolutely correct.

Even so, Shen Qi didn't know whether his goal could be achieved in the end. I hope those five pig teammates can win me over!