On the morning of July 3, Tsinghua No. 2 Teaching Building.

Erjiao is an old building, built before 1949.

It is rumored that the two religions often have supernatural events, commonly known as hauntings.

The second school is never open at night, and the school says it is to save water and electricity.

Tsinghua University, the highest scientific research and academic institution, naturally advocates science, and the ghosts, snakes, and gods only have the fate of being crushed in the face of powerful scientific forces, and they are not allowed to become refined after the founding of the People's Republic of China.

At this time, more than half of the college students have completed their final exams, and the second teacher is vacant, and this is the venue for the national preliminaries and national finals of this year's high school math league.

At 9 o'clock this morning, the national pre-production will be conducted.

With half an hour to go, a total of 192 players from 32 provinces and cities are all on standby in 201 and 202, and 10 teams with a total of 60 players will qualify for the national finals.

"Actually, I'm very satisfied to be able to come to the national races, really. Qi Jianhong, the youngest member of the Nanyue Provincial Mathematics Team, said.

Shen Qi scolded: "Qi Jianhong, you know a fart, you can't enter the national decision, let's come to Tsinghua for nothing." Do you think that you are a member of the five hegemons of Hubei, Hunan, Zhejiang, Beijing, and Shanghai, and you can get the signing of Qingbei if you are selected for the provincial team?"

Qi Jianhong was not convinced: "I don't rely on escort, can I get to Qingbei in the college entrance examination?"

Shen Qi asked, "You have good grades in other subjects?"

Qi Jianhong said proudly: "That is, in our high school, I have been the first in the whole grade for a long time, and if I can't get rid of the second place, more than 50 points will be counted as a loss." Math is just my hobby, and I dominate the whole grade by relying on invincible comprehensive strength. ”

"You're pretty awesome, but I don't care how awesome you are in your high school, you have to give me your highest level in this national preliminaries, otherwise I'll beat you." Shen Qi said resolutely.

"You, you...... It's so barbaric!" Qi Jianhong is only a little more than one meter and five, and he has no power to restrain the chicken, he will definitely not be able to beat Shen Qi, who is more than one meter and seven.

"In fact, what can I do if I beat you, from the beginning of the training camp, I repeatedly emphasized that we are a team, from the same place, and have a common dream. I can't beat the five of you alone, but I have the heart of a champion. And you guys, you're all spicy chicken. After Shen Qi finished speaking, he took his stationery set and left classroom 202 without looking back.

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

"Hmph, Shen Qi is pretending to be a coercive thing. ”

"We're not spicy chicken, we're strong!"

"Shen Qi, Soul Fade, I must defeat you!"

"I must be higher than you in the national preliminaries!"

“+1！”

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

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

Shen Qi took the exam in classroom 101, he got the national pre-examination paper, and first quickly skimmed through the three exam questions, each question was 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 score of the roll is getting lower and lower, but the difficulty is getting higher and higher.

In the first question, a pattern is drawn on the scroll.

There are two small islands floating in a river, and there are bridges between the islands and bridges between the islands.

It is a total of one river, two islands and eight bridges.

Q: How can a walker walk through eight bridges at once without repeating or missing a beat, and finally return to the starting point?

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

Shen Qi saw through everything at a glance, this question is a variant of "Euler Seven Bridges", Tsinghua Eight Bridges?

Ora, the god-level master in the history of mathematics, was energetic when he was young, he loved mathematics, and he also liked girls.

When Ora was in her twenties, she fell in love with a girl, a beautiful and gentle art teacher. He frantically pursued the art teacher and eventually achieved success, and the two got married and had 13 children...... It can be seen that Euler is not only academically top-notch, but also physically excellent.

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 gone to the appointment.

Euler was bored and began to study mathematics, and he found that there were two small islands suspended in a river in Königsberg Park, and there were seven bridges connecting the islands to the riverbank.

Euler was suddenly inspired, and he proposed that there was a path from any place where he could pass through seven bridges without missing or repeating them, and finally return to the starting point.

Euler later wrote a thesis on this idea and submitted it to the St. Petersburg Academy of Sciences under the title "Seven Bridges of Königsberg". Later generations also called it the "Euler Seven Bridges Problem".

Later, Euler himself disproved this assumption and proved that such a path could not exist.

To slap himself in the face, Euler invented a new method of proof, and he pioneered a new branch of mathematics --- geometric topology.

This is the pattern of top mathematicians, I am invincible, I have no opponents, my only opponent is myself, in order to defeat myself, I start 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 the Seven Bridges of Euler is not answered, and whether there is such a path for the Eight Bridges has to be calculated to know.

Shen Qi counts up and down, left and right, half an hour has passed, and he can't figure it out!

Whether the Eighth Bridge is the same as the Seven Bridges, there is no so-called path at all, and you can pass through each bridge without missing or repeating it, and finally return to the starting point.

"The national race is a national race after all, and the topology thing is very difficult to do, and I can't figure out the path or prove that it doesn't exist. ”

Shen Qi put down the pen ruler and pressed his temples vigorously, it was not good for him to be a teacher, it was not good for him to be a teacher.

Time passed minute by minute, Shen Qi couldn't write, he was a little obsessive-compulsive, so he had to make the first question and solve the next two questions.

"Euler, Seven Bridges, Eight Bridges...... By the way, why do I have to use Euler's theory to solve the variant problem based on Euler's Seven Bridges, this is a trap, an endless loop!"

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

If the two disconnect connections are exactly the same as before, then this is a permissible topology operation.

Otherwise, it is not allowed!

That's right, the singularity of the eight-bridge diagram is at both ends, so there is no such connection at all, and you can pass through each bridge without missing or repeating it.

The answer to this question is: No!

Shen Qi worked hard to write down the proof process, and he completed the proof in only 3 minutes, and the thinking process took 1 hour.

"Whew...... 7 points to hand, the next question. Shen Qi took a long breath and burned a lot of brain cells, so tired. But the battle has just begun, and he can't let up, he must complete all the answers within the allotted time and guarantee that he is absolutely correct.

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