A fat man who was reborn from the dead? He transforms into a perfect male god in a week.

That afternoon.

The Binhai University Gymnasium was packed with people.

Representatives from 122 counties in 14 prefecture-level cities across the province gathered together, filling the 5,000-person hall to capacity.

The Jiangcheng team's seats were arranged in the very back corner, so secluded that even the lights couldn't reach them.

"Damn it, this position... it's like standing there like a lackey!"

Teacher Wang from Jiangcheng No.1 Middle School couldn't help but mutter a complaint under his breath.

Teacher Li took it in stride: "There's nothing we can do; Jiangcheng is just a small place."

"The educational resources are incomparable to those in the provincial capital; it would be good if we could get a dozen or so competition slots combined."

Zhou Dapeng didn't speak, but squinted at the front of the hall.

There.

Under the spotlight.

The four teams stood out.

Changjun Middle School, Yali Middle School, Binhai No.1 Middle School, and Binhai Normal University Affiliated Middle School.

The four prestigious schools in the provincial capital are undoubtedly in the spotlight, surrounded by admirers.

Their students all stood tall and proud, their eyes radiating innate confidence...

Or rather, it's arrogance.

"See that? That's Qin Mo, the incredibly talented student from Changjun High School."

Lin Feng, sitting in the row in front of Jiang Chen, turned around, pointed to a handsome boy wearing black-rimmed glasses in the very front row, and said in a low voice:

"He won first prize in the provincial math competition last year when he was a junior in high school and had already been admitted to the math departments of Tsinghua and Peking Universities. He's participating again this year purely to boost his resume... His goal is to join the national team and win a gold medal at the IMO!"

Jiang Chen looked up.

Qin Mo was looking down at a thick English original mathematics book, his expression focused, as if everything around him was irrelevant.

"Pretentious show-off."

Li Fan, a contestant from Jiangcheng No. 2 Middle School, muttered to himself.

Tang Ruoxi smiled, pursing her lips.

Lin Feng continued, "There's also Zhou Cheng from Yali Middle School, Zhao Rui from Binhai No.1 Middle School, Su Baibai from the High School Affiliated to Normal University... These are all monsters on par with Qin Mo."

"I heard that the four of them often practice problems together and compare their skills, but their levels are about the same. Last year, they won four provincial first prizes and were all admitted to Tsinghua and Peking Universities through the recommendation system."

"This year, their first prize in the province is just the beginning. Their goal is to join the provincial team, win the national first prize, and then strive for the national team."

At this point, Lin Feng's tone was filled with obvious envy and inferiority:

Compared to these people, we... are really just here to make up the numbers.

Several students from Jiangcheng No.1 Middle School in the vicinity lowered their heads.

They are top students at school, the darlings of teachers, and gods in the eyes of their classmates.

But when we got here...

"Damn it, it feels like we're elementary school students who've wandered into a university classroom," someone complained quietly.

"Getting a third-place finish in the province would be great; I wouldn't even dare to dream of a second-place finish."

"I'll try to get half of the fill-in-the-blank questions right..."

Zhou Dapeng turned around, smiling, and said, "Don't be discouraged. This year we have Jiang Chen and Tang Ruoxi; maybe we can create a miracle?"

Lin Feng and the others looked at Jiang Chen.

then……

They suddenly felt that... it wasn't entirely hopeless?

After all, the image of getting everything right in that minute on the bus is still etched in my mind.

"Jiang Chen," Lin Feng couldn't help but ask, "how do you think you compare to Qin Mo and the others?"

Jiang Chen was looking down at his phone when he heard this. He looked up and glanced at the "star players" in the front row.

Then he laughed.

"I haven't competed, so I don't know."

He paused, then added:

"But I think math... shouldn't be judged by appearance, right?"

Lin Feng: "???"

Tang Ruoxi couldn't help but burst out laughing.

Li Fan gave a thumbs up: "Jiang Chen, when it comes to showing off, you're the best."

Zhou Dapeng chuckled, "Jiang Chen, it's good to have confidence, but you can't underestimate the exam tomorrow."

Jiang Chen nodded: "Don't worry, Teacher Zhou, I never underestimate my opponents."

Because he didn't consider these people as opponents at all.

What does an IQ of 168 mean?

Stephen Hawking was only 165 cm tall.

Einstein 170.

He's now only two points away from being Einstein.

Compete in math with a group of high school students?

Isn't that bullying a child?

……

The opening ceremony was boring.

Speeches by leaders, speeches by teacher representatives, oaths by student representatives... the whole process took an hour and a half.

As the event ended, students from the four prestigious universities were surrounded by reporters.

"Qin Mo, are you confident you can get first place in the province again this year?"

"Zhou Cheng, I heard you've been researching cutting-edge issues in algebraic geometry lately?"

"Zhao Rui..."

The flashbulbs clicked, like they were filming a celebrity.

The Jiangcheng team walked past silently, and no one even glanced at them.

Lin Feng and the others lowered their heads and quickly left.

Jiang Chen glanced at Qin Mo more than once.

Qin Mo happened to be looking over as well.

Their eyes met briefly in mid-air.

Qin Mo's eyes were calm, with a hint of scrutiny, before he quickly looked away.

That expression seemed to say, "Oh, just another random passerby, but he's a bit more handsome..."

Jiang Chen smiled and didn't mind.

As they walked out of the clubhouse, Zhou Dapeng patted Jiang Chen and Tang Ruoxi on the shoulders:

"Do your best on the exam tomorrow, don't be nervous."

"Whether Jiangcheng No. 3 Middle School can become an instant success depends on the two of you!"

……

The next day, Sunday.

At 7:30 a.m., the area outside the examination hall of Binhai University was already packed with people.

When Jiang Chen arrived, Tang Ruoxi was already waiting at the door.

"Old Chen, breakfast." She handed over a plastic bag containing steamed buns and soy milk.

Jiang Chen took it, took a bite, and asked, "Have you eaten?"

"I've eaten." Tang Ruoxi nodded. "Were you nervous?"

"What's there to be nervous about?" Jiang Chen finished a steamed bun in three bites. "Just treat it like doing practice problems."

Several students from other schools nearby couldn't help but glance at him upon hearing this.

"Pretentious."

"You'll know you're going to cry when you get into the exam room."

"Every year there are these stubborn people who end up handing in a blank paper and are in a worse situation than anyone else."

Jiang Chen ignored them, finished his breakfast in a few bites, and threw the trash into the bin.

At 8:00 AM sharp, the entry bell rang.

The first test lasted 80 minutes and the total score was 120 points.

Jiang Chen found his seat... Exam Room 48, last row by the window.

The location is quite remote, but the natural light is good.

Try curling my hair.

Jiang Chen glanced at the title: "First Round Questions of the Jiangnan Province High School Mathematics League".

Then he laughed.

"this one?"

It's not that he's arrogant.

This question... is ridiculously easy.

Question 1: Fill in the blanks (8 points)

Let the function f(x) = x³ - 3x + 1, then the value of f(f(1)) is ______.

江辰内心：「f(1)= -1，f(-1)= 3，答案3。」

Without even touching the pen, I wrote 3 directly on the answer sheet.

[Question 2: Fill in the blanks (8 points)]

Given a complex number z that satisfies |z|=1, the maximum value of |z² - z + 1| is ______.

Jiang Chen thought to himself: "A point on the unit circle, represented by a triangle, has a maximum value of √3."

Write: √3.

Question 3: Fill in the blanks (8 points)

In triangle ABC, ∠A = 60°, BC = 2, then the maximum value of AB·AC is ______.

Jiang Chen thought to himself: "The Law of Cosines + the AM-GM inequality, the maximum value is 2."

Write: 2.

Question 4: Fill in the blanks (8 points)

Given a sequence {an} satisfying a₁=1 and a_{n+1}=a_n + 1/a_n, then the integer part of a₂₀₂₅ is ______.

Jiang Chen thought to himself: "The recursive inequality has an integer part of 89."

Write: 89.

……

Jiang Chen didn't even touch the scratch paper for the eight fill-in-the-blank questions.

The eyes scan the area, the brain automatically calculates, and the answer is given instantly.

In less than a minute, all the fill-in-the-blank questions were finished.

Next are three short answer questions.

Question 9 (16 points)

Given positive real numbers x, y, and z that satisfy x + y + z = 1, prove that (1/x - 1)(1/y - 1)(1/z - 1) ≥ 8.

Jiang Chen glanced at it, then picked up his pen and wrote:

"Proof 1: Homogeneity, let x = a/(a+b+c) etc., substitute and simplify to get (a+b)(b+c)(c+a)≥8abc, which is obviously true by the AM-GM inequality."

"Proof 2: Direct expansion, the original expression is equivalent to proving (1-x)(1-y)(1-z)≥8xyz. From x+y+z=1, we get 1-x=y+z≥2√(yz). Similarly, multiplying the three expressions together gives the result."

「证法三：换元法，令x=1/(1+a)等，则条件化为1/(1+a)+1/(1+b)+1/(1+c)=1，需证abc≥8，由条件可推出a+b+c≥6，再由均值得abc≥8。」

Three solutions, flowing smoothly.

Finished writing in two minutes.

Question 10 (20 points)

In a Cartesian coordinate system, given the parabola C: y = x². Let A and B be two distinct moving points on C, satisfying OA⊥OB (O is the origin). Find the equation of the locus of the midpoint M of line segment AB.

Jiang Chen glanced at it and immediately came up with a solution.

"Let A(t₁,t₁²) and B(t₂,t₂²). Since OA⊥OB, we have t₁t₂(t₁t₂+1)=0."

"Because A≠B, t₁t₂=-1."

"Then find the coordinates of the midpoint, eliminate the parameters, and the equation of the trajectory is: y = 2x² + 1/2."

"He added a second solution...using the polar line theory, yielding the result in one step."

Finished writing in three minutes.

Question 11 (20 points)

Let n be a positive integer. Prove that there exist n distinct positive integers such that their sum equals their product.

This question... looks somewhat familiar to Jiang Chen.

Oh, I did something similar in the office a few days ago, and he wrote down three solutions.

Since there was limited blank space on the exam paper, he thought for a moment and decided that writing two kinds would be enough.

「证法一：构造法。取前n-1个正整数1,2,…,n-1，以及第n个数S=n(n-1)/2。验证和=积=n(n-1)/2 + n(n-1)/2 = n(n-1)，构造成立。」

"Proof 2: Mathematical Induction. Taking 1 when n=1 is obviously true. Suppose that when n=k, there exists {a₁,…,a_k} satisfying the condition. Let S=∑a_i, P=∏a_i, and S=P. Consider the case of k+1, taking a new sequence {a₁,…,a_k, S+1}. Then the new sum = 2S+1, and the new product = P(S+1) = S(S+1). We need to prove 2S+1 = S(S+1), i.e., S²-S-1=0, but S is an integer, so this is not true. We need to adjust the construction..."

He stopped writing abruptly at this point.

It's not that I don't know how, it's just that I think writing it this way is too wordy.

He changed his approach and wrote directly below:

「更简洁的构造：取数列{2,3,1,1,…,1}（共n个1），但需调整。实际上，标準构造为：取a₁=1, a₂=2, a₃=3, 其余a_i=1（i≥4），则和为n+5，积为6，需n+5=6，故n=1时成立，n＞1时需另寻构造。」

「最终构造（经计算）：当n=1时取{2}（和=积=2）；当n=2时取{2,2}（和=积=4）；当n≥3时，取数列{1,2,3,1,1,…,1}（后n-3项均为1），则和为n+3，积为6，令n+3=6得n=3，即{1,2,3}满足。对n＞3，需调整：取{1,2,3, k,1,1,…,1}，使3k=n+3+k，即2k=n+3，故k=(n+3)/2需为整数，当n为奇数时成立。」

"In summary, there exists a construction for any n."

After finishing writing, Jiang Chen checked his watch.

8: 09.