The Weakest Team in the Country?

On July 2, nine members of the Nanyue Province Math Olympiad team arrived in the capital. They were assigned rooms at Shuimu University.

Tomorrow, this year's High School Mathematics League national competition would begin. It was being held at Shuimu University.

The organizer was the Chinese Mathematical Society, China's most authoritative mathematics association.

Of all the universities in China, only one objected to holding this year's national competition at Shuimu University: Yanjing University.

Yanjing University argued that it was unfair. Why were both the National Preliminary and the National Finals being held at Shuimu? They would have been fine with the Mathematics Society choosing a neutral venue.

The Chinese Mathematical Society explained, "We always handle things fairly. The National Preliminary and National Finals were held at Yanjing last year, weren't they? Surely it's Shuimu's turn this year."

Yanjing University countered that both competitions had been held at Shuimu the year before last and the year before that, which was completely unfair. The Chinese Mathematical Society was clearly biased.

The president of the Chinese Mathematical Society replied, "I only took office last year. What happened the year before last and the year before that has nothing to do with me."

Yanjing University: "Hmph. Just you wait. You'll see."

And that was the end of it.

China's two most prestigious universities were famous for competing over talented students. This year, the National Preliminary and National Finals were being held at Shuimu University, and more than a hundred of the country's top math students would be staying there for a week. They would spend every day on Shuimu's campus, and surely that would make them like the university a little more.

Take Shen Qi, for example. He'd noticed plenty of pretty young women on campus, and they were nothing like the female academic overachievers he'd imagined.

This was Shen Qi's first time in the capital, and there were plenty of places he wanted to explore. Unfortunately, with the big competition right around the corner, there wasn't much time. After wandering along the street outside the campus gates, he returned to the temporary dormitory at Shuimu University.

In one of the dorm rooms assigned to the Nanyue Province Math Olympiad team, the team leader, deputy leader, and six team members gathered together.

"I'm going to go over the National Preliminary and National Finals rules. I've explained them many times, but I'm going to repeat myself anyway." Team leader Teacher Tian looked less than optimistic. "The National Preliminary has three questions worth seven points each, for a total of twenty-one points. You'll have three hours to finish. The format is exactly the same as our provincial semifinals. In fact, our provincial semifinals are modeled on the National Preliminary."

"The National Preliminary starts at nine tomorrow morning, July 3. Teams from all thirty-two provinces, municipalities, and autonomous regions will take the exam at the same time. Each team has six members, and everyone will take the same test."

"The qualification format is thirty-two teams down to ten. Ten of the thirty-two teams advance to the National Finals. The teams will be ranked by their total scores, and the bottom twenty-two will be eliminated."

"Alright, as long as you understand the format, that's enough. Take it easy and don't put too much pressure on yourselves. Get to bed early tonight, and meet in the lobby at seven tomorrow morning." With that, Teacher Tian was ready to leave and return to his room.

Shen Qi asked, "By the way, Teacher Tian, you only briefly mentioned the National Finals. What exactly is the format this year? I found some information online, but I'm not sure if it's true. You should have the official rules from the organizing committee, right?"

"Let's talk about that if you make it to the National Finals. I sincerely wish you good luck. Do your best, boys," Teacher Tian said.

"Teacher Tian, you don't seem very confident in our team." Shen Qi had noticed that Teacher Tian had changed completely since they'd arrived in the capital. He was under so much pressure that he barely smiled, and he was smoking two packs a day.

"The Chinese Mathematical Society can be very heavy-handed. The National Finals have always used a thirty-two-teams-down-to-sixteen format. This year, they arbitrarily changed it to thirty-two down to ten without even asking the provincial mathematics associations what they thought." Teacher Tian voiced his protest, but it was no use.

"If it's thirty-two down to ten, does that mean our team has no chance?" Shen Qi was young and fearless; he refused to believe it.

"There's a chance, but it'll be extremely difficult. The teams from Hubei, Hunan, and Zhejiang are the top contenders. They've long been the strongest provinces in mathematics. Even if you, Shen Qi, joined one of their teams, you might not make the starting lineup." Teacher Tian glanced at Shen Qi as he spoke.

"The teams from the two municipalities, Beijing and Shanghai, are just below the top tier. One's the capital, the other's the Magic City. They have strong economies and plenty of resources, attracting talent from all over the country. If you joined the Beijing or Shanghai team, Shen Qi, you might just make the starting lineup."

"There are four second-tier regions in mathematics: Sichuan, Chongqing, Liaoning, and Jiangsu. Add those to the five top-tier teams I just mentioned, and that makes nine already. So the thirty-two-down-to-ten format is a huge challenge for our team, but we should still hold on to hope. Shen Qi, your optimism is right. I'm the one who's wrong—I shouldn't be so pessimistic." Teacher Tian said.

"Then where does Nanyue Province rank in the country's math scene?" Shen Qi had thought Nanyue Province would be second-tier. Could it really be third, fourth, fifth, sixth, seventh, or eighth?

Teacher Tian ran a hand through the few wisps of hair left on his head and said helplessly, "Apart from the five top-tier teams and the four second-tier teams, the Chinese Mathematical Society, Shuimu, and Yanjing classify the remaining twenty-four provinces as 'average in math competitions.' Our province is third-tier. That's more or less accurate. We can't compete with the five top-tier teams or the four second-tier teams in overall strength. I'm not putting us down; our province's overall math competition level really is third-tier."

Shen Qi nodded. "Got it. We're a weak team. A bunch of losers."

The National Preliminary ranked each team by the combined scores of its six members. No matter how strong Shen Qi was individually, he couldn't take on six people by himself. The test was worth only twenty-one points in total, so even a perfect score would only earn twenty-one points. The team's overall strength was what would carry them into the National Finals.

"Don't overthink it, boys. You'll learn something just from seeing the world. At least you can say you've stayed in Shuimu's dorms. Alright, get some rest. See you tomorrow." Teacher Tian and the deputy leader left the dormitory.

"Luo Ming, Shu Minbo, Yang Huan, Cheng Le, Qi Jianhong, remember, we're a team. Everyone has to pull their weight! Our goal is to qualify for the National Finals. I gave a speech as our team's representative at the provincial awards ceremony and made big promises to the provincial leaders and all the math experts. Don't let me down!" Shen Qi was fired up. He wanted his team to go as far as possible; he didn't want them to finish the National Preliminary and slink home in defeat.

"I'm shaking in my boots, Shen Qi. I only scored thirty points in the provincial semifinals, half of what you got..." The youngest, Qi Jianhong, had little confidence. He'd only just turned sixteen.

"Qi Jianhong, don't make me lose my temper. I'm telling you, you'd better score at least twelve points on tomorrow's National Preliminary. Otherwise, you're a useless teammate for life!" Shen Qi looked out the window. It was late, and there were no stars. He could talk big, but tomorrow's National Preliminary was out of his hands. All he could do was score as high as possible. The rest was up to luck...