Chapter Twenty-Three: Mathematical Olympiad

Tuesday saw the excitement stirred by Wu Tong’s perfect scores in all five subjects finally begin to subside. After dinner, upon returning to school, class monitor Lin Yang found Wu Tong. “Mr. Chen said you’ll also be participating in the math olympiad. There’s training tonight—shall we go together?”

“Sure,” Wu Tong replied, closing her advanced mathematics book, picking up her neatly bound draft papers and pencil case, and rising to leave the classroom with Lin Yang.

Each academic building on campus bore its own name. Their class was housed in the Building of Erudition; ahead stood the Minghua Building, and in front of that lay the school’s athletic field.

The Minghua Building’s faculty research room was now serving as the training classroom for the math olympiad. By the time Wu Tong and Lin Yang arrived, most of the students had already gathered.

The group was small—barely a dozen. Apart from the handful genuinely interested in mathematical olympiads, most had been selected for their high rankings in mathematics, with the majority hailing from the elite classes situated in this building.

Wu Tong was a new face when she entered. The top math students rarely changed much; many of them had participated in olympiad training since their first year and were already familiar with one another.

Seeing Lin Yang walk in with her, the students quickly realized that this must be the now-famous Wu Tong—the one who had scored perfect marks in all five subjects. Lin Yang belonged to Class Seven, and the newcomer accompanying him could be none other than Wu Tong.

It was only the third week of the new term, and the freshmen had yet to make their mark.

The instructor for the olympiad training, Mr. Duan Hong, was someone Wu Tong had already met. He was sitting at the podium, having arrived early.

“Wu Tong, you’re here!” he greeted her with a warm smile, his gaze falling on the book in her hands. He recognized it: Advanced Mathematics. Duan Hong paused, then nodded—indeed, a student who had thoroughly mastered high school mathematics would naturally seek higher knowledge. There was nothing amiss in reading such a book.

“Can you understand it?” he asked.

“It’s manageable. It was tough at first, but as my logical thinking has developed these past days, it’s gotten easier,” Wu Tong nodded. Nowadays, the subject teachers rarely interfered with her studies, save for the occasional deep question posed when the class failed to answer. Otherwise, her learning was largely self-directed.

Her schedule was flexible, allowing her to devote extra time to the advanced mathematics book. She had already worked through most of it and expected to finish within the week.

“It’s good you can get into it. Take your time—high school math and university mathematics are worlds apart,” Duan Hong encouraged her. “If there’s anything you don’t understand, feel free to consult me—or any math teacher here. We’d be happy to help!”

Reflecting on Wu Tong’s progress with university-level material while the others were still struggling with high school problems, he felt compelled to give the group a little push.

He introduced her to the class, “This is Wu Tong. You should all be familiar with her name—she’s the only student to score a perfect mark in the recent placement test. And, on the day the results were released, she completed this year’s college entrance exam paper and scored a perfect mark again!”

“There’s always someone greater out there. You must learn from Wu Tong—don’t think that just because you’re good at math, you’re the best in the world!”

“Understood, Mr. Duan! Comparing us to such a mathematical genius—don’t you feel bad for us?” one of the bright, outgoing students called out, half-jokingly. Those admitted to this class all had excellent grades, and their relationship with the teacher was naturally close and amicable.

“Exactly!” others chimed in. A genius who could ace the college entrance exam, had finished all high school material, and was already studying university-level mathematics—how could ordinary “math lovers” compare? Mr. Duan was clearly overestimating them!

“I think you’re all too comfortable—your mouths are sharper than your minds. Today, you’ll each do a practice paper!” Duan Hong retorted, nearly amused by their antics. “Wu Tong, find a seat. Today, you’ll work through a real olympiad practice paper—the competition is quite different from regular exams.”

There were plenty of empty seats in the research room. Lin Yang went to his usual spot, and Wu Tong chose a vacant seat near the center.

Duan Hong began handing out papers. A boy in the front row, wearing glasses that couldn’t hide his lively eyes and round, baby-faced cheeks, turned around and passed the paper to her, greeting her cheerfully, “Hey, I’m Sun Chao from Class One. Nice to meet you, genius!”

Wu Tong recognized him—he’d been the first to joke about Mr. Duan’s “conscience.”

“Wu Tong from Class Seven. Genius, nice to meet you!” If memory served, he was the one nicknamed the Science Prince. Math was often his strongest subject, usually scoring full marks; this time, he’d gotten 148. His science scores were either perfect or nearly so, but his Chinese and English lagged, hovering around a hundred. Still, his name frequently appeared among the top rankings.

As the papers were handed out, everyone focused their attention, gathering their concentration on the exam. They were all top students, well-skilled in self-control.

Wu Tong examined the paper in her hands. There were only four main questions, but they spanned the breadth of mathematics—plane geometry, algebra, number theory, combinatorics. Compared to the foundational papers she’d practiced before, the difficulty was on an entirely different level.

The first question was a plane geometry problem: In an acute triangle ABC, the altitude CE from AB and the altitude BD from AC intersect at point H. The circle with diameter DE intersects AB and AC at points F and G, respectively; FG and AH intersect at point K. Given BC = 25, BD = 20, BE = 7, find the length of AK.

Wu Tong had encountered similar problems during her summer vacation, though not many. After finishing her high school courses and deciding to participate in the olympiad, she began paying attention to such practice problems, but time had been limited, and she had not yet delved deeply.

For the olympiad, she was just at the threshold.

Still, high school olympiad problems ultimately test high school knowledge. Even if Wu Tong had not yet cultivated an olympiad mindset or become familiar with their unique angles, she had mastered the curriculum and was already studying ahead. In the end, it all came down to problem-solving—a skill she did not fear.

Carefully reading the question, Wu Tong’s mind began to formulate an approach. She scribbled a few notes on her draft paper to organize her thoughts, then started writing on the exam:

Given BC = 25...
AC·BD = CE·AB...
...AK = 9*24/25 = 216/25.

The first question was solved smoothly—a warm-up for Wu Tong, not particularly challenging. She spent more time detailing her solution than actually thinking it through.

She moved on to the second question, which had two parts, each harder than the last.

Wu Tong felt a bit hazy on her first read—a rare occurrence these days. After rereading and thinking carefully, her mind quickly connected the necessary concepts, forming a clear solution pathway, which she then laid out in detail.

The second question fell, too, her pen racing through the complex solution.

Most of the class was still wrestling with the first problem, searching for a way in, while Wu Tong’s steady writing was conspicuous in the quiet room. Her classmates glanced at her with awe and envy—already on the second question, while they hadn’t cracked the first! Was this how formidable a genius could be? The group hurriedly picked up the pace, determined not to let her finish before they’d even solved the first problem. Wu Tong’s habit of submitting her papers well ahead of time was already legendary among them.