Chapter Thirty-Two: The Tournament-Back Before the College Entrance Exam, I Became a Sensation in the Science Community(Flowing waters fill the goblet.)

After receiving the test paper, Wu Tong flipped through the pages to ensure nothing was missing or misprinted. She then skimmed the contents; the questions were not difficult, and even the final, most challenging problem was only of moderate difficulty compared to the competition problems she had solved. It seemed this year's exam would be manageable. Yet she overlooked the fact that the problems she practiced were mostly at the level of the national competition, and some even came from Duan Hong, featuring genuine past questions from the International Mathematical Olympiad.

At eight o'clock sharp, the exam officially began. Wu Tong carefully filled in her identification details and started answering the questions. During her initial review, she had already mapped out the answers for the fill-in-the-blank section in her mind. Now, as she read each question again, it was like a second verification. Her pen moved almost without pause, filling in the answers one after another.

First question, second question, third question…

Around twenty-four minutes in, Wu Tong elegantly solved the final problem, her approach calm and unhurried. She had finished the first round of the exam. She had nearly completed a university-level mathematics textbook; now, tackling high school problems—even those meant for the Olympiad—required little time or thought from her.

Picking up her test paper, Wu Tong meticulously checked her answers once more, re-deriving the solutions to the written questions with alternate methods. This took only another fifteen minutes.

With the exam halfway through, Wu Tong raised her hand to submit her paper.

The proctor walked over and saw that Wu Tong had filled in every answer, her scratch paper densely covered with calculations. He couldn't help but arch his brows in surprise. Was a miracle about to occur in this exam room? Or were the questions this year simply too easy? How could a student finish and turn in their paper with only half the time gone?

As a member of the Provincial Mathematical Society, his own mathematical ability was respectable. Taking Wu Tong's test back to the podium, he curiously scanned a few questions, only to find every answer correct. Remarkable—today's children are truly extraordinary!

Wu Tong rose and left the exam room. The other students glanced at her departing figure. Was she a prodigy, or had she simply given up? Most assumed she had surrendered; even the fastest among them were just starting on the major problems.

So difficult—their heads felt ready to burst!

There was another exam to come. Students who finished early were not allowed to leave freely. Wu Tong was directed to a waiting room at the end of the hall.

Outside, she retrieved her backpack. Wu Tong took out her newly acquired textbook on complex functions, purchased two days before the trip, and began to read. This time, she remembered to borrow the university-level physics book as well.

The second round began an hour later, starting at 9:40 and ending at 12:30. Wu Tong checked her paper, filled in her information, skimmed the questions, and then sat down to work through them step by step, with calm precision. Many students marveled at her composure—how quickly she recovered after supposedly submitting a hasty first-round paper, returning to tackle the second as though nothing had happened. Compared to those who simply gave up, her courage was admirable.

The scrutiny of others meant nothing to Wu Tong. Though the second round lasted nearly three hours, it consisted of only four major questions, each requiring a written solution.

The first was a geometric proof. After reading it through, Wu Tong had already formulated her approach. She conducted a rough derivation on her scratch paper, then carefully transcribed her solution onto the test paper.

The second question consisted of a single sentence: prove the inequality. Somewhat difficult, but still manageable. Ten minutes later, Wu Tong had dispatched it. Most of her time was spent writing out the proof process both on scratch paper and the exam sheet. Both questions were worth forty points each.

The third question seemed a bit harder: prove the existence of infinitely many positive integers… This topic delved into deeper territory.

The fourth question's statement nearly took up an entire page—a rarity. Wu Tong's interest was piqued. She read the entire problem carefully, forming initial ideas.

The difficulty of this problem was high, even among the many questions she had solved—surpassing some national competition problems, and feeling like a watershed for the league exam. For ordinary students, the question alone was hard to comprehend, let alone solve. Yet, for Wu Tong, it was still within the scope of high school material, albeit deeply explored.

Seeking accuracy, Wu Tong reread the problem statement from the beginning. The steps unfolded in her mind as she began to write her solution on the scratch paper.

Once her strategy was clear, many conditions were extractable from the problem itself. By understanding the properties they satisfied, she could ultimately construct the proof.

…From the requirements for S, one could deduce the object sought in the final part…

Completing this proof signified the approaching end of Wu Tong's competition. After checking her answers once more and confirming everything was correct, she raised her hand to submit her paper.

Nearby students, noticing Wu Tong's actions, wondered if another had succumbed to the exam's difficulty. Perhaps more would give up soon; they'd just have to endure a little longer.

The process had to be attempted, or how could the school explain their performance? Could they admit they simply couldn't understand the questions?

The proctor, who had been circulating the room, wasn't surprised to see Wu Tong again. From the start, he had wondered if she would finish early once more. When the papers were distributed, while other students sat bewildered, he observed Wu Tong writing almost nonstop, her pen gliding as though she were not struggling with advanced league competition problems.

He had sources of information and knew that last year's provincial team performed only moderately—three first prizes, none qualifying for the national team. To select true talents for the national team, this year's competition had increased in difficulty step by step, with the final problem matching or exceeding national competition standards. Even he would need to deliberate carefully; most teachers probably couldn't solve it.

With such difficulty, he expected some students to score zero; that Wu Tong could finish early was astonishing.

Checking the time, nearly three hours allocated, but only fifty minutes had passed—two hours remained. From his recent circuit around the room, he saw some students still stuck on the first question, and few had begun the second.

Wu Tong's speed truly amazed him. Perhaps this year, their provincial team would produce a miracle student.

Seeing such a promising competitor, the proctor spoke with special care: "Is your team leader outside? If so, you may leave the school. If not, please wait in the lounge!"

At her age, she was still young, and talents like hers needed careful attention.

"He is, thank you!" Wu Tong shouldered her backpack and followed the route she had taken that morning out of the school gates. Outside, teachers from various schools waited for their students. Seeing Wu Tong exit, they assumed she had given up right after the exam began and whispered among themselves about her mental state.