Chapter Thirty-Nine: The Competition Begins

The nine team members participating in the training nodded earnestly—this was an issue they had to avoid at all costs, something they must keep in mind. Their opponents were among the top-ranked high school students in the country, each one a prodigy. In pursuit of better results, there was no room for the slightest negligence.

All of them were math whizzes, and with a quick turn of thought, they realized that Old Zhang had only called out nine names. The one left was that legendary figure. Instinctively, they glanced sideways at Wu Tong, eager to see how Old Zhang would explain the province’s confidence in this ace up their sleeve.

“Stop looking. As for Wu Tong, there’s nothing much to say. Just perform as usual; the national competition is not your final destination. Here’s a small goal—secure a spot on the national team first!”

With a perfect score in the league, casually solving classic IMO problems, and already working through number theory in university textbooks, what more could he say? Seeing the girl treat “normal performance” with such nonchalance, he didn’t even need to remind her to maintain composure or a positive mindset.

He even allowed himself the extravagant hope that the girl could make the national team, win a perfect-score gold medal at the IMO, and bring unprecedented glory to the Central Plains Province.

“Anything else to arrange, Teacher Zhang?” someone asked.

“You’ve all prepared thoroughly—there’s no need to pile on extra practice today. Just keep a good mindset, rest well, and face the competition with full energy. Above all, don’t get so excited before the exam that you can’t sleep—it’s not worth it if it affects your performance!” As the province team’s steward, Teacher Zhang reminded them of these details.

On the fourteenth, this year’s Chinese High School Mathematics Olympiad officially commenced.

“Here, I wish you all the best of luck and great success!” With the passionate encouragement of Old Zhang and Young Zhang, all members of the Central Plains team, along with hundreds of contestants from across the country, strode into the examination hall, spirits high.

At 7:40, all candidates took their seats.

At 8:00,

The test papers were distributed, and the twenty-fourth Chinese High School Mathematics Olympiad officially began.

The CMO fully emulates the format of the International Mathematical Olympiad (IMO): the competition lasts two days, with one session per day, each limited to 4.5 hours, and three questions per session. The main difference lies in the scoring: each CMO question is worth 21 points, so six problems over two days totals 126 points—three times the IMO’s 42 points. This is to better match local expectations. The IMO, by contrast, assigns 7 points per question.

Four and a half hours may seem lengthy for an ordinary exam, but for CMO contestants, time is still tight. Although there are only three problems per session, these are not questions one can solve casually. For many contestants, even twice the time would not be enough.

Especially since this is an odd-numbered year, and by tradition, such years bring more difficult problems than even years. In the last two years, the Chinese team has shone at the Olympiad, winning the team championship last year with five golds, one silver, and a spectacular total score of 217. To continue this glory and select talents for the international stage, the level of this year’s problems could be imagined.

Many students, upon reading the first question, already felt lost, their minds racing in desperate thought. Only a handful began writing and working through the problems.

Wu Tong received her paper, filled in her information as usual, then gave the questions a quick scan. As always, the CMO followed its customary approach: the first question was a geometric proof, with two parts, both obviously demanding substantial work.

She gauged the difficulty. It didn’t quite reach the level of classic IMO problems, but it surpassed that of ordinary national competition questions. The second problem was already on par with the usual final “boss” question of the national round.

Still, for Wu Tong, this level was no obstacle.

She read the problem carefully, her mind sparking with a torrent of ideas. Her thoughts raced, inspiration ignited, and logical paths emerged smoothly, like water flowing downstream. Her pen moved across the scratch paper.

Let Q and R be the midpoints of OB and OC, respectively.
Connect EQ, MQ...
Thus, triangle EQM equals MRF, so EM equals FM.
Similarly, EN equals FN.
Therefore, EM·FN = EN·FM.

The first part was done. The second part unfolded just as smoothly—though more complex, Wu Tong’s proof filled an entire page, finally establishing a negative result.

As long as the reasoning was clear, proof problems were in fact simpler than computation-heavy ones. There was no need for tedious calculations—just step-by-step deduction, which Wu Tong found quite enjoyable.

Having organized her work, Wu Tong transcribed the proof onto the answer sheet. First question, complete.

The second problem was about prime numbers. The statement was deceptively simple—just a single sentence—but the solution set was broad, requiring all pairs of primes (p, q) that satisfied the condition... The difficulty spiked, but Wu Tong carefully worked through it on scratch paper and quickly found a direction.

If 2 divides pq, set p = 2, then 2q = ...
By Fermat’s Little Theorem, ...

Similarly, K...

In summary, all pairs of primes (p, q) that meet the conditions are (2, 3), (3, 2), (2, 5), (5, 2), (5, 5), (5, 313), and (313, 5).

Second question, solved. Wu Tong moved on to the final major problem.

This one posed no barrier to her progress. Inspiration flared—she quickly devised an ingenious solution: first proving a lemma, then deducing the required conditions, and finally, in two steps, completely resolving the problem—counting the number of convex m-gons with vertices belonging to P and exactly two acute interior angles. Her answer was exceptionally elegant.

For Wu Tong, the main challenge in this problem was simply to write the mathematical notation neatly and clearly.

Having transcribed her solution to the third problem, Wu Tong had now completed all three problems for the first day. She glanced at the clock: just over an hour had passed. She was confident in her answers—if she hadn’t misread any question, her solutions could not possibly be wrong.

She spent about ten minutes carefully checking her work, essentially re-deriving everything in her mind at a faster pace. Confirming everything was correct, she raised her hand to submit her paper. At that moment, only about an hour and a half had elapsed since the exam began.

In the exam hall, many students were still struggling with the first problem, some only just moving on to the second, almost none had reached the third.

These were academic stars from various schools, all ranked within the top few hundred nationwide, yet at this moment they deeply felt like the underachievers at school, their minds blank, brains nearly wrung dry by the difficulty.

At this moment, Wu Tong’s action was nothing short of a thunderclap to those who noticed it.

How long had it been? Someone was already submitting their paper? Were they wasting too much time, or had someone simply given up?

Even the proctor was startled—only an hour and a half had passed, and this candidate wanted to hand in her paper? But when he saw Wu Tong’s neatly written answer sheets, his doubts were replaced by silent awe.

Kids these days are truly remarkable! With this year’s unprecedentedly difficult questions, even he couldn’t have finished so quickly. For a contestant to submit three hours early—this must be a truly top-tier student, a shoo-in for a spot on the national team!