Holy Crap, Someone's Here

Alright, alright, you're amazing.

Shen Qi couldn't be bothered to talk to the guys around him anymore.

Who among those who could make it here wasn't a top student? It was normal for top students to have a bit of pride.

Ten minutes later, the 12 finalists were led into the examination hall.

The hall was set up in a large conference room, spacious and bright, capable of seating nearly a hundred people simultaneously.

With only 12 contestants taking the exam now, it felt empty. The distance between each contestant's seat and the nearest person was over 5 meters.

Before the exam began, the Vice President of the Provincial Mathematics Society personally announced the rules for the finals: "Students, you are the mathematical elites from various schools across the province. First, I wish you all the best in the finals."

"The rules for the finals are very simple. The exam paper you will receive has three questions, totaling 60 points. You may use any arguments or evidence to solve or prove the propositions. The time limit is 3 hours."

"In principle, you are not allowed to leave your seats during the exam. If you have an urgent matter, please raise your hand to request permission from the invigilator."

"The final ranking in the finals will be based on the scores on the exam paper. The top six will enter the provincial team to prepare for the national competition. Those ranked seventh to twelfth will receive a special prize in this year's Provincial High School Mathematics League. Believe me, the special prize awarded by me will, more or less, help your future academic journey."

"So, you have already succeeded. There are no losers in this final. Keep it up, and good luck! I now declare the finals open. Please, invigilators, distribute scratch paper and the exam papers."

Scratch paper and exam papers were quickly distributed to the 12 finalists, and the exam began.

Shen Qi was already prepared. Upon receiving the exam paper, he saw that there were indeed only three questions.

The exam paper consisted of three sheets of white paper, with a proposition written in the upper left corner of each sheet and the rest of the space blank.

The first question was Geometry, worth 15 points.

The second question was Algebra, worth 20 points.

The third question was Geometry again, worth 25 points.

All were proof and solution-based questions.

Judging by the point distribution, the higher-scoring questions were more difficult, which was a common pattern.

Shen Qi decided to tackle the theoretically simplest question first, the first one.

Although this plane geometry problem was only worth 15 points, it would surely make 99.99% of high school students in China want to tear up their papers immediately after seeing it.

The complex diagram on the paper was composed of seven circles of different radii and twelve triangles of varying sizes.

Circles intersected with circles, circles intersected with triangles, triangles were inscribed in circles, large triangles enclosed small triangles, and eighteen lines passed through the circles and triangles, intersecting horizontally, vertically, and diagonally.

Could you even imagine this beautiful, breathtaking geometric diagram?

The problem provided two known conditions: the radius of the smallest circle and the length of the shortest line.

The task required the solver to find the sine of an angle ψ in triangle WYQ.

The English alphabet had reached Y, and the Greek alphabet had reached ψ, the second to last, indicating that this question was by no means simple.

"This question is... truly skillful!" Shen Qi spent ten minutes examining the problem, hesitating to start writing.

This question was meticulously crafted, pushing Euclidean geometry to its absolute limit.

Shen Qi felt it would be difficult for high school students to solve for the sine of ∠ψ using the geometry knowledge from their high school textbooks.

Gauss's new geometric theories were useless here, J. Bolyai's Discourse on Non-Euclidean Geometry was difficult to apply, and Lobachevsky's non-Euclidean trigonometry was akin to heresy.

The vast amount of mathematical knowledge Shen Qi possessed was almost unusable for this first plane geometry problem.

It could be said that Shen Qi's powerful magic was sealed by some mysterious and ancient curse, and all he could do now was fight monsters in the most primitive way, picking up cold weapons for close combat.

"The person who created this question must be a master among masters. Not only are they proficient in middle school mathematics, but they are also deeply knowledgeable in undergraduate, graduate, and even doctoral level mathematics. They've made me very uncomfortable, very awkward. I've self-studied so much university-level math, and yet I can barely use it," Shen Qi frowned. He had encountered several math exams in the past few months, but this was the first time he found himself unable to start writing.

The Vice President of the Provincial Mathematics Society, a man in his fifties who graduated from Fudan University's mathematics department, paced the examination hall as one of the invigilators.

All three questions on the final exam paper were created by the Vice President himself. He had spent several days pondering these three questions, losing quite a bit of hair, and only finalized them last night.

The Vice President quietly walked behind Shen Qi and observed him.

"Nangang Second High School, Shen Qi, that's him. He got a perfect score on the first test." The Vice President remembered Shen Qi's name, quite vividly. The fact that all three questions for the finals were personally created by the Vice President was partly related to Shen Qi.

"Stumped, aren't you, young man? The questions I personally created are enough to fry a lot of your brain cells," the Vice President chuckled subtly, Shen Qi's inability to start writing being exactly as he expected.

Completely focused on the exam paper, Shen Qi didn't notice the middle-aged man standing behind him. This man was the master among masters, the one who made Shen Qi feel so uncomfortable.

Twenty minutes passed. Shen Qi, who hadn't written a single word, couldn't wait any longer. He tried to use the Nine-Point Circle Theorem to find a breakthrough.

The Nine-Point Circle Theorem is also known as the "Feuerbach Circle," which states that the nine points consisting of the midpoints of the three sides, the feet of the three altitudes, and the midpoints of the segments connecting the orthocenter to the vertices, are concyclic.

The Nine-Point Circle is a fundamental concept in high school geometry, covered in high school math textbooks.

Shen Qi was using the most basic, simplest mathematical theorem to solve an incredibly complex geometry problem.

This was a pure test of logical deduction ability, a challenge to observational skills. Advanced mathematical theories were no longer useful here. All Shen Qi could do was take it step by step, without rushing or panicking, advancing cautiously to uncover clues and ultimately find the correct answer.

Forty minutes passed, and Shen Qi finally made a breakthrough. On the extremely complex original diagram, he drew an Euler line with his pencil, naming this auxiliary line K1K2.

All 26 English letters had been used, so Shen Qi had to resort to naming points starting with K, taking K1 and K2, and connecting them to form the line K1K2.

"Oh ho!" The Vice President, after circling the room several times, found himself behind Shen Qi again. He couldn't help but let out a hum, quite surprised.

All 12 contestants in the hall were struggling with the first geometry question. Half of the contestants had already given up on the first question and moved on to the next two. However, the latter two questions seemed even more difficult, and they wore expressions of despair.

"This kid is quite something. He found this Euler line in just 40 minutes. His observation and deduction skills are quite impressive." The Vice President, very interested, continued to stand behind Shen Qi and observe.

Shen Qi suddenly felt a chill behind him. He instinctively glanced back: "Holy crap, someone's here!"

"Hey, stop with the 'holy crap' and get back to your answer!" the Vice President sternly reminded him, then walked forward, pretending he was just passing by.