Holy crap, there's someone

All right, all right, you're awesome.

Shen Qi couldn't be bothered talking to the guy beside him anymore.

Everyone who'd made it here was a top student. It was only natural for them to be a little arrogant.

Ten minutes later, the twelve semifinalists were led into the examination room.

The exam was being held in a large conference room that could seat nearly a hundred people. It was spacious and bright.

With only twelve contestants taking the exam, the room felt empty. Each contestant sat more than five meters from the nearest person.

Before the exam began, the Vice President of the Provincial Mathematics Society personally announced the rules. "Students, you're the best at mathematics from schools across the province. First of all, I wish you the best of luck in the semifinal."

"The rules are very simple. The exam paper you're about to receive has three questions, worth a total of sixty points. You may use any arguments and evidence to solve or prove the propositions. You'll have three hours."

"In principle, you may not leave your seat during the exam. If you have an urgent need, please raise your hand and ask a proctor."

"Your final ranking will be determined by your score. The top six will join the provincial team and prepare for the national competition. Those ranked seventh through twelfth will receive the Special Prize in this year's Provincial High School Mathematics League. Believe me, the Special Prize awarded by our society will help you, to some extent, in your future studies."

"So you've already succeeded. There are no losers in this semifinal. Do your best, and good luck! I now declare the semifinal open. Proctors, please hand out the scratch paper and exam papers."

The scratch paper and exam papers were quickly handed out to the twelve semifinalists, and the exam began.

Shen Qi had been ready for this. He took a look at the exam paper and, sure enough, there were only three questions.

The exam paper consisted of three sheets of white paper. A proposition was written in the upper-left corner of each sheet, and the rest was blank.

The first question was geometry, worth fifteen points.

The second was algebra, worth twenty points.

The third was another geometry question, worth twenty-five points.

They were all proof and solution questions.

Judging by the points assigned, the higher the score, the harder the question. That was generally how it worked.

Shen Qi started with the easiest question in theory: the first one.

Although this plane geometry question was worth only fifteen points, it could make 99.99 percent of high school students in China want to tear up the exam paper the moment they saw it.

The complicated diagram on the page consisted of seven circles of different radii and twelve triangles of various sizes.

The circles intersected one another and the triangles. Some triangles were inscribed in circles, and large triangles contained smaller ones. No fewer than eighteen lines passed through the circles and triangles, crisscrossing horizontally and vertically, with some slanting across as well.

Could you imagine this beautiful geometric diagram, beautiful enough to take your breath away?

The question gave two known values: the radius of the smallest circle and the length of the shortest line.

It asked the test-taker to find the sine of angle ψ in triangle WYQ.

The English letters had gone all the way to Y, and the Greek letters nearly to the end, at ψ. It was clear this question was no simple matter.

"Whoever set this question... really knew their stuff!" Shen Qi spent ten minutes studying it without putting his pencil to the paper.

The question was extremely rigorous, and it could be said to push Euclidean geometry to its limits.

Shen Qi thought it would be difficult for a high school student to find the sine of ∠ψ using the geometry taught in high school textbooks.

Gauss's new geometric theories were useless here, J. Bolyai's Discourse on Non-Euclidean Geometry was hard to apply, and Lobachevsky's trigonometry of Non-Euclidean Geometry was as good as fallacious.

Almost all the mathematical knowledge Shen Qi had accumulated was unusable on this first plane geometry question.

It was as if Shen Qi's powerful magic had been sealed by some mysterious, ancient curse. All he could do now was fight the monster the primitive way, picking up a cold weapon and battling it hand to hand.

"Whoever wrote this question must be a master among masters. Not only does he know middle school math inside out, he's also well versed in university, graduate, and even doctoral-level mathematics. He's making me incredibly uncomfortable. I've taught myself so much university math, and yet I can barely put any of it to use." Shen Qi frowned. He'd taken several math exams over the past few months, and this was the first time he'd been stumped so badly that he couldn't even start writing.

The Vice President of the Provincial Mathematics Society was in his fifties and had graduated from Fudan University's Mathematics Department. He paced around the exam room as one of the many proctors.

The Vice President had set all three questions on the semifinal exam by himself. He'd spent several days thinking them over, pulling out quite a bit of hair before finally settling on the final version just last night.

The Vice President quietly came up behind Shen Qi and watched in silence.

"Nangang Second High School, Shen Qi. That's him—the one who got a perfect score on the First Test." The Vice President recognized Shen Qi's name and remembered it well. There was a reason he'd set all three semifinal questions himself, and Shen Qi had played a part in it.

"Stumped, huh, young man? I wrote these questions myself. They're enough to burn through a lot of your brain cells." The Vice President smiled subtly. Shen Qi's inability to begin writing was just what he'd expected.

Shen Qi, completely absorbed in the exam paper, hadn't noticed the middle-aged man standing behind him. This man was a master among masters—the very person making him so uncomfortable.

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

The Nine-Point Circle Theorem, also known as the Feuerbach Circle, stated that the midpoints of a triangle's three sides, the feet of its three altitudes, and the midpoints of the segments joining its orthocenter to each vertex all lay on the same circle.

The Nine-Point Circle was basic knowledge in high school geometry, and it was covered in high school math textbooks.

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

This was a pure test of logical deduction and a challenge to one's ability to observe figures. Advanced mathematical theories were no longer of use here. All Shen Qi could do was take it step by step, stay calm, and patiently search for clues, until he found the key and worked out the correct answer.

Forty minutes passed. Shen Qi finally made a breakthrough. On the extremely complicated original diagram, he drew an Euler line in pencil and named this auxiliary line K1K2.

He'd used up all twenty-six English letters. So he had to go back to K, pick the points K1 and K2, and connect them with a straight line, K1K2.

"Would you look at that!" The Vice President made another lap around the room and ended up behind Shen Qi again. He couldn't help letting out a little hum of surprise.

All twelve contestants had run into trouble on the first geometry question. Half of them had already given up on it and moved on to the other two. But those seemed even harder, and they wore looks of utter despair.

"This kid's pretty good. It only took him forty minutes to find that Euler line. His powers of observation and deduction are quite impressive." The Vice President stood behind Shen Qi with great interest, continuing to watch.

Shen Qi suddenly felt a chill behind him. He glanced over his shoulder on instinct. "Holy crap, there's someone!"

"Hey, stop saying 'holy crap' and get back to work!" the Vice President reminded him sternly, then walked on, pretending he'd only been passing by.