Chapter 56 - 40: Morning
「Nine o’clock sharp.」
The first session was Math Test I.
Also known as the preliminary round.
It was mostly fill-in-the-blanks and multiple-choice. The sheer volume of questions and broad scope tested one’s fundamentals and speed.
For the vast majority of competitors, this was supposed to be a warm-up.
But the atmosphere this year felt a little off.
Only fifteen minutes had passed since the papers were distributed.
And the air in the examination hall had already fallen silent.
The initially uniform sound of scribbling pens had now become sparse and sporadic.
In its place was a medley of anxious noises.
The boy to the front-left began to frequently click the spring of his ballpoint pen.
The girl to the right seemed to be sighing, though the sound was too faint to be certain.
Chen Zhuo ignored all of it.
He kept his head down, his eyes fixed on the eighth fill-in-the-blank question.
Just two dry lines of text described the trajectory equation of a moving point between a parabola and a circle.
The conventional method was to set up a system of simultaneous equations and then find the derivative, or use the discriminant.
But the amount of calculation required would take ages even with a computer, let alone by hand.
’This is a trap.’
’The person who wrote this question is a master psychologist.’
’He’s betting that the students won’t dare to use the special value method.’
’He’s betting on the deep-rooted belief, drilled into these top students, that every step in a competition must be rigorously proven.’
Chen Zhuo twirled his pen.
He didn’t write out any equations.
He sketched a rough diagram on his scratch paper and directly used the extreme position at the parabola’s vertex.
Substitute, calculate.
√2
The whole process took less than thirty seconds.
He filled in the answer and moved on to the next question.
The sighing around him grew heavier.
The boy clicking his pen had already taken it apart. The pieces were laid out on his desk; it looked like he was about ready to give up.
Chen Zhuo turned a page of his test paper.
The rustle of the paper sounded exceptionally jarring in the quiet classroom.
Several people snapped their heads up, staring at Chen Zhuo in horror.
Their gazes were like they were watching a madman who had started sprinting at the beginning of a marathon.
Chen Zhuo didn’t look at them.
He just thought the paper had a bit of a strong smell that made his nose itch.
He even had the spare mental capacity to think about the half-eaten burger from last night, and the seven or eight ketchup packets Liu Kai had taken back to the guesthouse.
This mental wandering didn’t affect the speed of his work.
Compared to the problems he usually studied,
these questions didn’t even require thought. He just needed to retrieve the knowledge from his brain.
The formulas, theorems, and models were like components neatly arranged in a warehouse. The moment he saw the blueprint, his hand would automatically reach for the corresponding part.
「Ten-twenty.」
The bell for Test I didn’t ring.
There was no break. The proctors collected the Test I papers and immediately handed out the papers for Test II.
The oppressive feeling of this seamless transition was a unique form of torture reserved for competitions.
An invigilator walked over and snatched away his completely filled-out answer sheet.
The girl who had been sighing earlier held her answer sheet down, refusing to let go.
"Teacher, just one more minute... please, just one minute..."
Her voice was on the verge of tears.
The invigilator expressionlessly yanked the paper away.
"Let go, or it will be treated as cheating."
The moment the paper left her hand, it was as if all her spirit had been drained away. She stared blankly at the ceiling.
Before she could even catch her breath, the second test paper was handed out.
Thicker, heavier.
Test II.
It began.
If Test I was a sprint that relied on explosive power,
then Test II was a weighted cross-country race where you truly had to fight for your life.
Three long-form problems.
One in plane geometry, one in algebraic inequalities, and one mishmash of number theory and combinatorics.
The examination hall fell completely silent.
Even the anxious clicks and scribbles had vanished.
In their place was a despairing silence.
Like the suffocating calm on the sea’s surface before a storm.
Everyone was staring blankly at their papers.
Someone fiddled with a compass, drawing a circle on the paper, erasing it, drawing another, erasing it, drawing another, erasing it again.
The scratch paper finally tore, revealing the black desktop underneath.
Chen Zhuo looked at the second geometry problem.
The diagram was complex.
Two tangent circles, a secant line, and several triangles embedded within, intersecting in a chaotic mess.
Prove that three points are collinear.
It was a variation on the classic Menelaus’s theorem or Simson line, but the question writer had added countless distracting conditions, disguising the once-elegant geometric figure as a tangled mess.
The conventional auxiliary line method required extremely strong geometric intuition.
You had to find that one precise line within the tangled mess.
Connect it,
and everything would fall into place.
Fail to connect it,
and you’d just be running in circles in a maze until you smashed your head against a wall.
Chen Zhuo stared at the diagram for half a minute.
He couldn’t find the line.
He wasn’t that kind of inspiration-driven genius.
He didn’t have the superpower of knowing where to draw the auxiliary line with a single glance.
He sighed.
He put down his compass.
He picked up his ruler.
He drew a large cross over the figure.
’Time to build a coordinate system.’
’If I can’t find the key to this problem, I’ll just blast the door open with a cannon!’
Analytic geometry.
Turn all the points into coordinates (x, y), and all the lines into equations Ax+By+C=0.
Transform elegant logical reasoning into direct, brutal algebraic computation.
It was a clumsy method.
The amount of calculation was ten, even a hundred times that of the geometric method.
One mistake with a plus or minus sign, and the entire proof would be ruined.
But for the current Chen Zhuo,
it couldn’t be better.
No inspiration required, only calculation.
As long as his hand didn’t tremble, his heart didn’t panic, and he hadn’t forgotten his multiplication tables, he could get the answer.
And so, Chen Zhuo began to calculate.
His scratch paper was instantly filled with dense formulas.
Square roots within square roots, fractions stacked upon fractions.
The tip of his pen flew across the paper, the ink flowing into a stream of numbers.
In the dead-silent examination hall, this sound was practically a form of psychological warfare.
The girl beside him lifted her head, her eyes red, and glanced at Chen Zhuo.
She looked at the blank paper in front of her, which had nothing but two circles drawn on it. A tear finally escaped, falling onto the test paper with a SPLAT.
It smudged a pool of ink.
Chen Zhuo didn’t see it.
He was immersed in a torrent of numbers.
To him, this was no longer a math problem, but an engineering one.
Define points, formulate equations, solve simultaneously, eliminate variables, simplify.
It was a tedious, mechanical, yet strangely rhythmic process.
The third page of scratch paper was full.
The final line.
k1=k2.
The slopes are equal.
The three points are collinear.
Q.E.D.
Chen Zhuo let out a long breath.
His wrist ached as if he had just finished a game of badminton.
He glanced at his watch.
「Eleven-fifty.」
Perfect.
He copied his answer neatly onto the answer sheet.
Then he put down his pen and shook out his wrist.
The surroundings were still silent.
Except, this silence was now punctuated by a few irrepressible sobs.
It was the sound of mental states completely breaking down.