Unmeasurable by Common Sense
The hand gripping the pencil never stopped moving. The scratch of the pen tip continued in steady rhythm.
While the other kids were still mulling over the conditions of the problems, I had just finished solving one and moved on to the next.
Problem 15: When forming a 5-digit natural number using the distinct digits 1, 2, 3, 4, 5 exactly once each, how many such numbers are even and multiples of 3?
The moment I saw it, I caught the intent. It wasn't just testing calculation speed—it was about interpreting conditions and organizing them efficiently. I had to filter out unnecessary ones and quickly derive the answer.
On the surface, it's asking for even numbers that are multiples of 3... But I realized the multiple-of-3 condition was essentially meaningless.
This is really just about counting even numbers. So, I need to see if the conditions can be separated independently.
Once I grasped the problem's intent, I jotted down the answer in a flash.
Scratch-scratch!
"Huh?"
Amid the noise, there was one other girl whose pencil moved without pause. The genius girl from Samcheong-dong.
Her name was Cha Eun-seol, right?
True to her nickname, Cha Eun-seol wielded her pencil without a hint of hesitation.
Huh. This exam might actually be fun.
The air over the test paper shifted subtly. It turned into a contest of who could pierce the exam's essence faster and more accurately.
My pencil and Cha Eun-seol's moved in near-perfect sync, slicing through the paper. We dove into the next solutions simultaneously, no one leading.
When I was tackling problem 17, she was on 14. Leaving aside the answers, her speed matched mine—if not exceeded it.
The other kids were just stepping into problem 5.
Problem 18: Find the smallest natural number N such that when divided by 6, the remainder is 3, and when divided by 8, the remainder is 7.
This one tested mixed reasoning skills. The problem defined a natural number N: remainder 3 when divided by 6, remainder 7 when divided by 8.
Surprisingly, it didn't require formulas—just understanding the principle made it simple.
Simplify with congruences, and it's done.
I wrote the answer instantly and glanced at Cha Eun-seol. She was just past 15.
Fast.
I'd planned to take it easy, but she was no pushover. A smirk tugged at my lips.
Her skills would rank top 5% even in high school. The competition mixes in advanced topics occasionally.
A high schooler might solve it without much trouble. But Cha Eun-seol was at most a fifth-grader at Yeonhwa Elementary—nowhere near middle school curriculum.
Yet that speed and precision... The Samcheong-dong genius girl was leagues beyond "smart."
No wonder they called her that.
Time to up the tempo?
My pencil doubled in speed. In my past life, I was one of three perfect scorers on the college entrance exam—and the fastest among all test-takers nationwide. I remembered bulldozing through without a single snag.
Glancing at the clock, plenty of time remained. Ramping up, I reached the final page.
Let's see...
I turned to check on Cha Eun-seol.
"Huh?"
"......"
Our eyes met. But tears glistened in the Samcheong-dong genius girl's eyes.
What? Crying during the exam? Did I upset her by staring?
"Uuugh..."
She looked plunged into deep despair, realizing she couldn't catch up.
That kid's a first-grader in elementary school?
Cha Eun-seol had been hailed as a genius since childhood. But for the first time, staring at the incomprehensible being before her, she felt a true wall.
The solving speed was absurd. How did she derive answers without even reading fully?
Her hand trembled faintly on the pencil. True to her title, she'd never chased anyone's back before—let alone been so overwhelmingly outpaced.
Her breath grew ragged. Problems blurred from view, like someone had erased her mind with a rubber.
Exams aren't just about speed. You need sustained accuracy and focus; scores decide everything. Solving fastest means nothing if accuracy dips below 50%—it's a failure.
Cha Eun-seol sneaked a peek at Han Seoyeon's face. One corner of her mouth lifted, savoring the test.
Competition problems ramped up in difficulty. Multiple choice could be guessed, but subjective ones were another level—some even demanded proofs.
Proofs were tough because starting points weren't clear. Calculations had intuitive paths, but proofs required forging your own from interpretation to development.
Not following a set road—you built it yourself.
Problem 25: Prove that the sum of any three consecutive natural numbers is always a multiple of 3.
"......"
She stalled at 25. The pencil tip froze on the paper. The flow from seconds ago vanished like a lie.
Proving three consecutive naturals sum to a multiple of 3. She knew the answer but proving it felt impossible.
1+1=2. But why? Most accept it without logical explanation.
Her wall was the same.
How to express three consecutive naturals? Factor after algebraic setup? Or is the approach flawed from the start?
Her gaze wavered. In proofs, the real danger wasn't miscalculation—wrong starting point invalidated everything after.
Assume generalization.
Examples flashed: 1+2+3, 2+3+4, 3+4+5... A pattern existed, but formalizing it halted her hand.
Intuition, yes—but no logical anchor.
Define the consecutive as variables?
In her struggle, she unconsciously turned. The neighboring scratch-scratch had stopped.
"...!"
Han Seoyeon had paused, shoulders slumped back, a satisfied smile.
My God! Done already? All of it?
No blank space left—solutions filled to the last line. She'd solved even 25, her current hurdle.
Defeat crushed her barely held resolve. The Samcheong-dong genius girl lived in a rundown hanok on the neighborhood's edge. Dad's leg injury kept him jobless; Mom scraped by at a restaurant from dawn till late.
To bring joy to her struggling parents, Cha Eun-seol pushed relentlessly. Good grades made them beam with pride.
"Uuugh..."
Sobs welled from deep in her throat. Vision blurred despite knowing she must hold back.
Can't break here!
She gritted her teeth, reaching for the pencil—but her fingers lacked strength.
All her piled efforts felt futile. Late-night studies, parents' quiet smiles—everything shook, devouring her from within.
Hehe~ That was fun.
A meaningful time after so long. Competing on equal footing meant a lot. Sure, the Samcheong-dong girl stared blankly midway, but whatever.
Exam time ended. Other kids grumbled regrets, filing out.
"How can you solve so fast?"
Huh? A familiar voice. It was Cha Eun-seol, the so-called genius, eyeing me.
"Hmm, well... When I see a problem, how to organize it just pops up first, I guess?"
I smiled lightly. I'd solved without overthinking. Full marks? Confident.
"I think about reshaping conditions before calculating. Then the solution follows almost automatically."
"......"
She just stared, speechless.
"You finish comp exams that fast just by doing that?"
"Once conditions are sorted, the solution's half-done—objective, subjective, proof. Break down givens, merge overlaps, trim extras, derive answer."
"...I won't lose next time."
"Pardon?"
"I lost this round, but next time, I'll win for sure!"
With a squeaky screeech!, she bolted from the room.
What? Did I do something wrong?
Sunbaes and Jeong Hae-won clustered at the entrance, debating.
"Hey! Seoyeon! How'd it go?"
Perfect score incoming, but no need to brag. Surprisingly, everyone looked pleased—must've done well.
"How about you, Hae-won unnie?"
"Me? Heh! What do you think?"
"Hmm?"
"Seoyeon, those problems you picked? They came straight up. Breezed through without snags. Maybe 70 points?"
70 in the regional academic competition? Solid.
Gwang-woo oppa and Mi-yeon unnie flashed V-signs.
"Oh! Seoyeon? Something happen in there?"
"Why?"
"That Samcheong-dong genius girl ran out crying..."
"Ah... Well, see..."
My explanation drew nods. They got it.
"Th-that!"