The second round of the KMO is being held at KAIST.
I had been worried that I might have to go to Seoul, but fortunately, test centers had been arranged in every province.
It wasn’t that I disliked Seoul, but the traffic was always terrible and the air wasn’t good, so every time I went there, I felt stifled.
“I’ll do well and come back.”
“Okay. Call me when you’re done!”
The area around the university’s main gate was too crowded, so I got out ahead of time instead of going all the way in.
After seeing Dad off, I trudged along the road.
Mom had been making food since dawn, so I had woken up early too. There were six problems in total. The test was divided into two sessions of two and a half hours each. There was, of course, a lunch break in between.
‘You didn’t have to make all this for me…’
I felt a little embarrassed holding the insulated lunchbox.
Still, it was sure to be packed with delicious food, so I was looking forward to lunchtime.
As I walked, I spotted a pond.
“Duck Pond?”
What an unimaginative name.
When I approached, I saw that there were many ducks floating leisurely on the water. I stood there blankly, watching them for quite some time.
Their kind eyes and broad yellow bills.
Their soft, warm feathers and bodies sleekly streamlined by fluid dynamics.
Unlike chickens, ducks even knew how to share food with one another.
And on top of that, they had the cuteness of waddling when they walked.
‘Their toes are cute too.’
More than anything, it was amazing that all of this harmony had been created as the result of natural selection.
I had liked ducks ever since the days when I used to pore over encyclopedias.
‘Could there be any souvenirs?’
When I hurried over to the shop, I found it filled with blue dolls that looked stupid.
The more I looked at them, the cuter they seemed, so I bought one along with some duck merchandise.
‘I should give it to Seoeun.’
“Ah!”
Without realizing it, I had gotten completely distracted by the ducks.
I could almost hear my teacher nagging me. He had reminded me several times before I came to take the test.
“Don’t expect the graders to understand everything you write. They have to grade 200 pages of answer sheets. Do you think the professors will do all of that themselves? There are some truly stupid people among the teaching assistants, so you have to remember this.
How did I tell you to write your answers?”
“In simple terms. In a way anyone can understand.”
“Right. You can’t write your answers the way things are automatically omitted in your head, understand?”
I had listened to that lecture until my ears were numb.
Quickly, quickly.
My steps toward the lecture hall grew faster.
I arrived at the Natural Sciences Building and found the examination room.
Clatter.
When I opened the door and went in, there were many faces that looked vaguely familiar.
“Yu Seoha! I knew you’d come too.”
Noona Sujeong, who had been sitting quietly in a corner, raised her hand in greeting.
I felt embarrassed. Pretending not to notice her gaze, I looked for the seat written on my admission ticket.
“That’s him, right?”
“Is an elementary school student really allowed to compete in the IMO?”
“There have been cases overseas. I heard Eliya Kronen started competing when she was ten.”
The whispers had become something I was used to by now.
I wanted to become an adult quickly. Even if only by a few years.
A group of students who seemed to be together gathered around and deliberately began talking loudly.
Ah! I remembered reading about this in an encyclopedia.
Social safety nets, conformity pressure, symbolic displays.
An attempt to gain psychological stability by forming a group in an unfamiliar place.
Everyone was nervous.
Thinking of it that way, they didn’t seem entirely bad.
The large student among them pointed at someone and asked,
“Hey! Choi Yujin. Guess you’re not the youngest anymore?”
“Hyung! How long did you think I’d stay an elementary school kid?”
His voice was irritated.
If I’d known this would happen, I should have spent more time at the souvenir shop.
“Why don’t you go say hello? You’re going to be seeing each other often from now on.”
“Ugh, what a pain.”
Step, step.
Until now, whenever I went to a test center, people had pretended not to see me.
So despite the discomfort, it hadn’t interfered much with the tests themselves. But the atmosphere here was completely different.
‘Like an inner circle?’
It was clear that they felt a certain degree of kinship with me as well.
But why?
At most, they might have occasionally seen my face while coming and going.
“Hey, Yu Seoha!”
Choi Yujin called out to me. I could no longer pretend not to hear him.
“Yes?”
“You’re in fifth grade, right? Where are you from?”
Why was he suddenly conducting a background check?
I felt a rebellious impulse, but my body was honest. Older boys were frightening.
“Okcheon County, North Chungcheong Province.”
“No, not that! You know what I mean!”
He suddenly shouted in exasperation.
My shoulders hunched.
“D-Dodam Elementary School?”
Only then did he seem to realize that something was strange.
“What? You’re not from a gifted education center?”
“No.”
He laughed as if he found that ridiculous.
“Wow! This is hilarious. You came here at your age without ever attending a gifted education center? I’ve never even heard of such a thing.”
“Is that strange?”
“Of course it’s strange. All the middle school students here came from the same gifted education center. Noona Sujeong over there too.”
I had had no idea.
I glanced behind me, and Sujeong noona shrugged.
“Anyway, I’ll take good care of you from now on. You won first place in the Seoul Mathematics Competition, so you’re going to pass the second round, right? Just trust your hyung. I’ll even let you join our study group. It’ll help you a lot, you know? I don’t do this for just anybody. I’ve been the youngest until now, and finally, someone younger than me has joined.”
Joined what, exactly?
And when had he gotten close enough to call himself my hyung?
Unlike at first, when he had made it abundantly clear that he didn’t want me around, he was an incredibly talkative person.
“Yes, thank you.”
Unable to think of anything else to say, I bowed politely.
Apparently satisfied, he patted me on the shoulder.
Clatter.
“Everyone’s here, right? Let’s start the test.”
Once the proctors entered, the lecture hall settled down.
A woman wearing glasses and a young man dressed in shabby clothes.
They made a strangely well-matched pair.
Ssshh.
The bell rang, and the test papers were handed out.
Now it was time entirely for me.
Problem 1.
[At a party attended by six people, prove that whenever any three people are selected, there must exist three people who all know one another or three people who are all strangers to one another.]
It was a classical Ramsey theory problem involving the pigeonhole principle.
Scratch, scratch.
The morning problems seemed largely focused on gauging the depth of one’s reasoning.
‘Do I really need two and a half hours?’
Remembering my teacher’s advice, I tried to spend as much time as possible writing out a clear and detailed explanation.
「…Therefore, in every case, there must exist three people who satisfy the condition.」
Problem 2.
[Prove that among any 1,000 consecutive natural numbers, there must be a number that is not prime.]
A number theory problem.
Seeing a problem related to prime numbers made me smile.
Seoeun had been enjoying playing with numbers lately, and it seemed she had memorized every prime number under 500. Since that wouldn’t be much fun anymore, I decided that from now on, I would play with her by starting at 1,000 and counting downward.
Scratch, scratch.
「…Therefore, 1001! + k is divisible by k and is thus composite. In this way, we can construct 1,000 consecutive composite numbers.」
Problem 3 was about planetary orbits, something I had once seen hanging on the wall when I was young.
When I closed my eyes, a beautiful universe unfolded before me.
The beauty of elliptical orbits expressed in polar coordinates. Although an ellipse had two foci, the sum of the distances from a planet to the two foci was always constant.
The complex movements of the planets in the solar system, unfolding according to such simple mathematical rules.
A perfect cosmos without a single error.
How happy must Kepler have been when he discovered it through calculation?
I wanted to experience that same joy.
The problem had tried to give me something to puzzle over, but it wasn’t difficult if one understood celestial motion well.
Beep—
“Stop! Submit your answer sheets, and then go have lunch.”
When the proctors left, voices rose all around the room.
“Hey, wasn’t number three way too hard?”
“I was done for starting with number two.”
“Was number three for real? Wasn’t that graduate-school level?”
Ssshh.
I quietly stood up, carrying my lunchbox.
It was winter, so going outside would be difficult. Where should I eat?
Then I heard a voice behind me.
“Hey!”
Noona Im Sujeong?
She called out to me with her arms crossed and a pouty expression.
“Yes?”
“Let’s eat together. You probably don’t know anyone here besides me.”
“Thank you.”
I obediently followed her out.
I didn’t know the area, and there weren’t many suitable places nearby where I could eat alone.
We arrived at the cafeteria on the first floor.
I sat down and placed the insulated lunchbox I had brought on the table.
“Pfft. You’re still a kid, huh?”
I had already been self-conscious about it, but…
The moment Sujeong saw the colorful character lunchbox, she burst out laughing.
My face turned red. From next time on, I should pass it down to my younger sibling.
“When I was attending the gifted education center, my dad used to pack my lunch often too. I miss those days.”
She wore a wistful expression.
“What are you going to eat, noona?”
“I’ll buy something over there.”
When I turned my head, I saw all kinds of food being sold at the food court.
I began unpacking my lunch and waited for a moment, but the group from earlier approached us. I hurriedly turned my head away, but they seemed to be coming straight toward us.
“Yu Seoha! Why’d you rush off so quickly? Let’s eat together.”
Thump.
Three of them came over in an instant and set their trays down around me.
I should have refused, saying someone was already sitting there, but they had already picked up their spoons and begun eating.
“Hey! Why are you guys here again?”
As expected, Sujeong came up behind us and angrily confronted them.
“Let’s eat together. He’s alone too. And it’s been a while, Im Sujeong. Is attending Yeongjae High School manageable?”
“I don’t know!”
They seemed to be close, because the large student offered her the seat beside him. But my noona, looking displeased, avoided that seat, circled around to the other side, and sat down beside me.
Everyone must have been hungry, because they began eating.
“Tastes good.”
“It’s much better than our school cafeteria food.”
“But did you solve number three?”
“Our teacher said number three in the first session and number six in the second weren’t problems we were expected to solve. Finding an approach alone would be enough for a high score.”
“I heard that too.”
“I think I solved it properly.”
The large student gave a derisive chuckle, then took out a notebook and wrote down the problem.
Then he looked at me and asked,
“Hey, Yu Seoha. You haven’t learned this yet, have you?
My dad’s a university professor, so he taught me. To derive the orbital formula for this problem, you need to know celestial mechanics and orbital mechanics. It’s something that comes up in aerospace engineering, but…”
He pulled me closer.
At the same time, he kept glancing around, as if he was conscious of Sujeong noona.
“Im Sujeong, did you solve this?”
“No. I only wrote down my assumptions.”
“Then you should listen too. So, these six orbital elements…”
“Wait!”
He had written down his answer and was just about to explain orbital mechanics when noona cut him off. Then she looked at me.
“Yu Seoha, be honest. You got this one right, didn’t you?”
Why was she doing this to me?
But I couldn’t say I had gotten it wrong when I had solved it.
“Yes…”
She smiled as if she had expected that answer, then pointed with her chin at the large student’s notebook.
“Is what he wrote correct?”
A messy collection of formulas and incorrect derivations.
Could he not see the orbit described by the equations he had written? If it moved like that, the planets would eventually collide with one another.
“No. That problem doesn’t require orbital mechanics. You can derive the answer with just basic astronomy, Newtonian mechanics, and Kepler’s laws.”
The large student’s face turned red.
“Can you take responsibility for saying that?”
There was a threatening note in his voice.
I sighed. This was exactly why I hadn’t wanted to get involved…
But once I had started talking, I couldn’t back down. Besides, his attitude had been strangely unpleasant.
“Yes. I’ll show you.”
I took a notebook and my duck pencil out of my bag.
“First, according to Kepler’s First Law, a planet’s orbit is an ellipse with the sun at one of its foci.”
Scratch, scratch.
“And if we use Newton’s law of universal gravitation and centrifugal force…”
[F = GMm/r² = mv²/r]
“From here, we can find the angular velocity and apply Kepler’s Third Law to determine the relationship between the orbit’s semimajor axis and its orbital period.”
I worked through the equations step by step.
Before I knew it, the area around us had grown quiet. Everyone was watching the tip of my pencil.
“Therefore, if we substitute the conditions given in the problem…”
Once I finished the calculations, the exact answer emerged.
“Like this.”
When I put down my pencil and raised my head, silence filled the room.
The large student stared intently at the answer I had written, his mouth hanging open.
The students beside him looked at it skeptically.
“Is this really right?”
Did he not understand even after seeing the solution?
“Try plugging it in and checking.”
The group hurriedly pulled calculators from their bags.
Click, click, click.
A moment later, exactly the same number as the one written in my notebook appeared on their calculators.
“It really is…”
An awkward silence settled over us.
“This is hilarious! Who was trying to teach whom?”
A high-pitched voice that sounded oddly pleased.
Noona stood up, carrying her tray. Then she gestured with her eyes for me to follow.
“Two people from the IMO are enough for us. The rest of you can figure things out among yourselves.”
She pulled me away from the table.
Ah! I hadn’t finished the lunch Mom packed for me yet.