Translator: Dreamscribe
When he checked the time, the first thought that came to Seo-ha's mind wasn’t Woo-hyun’s urging that he must achieve overwhelming results at the IMO.
‘Oppa, you really have to bring back my gold medal too, right?’
His little sister waiting at home for her medal.
Knowing Seo-eun’s personality, she surely couldn’t help herself and had already drawn a picture in her sketchbook of herself wearing the gold medal.
‘If I don’t keep my promise, she’ll be really disappointed.’
Cold sweat ran down his back.
Seo-ha quickly scanned Problems 4 and 5.
It takes at least 10 minutes to solve a problem, and another 10 minutes to write the solution. Two problems remained, so double the time was needed. Since the solution process is included in the score, there was no room to cut time.
‘Ah! I guess there’s no choice.’
Seo-ha took a deep breath.
‘Ducky.’
Perhaps because he had prevented it from solving problem 6, there was no response.
‘Ducky, don’t you want to see Seo-eun happy too?’
In that instant, he felt something stir in his mind.
Seo-ha instinctively knew that Ducky cherished Seo-eun just as much as he did.
‘There’s not much time. I’m asking you. Let’s do this together.’
Seo-ha allowed Ducky to take over.
In that moment, he felt something release in his brain. Like tightly fastened screws loosening one by one, the abilities Seo-ha had always kept restrained were explosively unleashed.
Seo-ha began reading Problem 4.
[From point P inside a cube....]
He understood the moment he read it.
Geometry problem, optimization, symmetry, topology.
Ducky’s obsessive precision instantly constructed a complex coordinate system. At the moment Seo-ha’s intuition grasped the core idea, Ducky converted it into a perfect mathematical expression.
Seo-ha’s hand began moving at an incredible speed.
‘Coordinate setup P(a,b,c), distance to cube vertices....’
He read, understood, and wrote all at the same time.
The transmission time from eye to brain to hand was reduced to nearly zero.
Ducky systematically categorized all possible cases, and Seo-ha’s intuition picked out the key among them. The two abilities were in perfect harmony, producing powerful synergy.
But even so, the constraint of physical time still remained.
Seo-ha glanced at the clock.
‘I can’t write out the entire solution process.’
He reduced what should have been a 10-step process to five steps.
Problem 4 complete.
Time taken: 5 minutes.
He immediately moved on to the next problem.
[Select r marbles out of n....]
A fusion of combinatorics and probability.
As Seo-ha read through the problem, Ducky rearranged all possible patterns in his mind.
Inclusion-Exclusion Principle, recurrence relations, generating functions.
All the necessary tools flashed through his mind like lightning.
Seo-ha’s pencil glided across the paper like that of a professional scribe.
‘The essence of combination is choice and exclusion.’
Ducky arranged the n marbles in his mind into a perfect grid. Each possibility appeared as a mathematical probability.
‘This has a slightly deeper layer. Look at the chain reaction of conditional probabilities.’
Ducky responded instantly.
A complex probability distribution unfolded in his mind in the form of a perfect tree structure.
[First selection: P₁ = r/n]
[Second selection: P₂ = (r-1)/(n-1)]
[Product of conditional probabilities...]
Even so, Seo-ha’s hand didn’t stop.
The answer was completed simultaneously with his thinking.
'Not enough time. Only the essentials!'
A proof that would normally take 15 lines was compressed into 5 lines. But there were no logical leaps. By Seo-ha’s standards, every step had sufficient persuasive power.
Problem 5 complete.
“Time’s up!”
The exam ended the moment he wrote the final answer.
Marcello had been watching the entire process from two steps away.
The concentration and speed the boy displayed at the final moment.
He felt both pleased and uneasy, as if he had witnessed something that surpassed human limits.
Before he realized it, he approached Seo-ha and spoke to him.
“Are you alright?”
The boy wore a blank expression.
As if he hadn’t heard the question, he gave no response.
After submitting his answer sheet, he stood up and looked around.
With a somewhat uncomfortable expression, as if something didn’t sit right with him.
The boy muttered softly.
“Why did they arrange the desks like this? The symmetry is off. Why are there 21 desks in the third row? If they needed space, they should’ve just arranged them in a hexagonal shape instead....”
Seo-ha was genuinely feeling discomfort. The imperfect desk arrangement irritated him like a thorn stuck under his nail.
Marcello took a step closer and looked carefully into Seo-ha’s eyes.
His pupils were dilated, and the focus of his gaze kept shifting.
‘This is...’
Marcello, having spent decades immersed in mathematics and experienced extreme states of concentration, was able to quickly grasp the boy’s condition.
That the boy was currently in a kind of ‘high’ state.
When the brain becomes extremely activated in specific regions, the mind enters a hybrid state of hyper-focus (Flow) and hyper arousal.
‘No, is it something different?’
The way the boy had solved problems as if possessed seemed different from the flow state commonly referred to in psychology.
At that moment, a certain figure came to Marcello’s mind.
‘Ramanujan?’
There are records that say Ramanujan had similar episodes while doing mathematical research in the Cambridge library (Ramanujan studied mathematics at Cambridge).
A mysterious ability to produce answers without any proof.
Mathematical intuition rising from deep within the unconscious.
A surreal insight surpassing logical thinking.
That was how Seo-ha looked when he was solving Problem 6.
As if someone who already knew the answer was reconstructing the proof in reverse.
“Stop it, Ducky.”
Seo-ha muttered softly to himself, and then came out of the concentrated state.
But the way he gasped for breath still made him seem unstable.
Marcello, concerned, asked him once more.
“How are you feeling right now?”
Seo-ha lifted his head and gave a bright smile.
“Very good. I got to solve an amazingly cool problem.”
Only then did Marcello let out a small sigh.
‘Looks like I was worried for nothing.’
Seo-ha’s answer brought Marcello, the problem setter, a joy that couldn’t be greater.
***
The three days following the exam were free time.
Since the results would be announced at the awards ceremony four days later, the students were allowed to enjoy sightseeing in London in the meantime.
“It’s finally over!”
Ji-hoon shouted with both arms raised high.
It felt like all the tension built up until now had been released in an instant.
“Now I can finally live like a human being again.”
Do-kyung’s voice was full of liberation.
While preparing for the IMO, the Korean team had spent a more intense period of time than ever before. Since it was his last IMO, Do-kyung felt especially emotional.
“How do you feel?”
Su-jeong asked Seo-ha.
“I just want to go home quickly.”
Being overseas and apart from his family had made Seo-ha realize what loneliness felt like.
Besides that, there was something else he needed to confirm.
The euphoria he felt during the moment he solved the problems with Ducky. Seo-ha wanted to understand what that feeling truly was.
‘I wonder if Seo-eun is doing well.’
Because of the time difference, Seo-eun stayed up late into the night just to call Seo-ha.
“Yeah, you're still at the age when you miss your family.”
Su-jeong let out a fake sigh, acting like an adult, and patted Seo-ha on the shoulder.
“Good job, everyone.”
Professor Park looked around at the students with a proud smile.
Regardless of the results, he truly believed the students had done very well this year.
“For the next few days, don’t think about anything and just enjoy London. Is there anywhere you want to go?”
“Really?”
“Are we allowed to have fun?”
“Yes!”
Everyone screamed at Professor Park’s words.
“I want to go to the British Museum!”
“I want the Thames River cruise.”
“Let’s go to Buckingham Palace first!”
Even though they acted mature, they were still high school students, and had already decided on places to visit in between their studies.
Their model-student instincts were still intact, and the six of them quickly gathered, opened up a travel guide, and started planning the sightseeing schedule.
“Well, we’ve got to go to at least one Korean restaurant.”
“We’re all science students, why would we go to Shakespeare’s birthplace?!”
“Newton’s apple tree? Cambridge is too far!”
“The bookstore from Notting Hill? Wasn’t that movie made before we were even born?”
After a heated debate, the sightseeing course was finally decided.
The next morning, the Korean team took the Tube (London subway) together and headed to the British Museum.
Even those who had no interest in relics were intrigued upon hearing that admission was free.
“Wow! This is what’s great about the UK. Truly a developed country!”
Everyone was delighted at the sight of the free admission sign hanging at the entrance.
But once they entered the museum, the atmosphere began to shift slightly.
Inside the massive exhibition halls, artifacts from Egypt, Greece, and Mesopotamia were densely displayed.
“The scale is beyond imagination.”
Ji-ye muttered in a small voice.
Statues from the Parthenon, coffins of Egyptian pharaohs, Babylonian clay tablets, Seo-ha, who had read many books, could easily guess how these grand and majestic relics ended up in London.
“If I were Egyptian, I’d probably cry.”
Su-jeong frowned at the sight of a massive obelisk, as if feeling indignant.
Seeing the students’ expressions, Professor Park quietly spoke.
“You’ve started to think like adults.
It’s a complicated issue. Perhaps we could call it both the glory and the burden of the past? The British government is probably suffering from all the repatriation lawsuits. Still, it’s also true that thanks to that, we’re able to see things like this.”
After touring the major exhibits, the Korean team stopped by the souvenir shop.
“Oh! What’s that?”
Seo-ha’s eyes widened.
A variety of ducks were displayed on one side of the shelf.
There were ducks dressed as pharaohs, in Union Jack patterns, Greek mythology costumes, even Roman soldier outfits.
Seo-ha rushed over and carefully examined each one.
"They're Rubber Ducks (ducks that float in bathtubs). You really do like ducks, don't you?"
Su-jeong laughed, looking dumbfounded.
After looking at them for a long time, Seo-ha finally picked out a Union Jack duck.
***
The next day,
Kingston University Mathematics Department, 3rd floor conference room.
The six problem setters were utterly exhausted after three straight days of grading.
On the first day, they were all ecstatic upon seeing Seo-ha’s miraculous five-page proof.
A genius had appeared who perfectly solved a problem considered the most difficult in IMO history.
But the answer sheets they looked at afterward were the real issue.
Marcello, sleeves rolled up to his elbows, took off his glasses and rubbed his brow.
In front of him were already-reviewed answer sheets organized by score, and his coffee cup held nothing but dried cold coffee.
“Well then, let’s draw a conclusion today.”
At Marcello’s words, everyone nodded and pulled out the documents.
It was the answer sheet for Problems 4 and 5 written by Seo-ha.
“I still believe 3 points is the limit.”
Roberto unfolded the answer sheet.
"He jumps from here straight to here, skipping at least three steps in between."
That was indeed how it appeared.
But what troubled the committee wasn’t just that.
“These parts that appear to be skipped might not actually be omissions.”
Marcello stood and drew a simple diagram on the whiteboard.
“This student omitted unnecessary calculations and presented only the skeleton of the logic. There’s no flaw in reasoning. It’s just not kind.”
For the first time, the Russian judge spoke up.
“But this student’s logical development is extremely difficult to follow. Didn’t it take us over a day to interpret this answer? The answer and score will be publicly disclosed. If we award a high score, will the public be able to accept it?”
But Marcello had no intention of backing down.
“What matters is that this answer isn’t wrong.”
“The IMO is a competition for high school students, isn’t it? If we recognize this kind of answer, how are we supposed to grade in the future?”
“In that case, let me ask you the opposite.”
Marcello looked around at the judges.
“Can any of you find a logical contradiction or mathematical error in this answer?”
Silence fell.
“There isn’t one. Every step is correct, and the conclusion is also correct.”
Roberto admitted honestly.
“It’s just not in a form we’re used to seeing.”
Marcello concluded.
“Then this too is a perfect mathematical proof. Just because it’s written in a different ‘language’ doesn’t mean we have the right to deduct points.”
However, due to strong opposition from the majority of the judges, Seo-ha’s answer did not receive a perfect score.
No matter how free of logical flaws it was, it was still too far from being a model answer.