The library of Rajawali High School was not merely a repository for books. It was a sanctuary—a hallowed ground for those who worshipped academic excellence above all else. The floors were draped in thick, sound-dampening carpets that swallowed the sound of footsteps. The towering shelves were crafted from polished mahogany, and the central air conditioning was tuned to a temperature low enough to freeze the lingering intentions of any student looking to skip class.
In a secluded corner known as the "Competition Zone," fifteen select students sat around a massive circular table. This was a specialized coaching session, a crucible designed to forge the school's representatives for the National Science Olympiad (OSN).
The atmosphere was suffocatingly tense. The only sounds were the aggressive scratching of pens against high-quality paper and the occasional, heavy sigh of a frustrated student hitting a mental wall.
At one end of the table, Nadia sat as rigid as a queen presiding over a cabinet meeting. Spread before her were three thick, English-language reference books, a high-end scientific calculator, and a pencil case organized with a military-like color gradient. Her eyes were fixed on the problem sheet, her gaze so intense it seemed capable of burning holes through the paper.
Directly across from her sat a sight that was an affront to the room's prestige. Salim was slumped in his chair, his legs stretched out under the table—thankfully avoiding everyone's shins. He had no reference books. He held only a single, cheap ballpoint pen whose cap had vanished long ago. Before him lay a single sheet of scratch paper, crumpled and creased because he had spent the first ten minutes of the session folding it into a paper airplane.
Mrs. Laras, the young yet notoriously perfectionist Olympiad coordinator, tapped the small whiteboard beside the table.
"Right, pay attention," Mrs. Laras's voice sliced through the silence like a scalpel. "This is the final problem for today. It's a combinatorics challenge that appeared in the 2018 National Team selection. I want to see who in this room possesses the sharpest logic."
She began to write. It wasn't a problem of numbers, but of dizzying mathematical logic.
THE PROBLEM:
"There are 20 people in a room. Each person has exactly 3 enemies within the room. Prove that we can divide these 20 people into 2 groups such that every person has at most 1 enemy within their own group."
Nadia's hand instantly gripped her pen. Her eyes sparked with recognition. This was her territory: Graph Theory. She knew the theorems, she had memorized the lemmas, and she had practiced the induction steps until she could recite them in her sleep.
Meanwhile, Salim let out a long yawn. Dia began to twirl his pen between his fingers—a pen-spinning trick he had picked up from a YouTube tutorial while waiting in a long line for subsidized groceries.
"What's wrong, Salim? Giving up already?" a snide voice whispered from beside Nadia.
It was Rinto. He was there not because he was a mathematical genius, but because his parents were the library's largest donors. This secured him an "honorary seat" on the Physics team, which happened to be practicing in the same wing.
Salim glanced over lazily. "Nah, Rinto. I was just thinking... if every person here has exactly three enemies, then this is one hell of a toxic social circle."
A few students muffled their snickers, but Nadia slammed her palm lightly on the table.
"Can you be serious for once?" Nadia hissed, her voice trembling with irritation. "This is a selection process, Salim. If you're just here to play around, leave. Give that seat to an eleventh-grader who actually cares."
Salim shrugged. "I am serious. Dead serious about waiting for you to solve it."
Nadia scoffed and returned to her work. She began by drawing dots—vertices—representing the people, and lines—edges—representing their mutual animosity. She attempted to apply the Pigeonhole Principle combined with Turán's Theorem.
Her paper was soon cluttered with complex graphs and rigorous notations. She attempted a proof by mathematical induction.
Assume P(n) is the statement...
If we partition the set V into V1 and V2...
Fifteen minutes bled away. Beads of perspiration began to form on Nadia's forehead. Her proof was stalling. Every time she moved one 'person' to the other group to reduce their local enemies, it inadvertently increased the enemy count for someone already in that group. It was like pressing down on a water balloon; solve one side, and the other side bulges with a new problem.
"Two minutes remaining," Mrs. Laras warned, her voice acting as a countdown to a mental explosion.
Panic flared in Nadia's chest. She frantically scratched out a section of her work, trying a greedy algorithm approach. But the clock was relentless. Her logic was tangling itself into a knot she couldn't untie.
"Done," a flat, monotone voice announced.
It didn't come from Nadia. It came from across the table.
Every eye turned toward Salim. The scratch paper in front of him was still almost entirely blank. Pristine. No complex graphs, no Sigma notations, no sprawling lemmas.
"Where is your answer, Salim?" Mrs. Laras asked, an eyebrow arching in curiosity. "Your paper is empty."
"The answer is in my head, Ma'am. Writing it all down makes my wrist ache," Salim replied nonchalantly.
Nadia let out a forced, cynical laugh. "Don't be ridiculous. A proof requires steps. You can't just guess 'Proven' or 'Not Proven.' This isn't a multiple-choice question."
"Who said I was guessing?" Salim straightened his posture. His 'class clown' mask vanished, replaced by a gaze so sharp and cold it made the air feel even thinner. It was a side of him he rarely revealed—the predator within the genius.
"Alright, Queen of Formulas," Salim said, locking eyes with Nadia. "You tried to use induction, didn't you? And then you got stuck because you couldn't handle the overlapping variables of the enemy counts?"
Nadia went still. His guess was a direct hit.
"You're overthinking it," Salim continued. He took his pen and drew a single large circle on his paper, then split it down the middle with a line. "Mrs. Laras, may I explain verbally?"
"Go ahead," Mrs. Laras said, crossing her arms, intrigued.
Salim pointed to the two halves of the circle. "Let's say we just throw these 20 people randomly into two groups. Group A and Group B. Totally random, no order."
"That proves nothing, you idiot," Rinto interrupted.
"Shut it, Donor Boy," Salim snapped, his sharp tone turning Rinto's face a violent shade of red. "Listen and learn."
Salim turned back to the table. "Now, we check every person individually. Let's take a guy named Budi. If Budi has, say, 2 or 3 enemies in his own group—let's say he's in Group A—what do we do?"
Salim looked at Nadia, baiting her.
"We... we move him?" Nadia answered hesitantly.
"Exactly," Salim snapped his fingers. "We move Budi to Group B. Since he only has 3 enemies total in the whole room, if he has at least 2 in Group A, that means he has at most 1 enemy in Group B. So, by moving him, he becomes 'safe'—he now has at most one enemy in his group."
"But..." Nadia interjected, her mind racing to find a flaw. "If Budi moves to Group B, he might increase the enemy count for someone already in Group B! That ruins the stability of the other people!"
"Ah, and that's the point," Salim offered a slanted, ruthless smirk—one that made Nadia feel incredibly small. "That's the key. We don't care about individual stability yet. We look at the variable of the Total Number of Enemy Pairs within the groups."
Salim wrote a simple symbol: E_total.
"Every time we move a person who has 2 or 3 enemies in their current group to the other side, the total number of enemy pairs in the system must decrease. Why? Because we are cutting at least 2 enemy links in their original group and adding at most 1 link in the new group. -2 + 1 = -1. The total 'conflict' in the room goes down."
Salim set the pen down. "Since the number of enemy pairs is a finite whole number—it can't go below zero—this process of reduction cannot go on forever. It has to stop. And when does it stop? It stops when there is no longer anyone who has 2 or more enemies in their own group. At that point, the condition is met. Proven."
Silence.
A long, agonizing silence for Nadia.
Salim's explanation was so simple, so elegant, and so... human. He didn't use the complex notations from her expensive textbooks. He used the logic of movement and optimization—a concept that could be understood by a middle schooler, yet it solved a national-level problem.
Mrs. Laras beamed, a rare expression of pure delight. "The Descent Algorithm. Or proof by Invariant. Absolutely brilliant, Salim. You solved a complex problem by shifting the perspective into a simple optimization task."
Nadia stared down at her paper, which was cluttered with useless scribbles. Her hand trembled with a mixture of rage and profound humiliation. Again. She had lost again.
She attended the most expensive cram schools in the city every weekend. She devoured imported textbooks. Yet, this scholarship kid—whose motorcycle constantly broke down—was always one step ahead of her.
"That... that's cheating," Nadia whispered, her voice cracking.
"What's cheating, Nad?" Salim asked, his tone returning to its usual lazy, slightly mocking drawl. "Logic can't be cheated. You're just so busy memorizing the map that you forgot to look at the road."
Nadia stood up abruptly, her chair screeching harshly against the floor. She gathered her books with violent, jerky movements. "I have a headache, Ma'am. I'm requesting permission to leave early."
Without waiting for a response, Nadia stormed out of the library. Each footfall echoed her ego's defeat. Rinto scrambled to his feet, casting a murderous glare at Salim before chasing after her. "Nadia! Wait up! Just ignore that peasant!"
Salim simply shook his head at the drama. He slumped back into his seat.
"You were a bit hard on her, Salim," Mrs. Laras commented, though her tone wasn't truly scolding.
"I just answered the question, Ma'am. If she takes my answer as a personal attack, that's a problem between her and her ego," Salim replied indifferently.
Suddenly, Salim's phone vibrated in his pocket. A message from Dani.
DaniTheFridge: Yo, Lim! Get to the parking lot ASAP. A stray cat didn't pee on your bike, but your chain snapped again. I'm waiting. You're hitching a ride in my car. Rizki and Maya are coming too.
Salim offered a faint, tired smile. The contrast of his life was almost comical. Inside this room, he was an intellectual giant who had just humiliated the school's "queen." But the moment he stepped through those doors, he was just Salim—the scholarship kid with a broken bike who had to rely on his wealthy friend's luxury car.
He stood up, grabbing his near-blank scratch paper. To anyone else, it was trash, but to Salim, it was proof that he didn't need tools to think.
"I'm heading out, Ma'am. I have diplomatic duties. Specifically, the diplomacy of a broken bike chain," Salim joked.
As Salim walked down the hallways that were beginning to empty, he didn't notice Nadia standing behind a pillar in the corridor. Her eyes were red from holding back tears, her hands white-knuckled as she gripped her math book.
The hatred in Nadia's eyes was no longer mere academic rivalry. It was a grudge. A deep, festering resentment born from the feeling of having her pride stripped away, layer by layer, by someone she considered 'beneath' her.
"Just you wait, Salim," Nadia whispered to the empty air. "Someday, there will be a test you can't solve with your lazy logic. And when that day comes, I'll be the one laughing."
Little did Nadia know, her prayer would be answered much sooner and in a far more terrifying way than she could imagine. That test wouldn't be on paper; it would be written in blood. And in that test, Salim's 'lazy' logic might be the only thing separating them from an early grave.
Salim reached the parking lot. Dani was already waving from inside his garish yellow Mustang. Rizki sat in the front seat with his usual calm, while Maya sat in the back, leaving an empty spot beside her for Salim.
"Took you long enough, Professor!" Dani shouted. "What atomic formula did you solve this time?"
"The formula for giving Nadia high blood pressure," Salim replied as he climbed into the car, greeted by Dani's boisterous laughter and Maya's soft, knowing smile.
The car door thudded shut, isolating them in air-conditioned luxury. They left Rajawali High behind—a monument to ambition and intrigue. For a moment, life felt normal. Warm. Safe.
But it was only the calm before the storm. The hands of the clock were turning, drawing closer to the day of the study tour. The day when every formula, every rivalry, and every social status would be reset to zero.