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Part 1 of Their Unsolvable Equations of Life
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Published:
2025-12-19
Updated:
2026-01-10
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31/?
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Unsolvable Equation of Life

Chapter 4: Call for a Challenge

Notes:

(See the end of the chapter for notes.)

Chapter Text

For now, life in Musutafu is going well.

She rents a fairly spacious flat with three rooms, located about thirty minutes on foot from U.A. High. The building itself is modern and discreet, tucked away on a quiet street lined with neatly trimmed hedges and vending machines humming softly at night. Compared to the vast Fujiwara mansion in Kyoto—with its endless corridors, inner gardens, and servants’ quarters—the place feels almost comically small. Still, for one person, it is more than enough. The rooms are clean and bright, sunlight spilling in through wide windows, and the silence is comforting.

She has never done house chores or cooked before. Even when Sanae lived alone back in Kyoto, there were always people coming in regularly to clean, cook, and take care of everything else. Uncle Ryota had insisted she bring a caretaker with her to Musutafu, but she refused.

After all, Nee-san lived here alone too. If she could manage, then Sanae saw no reason why she couldn’t. Most people handled their own chores and meals; it was simply part of ordinary life. If they could do it, so could she.

On her first day, some of her family’s caretakers had taken charge of setting everything up—stocking the fridge, organizing the kitchen, making sure nothing was missing. At the time, she hadn’t had to worry about a thing. Now, however, the refrigerator that had once been filled to the brim was nearly empty, save for a few bottles and forgotten condiments.

“It’s Saturday today, so it’s not like I don’t have time,” she murmured to herself. “Time for groceries, I guess.”

The internet proved surprisingly helpful. It told her which grocery store was the closest, what time it was less crowded, and even provided simple recipes along with ingredient lists. Sanae carefully wrote everything down, double-checking the list more than once to make sure she hadn’t missed anything.

The grocery store itself was bright and lively, filled with the sound of carts rolling and soft background music. Shelves were neatly stocked, and the vegetable section smelled faintly of earth and freshness. Sanae stood in front of the produce, staring a little too intently at the vegetables, clearly unsure of where to begin.

“Hey, Fujiwara-san!”

A feminine voice called out to her. She turned around to see a brunette girl—one she recognized as the student who had gotten an infinite score in the throwing ball test.

“Hey… Uraka-san?” Sanae replied hesitantly, immediately blaming herself. 

Remembering nearly twenty new names a day was harder than she had expected. Still, everyone else seemed to remember hers just fine, which made the failure sting a little more.

“I’m Uraraka Ochako,” the girl said with a smile. Oh. She had almost gotten it. “It’s a surprise to see you around here.”

Is it? It’s a surprise for her too.

“This is my first time coming here,” she admitted shyly. “I’m trying to buy some vegetables, but I’m not really sure how to pick them.”

Uraraka’s face lit up instantly.

“I see! Do you want some help? I’m really good at this, you know!”

Is there a way to be good at groceries? She wasn’t sure, but the internet had warned her not to trust it blindly. Asking a real person seemed like a better idea.

“I would appreciate that. Thank you.”

It quickly became obvious that Uraraka truly knew what she was doing. She explained how to tell if vegetables were fresh, how to read ingredient labels properly, how to compare prices, and how to balance quality with cost. Sanae listened carefully, trying to memorize everything, wishing she had brought a notebook to write it all down.

“Do you live nearby, Fujiwara-san?” Uraraka asked as they headed toward the exit, their hands full of grocery bags.

“Yes. About five minutes from here, that way,” She replied, pointing down the street.

“Wait—that’s where I’m going too! We might live in the same area!”

It turned out they did. As they walked, the contrast between their buildings became painfully obvious. Sanae’s apartment complex was sleek and well-maintained, almost luxurious in its understated elegance, while Uraraka’s was far more modest and worn.

“So you’re living alone?” Uraraka asked. “Is this your first time?”

“Yes, it is.”

“Well then—here.” Uraraka handed her phone over. “Here’s my number, Fujiwara-san. If you ever need help with anything, you can call me.”

Warmth bloomed in Sanae’s chest. Uraraka was genuinely kind, without expecting anything in return.

“Thank you very much for offering your help, Uraraka-san,” Sanae replied, smiling as she saved the number into her phone. They waved goodbye before heading their separate ways.

Back home, after carefully putting the groceries away, Sanae followed the recipe step by step, making sure not to skip a single instruction. The result wasn’t bad—certainly edible—but it was nowhere near the refined meals she was used to at the Fujiwara domain.

Still, she ate with quiet satisfaction. It was her first meal made entirely by herself, and that alone made it special.

Even so, she made a mental note to ask the family chefs for their recipes the next time she saw them.

—-------------

 

School life naturally falls into two distinct parts.

Mornings are dedicated to general education classes—maths, history, English, and the like. Sanae often finds herself bored during these lessons, not because she struggles with them, but precisely because she doesn’t. Instead of taking notes, she spends the time quietly theorycrafting—running physics calculations in her head, refining the limits and applications of her quirk. The advantage of sitting at the back of the classroom is simple: the teachers can’t see what you’re actually doing. To everyone else, it just looks like she’s one of the rare students who genuinely pays attention.

It’s not that she’s a bad student. On the contrary, she excels in these subjects. She simply prefers to use that time to learn something new. That, in her opinion, is called using one’s time wisely.

Yaoyorozu caught up with her after the morning classes as they made their way toward the cafeteria. She asked about Sanae’s weekend, and Sanae could only answer honestly.

“Studying and training.”

Because that was exactly what she had done. She hesitated for a moment, wondering if she should mention meeting Uraraka at the grocery store. Was that even worth talking about? It didn’t sound particularly interesting.

She didn’t have time to think about it further—Uraraka found her first.

Seeing her again is nice. The brunette has a naturally warm presence, the kind that makes being around her feel easy. Midoriya and Iida were with her as well, which meant that, in the end, Sanae wasn’t just eating lunch with Yaoyorozu, but with three other classmates.

“I must admit, you’re very impressive, Fujiwara-san,” Iida said earnestly.

Sanae continued chewing on her omelette rice before replying. The cafeteria food is good—definitely better than what she can manage on her own.

“Thank you, Iida-kun,” she replied with a soft smile, which immediately sent a faint red tint to his cheeks. “You were impressive during the dash as well. You were the best among us.”

“As flattered as I am—especially coming from you—I must say it’s a small accomplishment compared to yours,” Iida replied, straightening his posture. “You were a beast in every test.”

“He’s right, Fujiwara-san,” Midoriya added quickly. “I don’t even know what your quirk is, but you might be the strongest in our class. Just—don’t let Kacchan hear this, or he’ll never let me live.”

“Kacchan?” The question lingered for barely a second before Sanae remembered. “Oh—Bakugou Katsuki.”

Midoriya nodded.

“That’s a cute nickname for him, Midoriya-kun,” she said thoughtfully. “You two sound… close?”

She hesitated before asking. From the nickname alone, one would assume so. But from what she had seen the last time they were together, “close” didn’t seem like the right word.

“Ah… it’s kind of complicated,” Midoriya replied awkwardly. “We grew up together, but Kacchan is—well, he can be difficult to deal with.”

“Midoriya-kun,” Yaoyorozu said calmly, taking a sip of water, “honestly, he looks more like your bully.”

“It’s okay, Deku-kun!” Uraraka said quickly, trying to lighten the mood. “You’ve got us now. If he’s mean to you again, we’ll help!”

“Thanks, guys,” Midoriya said with a nervous laugh. “Let’s talk about something else—something more interesting! Like you, Fujiwara-san. What’s your quirk?”

It’s obvious he wants to steer the conversation away from Bakugou. Sanae considers answering—but the idea of not answering is oddly appealing.

“We have training battles after lunch, right?” she replied instead, tilting her head slightly. “If you get to see me fight, I’d like you to guess what my quirk is~”

She punctuated it with a playful wink.

Midoriya turned red instantly, like a tomato.

Nee-san had once told her that teasing people every now and then was fun—and that, surprisingly, they tended to appreciate it.

—-------------

The first battle training of the class was being led by the legendary Symbol of Peace himself. All Might who was, as always, impossibly larger than life. Sanae knew that many of her classmates admired him, and many others drew inspiration from him to become heroes. Nee-san, for example, or even herself when she was younger—All Might had been that symbol of hope she had looked up to.

The students were instructed to change into their battle suits. 

Sanae had requested a customized outfit: a mix between a martial artist’s attire and protective gear, complete with gloves, elbow and knee pads, sturdy shoes built to support her flights and landings, and an IA headpiece to assist with her quirk calculations. The goal was simple: allow her to move as freely as possible while supporting her body through the intense maneuvers her quirk demanded. 

The headpiece was meant to give her back-view data and decrease calculation times by providing exact physics values for objects around her. She hadn’t expected U.A. to fulfill such a specific request—but apparently, they had.

The training would be 2v2 battles with a hero-versus-villain format. The objective was to either protect or capture a bomb. Sanae’s partner was the short, creepy boy with grape-colored hair: Mineta Minoru. Teamwork with him was going to be… complicated, to put it lightly. Still, she planned to follow the rules and make it work as best as she could.

The first match was the most attention-grabbing: Uraraka and Midoriya versus Iida and Bakugou. Sanae hoped it would go smoothly and that nothing would get out of hand.

“Good luck to you three! You’ll do fine!” Sanae waved with a gentle smile, trying to offer encouragement. Not far from her, Bakugou grumbled under his breath. “Good luck, Bakugou-kun!” she called out. 

She hadn’t spoken to him since their brief morning encounter, but it seemed only fair to show support to him as well.

“Shut up, I don’t need cheering,” he spat, walking away.

Watching the battle, she couldn’t help noticing the complicated history between Midoriya and Bakugou. Someone whispered in class that it was a rivalry, and Sanae didn’t know if she agreed. 

From Midoriya’s point of view, does rivalry involve you being so scared of someone else? And from Bakugou’s point of view, does it make you so angry at the other person every time?

After the two boys almost destroyed the entire building, the match ended with Midoriya and Uraraka winning. Midoriya had suffered a broken arm in the process but Recovery Girl’s healing quirk was strong, so he should be fine—though he wouldn’t be participating in the remaining battles. Her chance for him to guess her quirk would have to wait.

Afterward, All Might called the students together for a battle review. 

“Who wants to share their thoughts on the fight?”

Yaoyorozu’s hand shot up faster than anyone else’s. She launched into an exhaustive analysis, dissecting every move and strategy in a way that left even All Might speechless. Sanae silently thought that at best, she could probably manage only half as thorough a breakdown. 

Bakugou, predictably, remained awfully quiet for someone normally so loud and brash. She could tell he absolutely hated losing. She understood that sentiment herself—she hated losing too. The difference was in how you handled it.

The second match was less dramatic, though somehow still fascinating. Todoroki showcased his ice manipulation quirk, which was clearly powerful, along with his heating ability to prevent himself from freezing solid. Teamwork didn’t factor in much, but the winners still earned a respectable score. She was quietly relieved; it meant she didn’t have to work too closely with Mineta unless absolutely necessary.

The third match saw the oddly cute bird boy and his small avian companion win with his partner, the girl with the frog quirk. Then it was their turn: Sanae and Mineta versus Kaminari Denki and Jiro Kyouka. They had drawn the villain side, which was disappointing for Sanae—she would have much preferred playing hero.

Standing before the bomb, Mineta was, as usual, staring at her with drool at the corner of his mouth. Sanae sighed lightly but forced herself to focus. They had a brief preparation period before the battle officially began, and she intended to make the most of it.

“Mineta-kun.” Sanae called softly, her voice low enough to command attention.

“Yes, my goddess! What do you need of me?” He immediately replied, heart eyes forming and a thin trickle of blood running from his nose.

“I absolutely despise the way you’re looking at me.”

“Ah, it’s not—Fujiwara, you’re the prettiest, of course I—”

“You see this rock?” Sanae lifted a medium-sized stone she had been carrying for just this moment. She reduced its density, then amplified the force so that it shattered like a cracker in her hand. She could feel the fear radiating from Mineta’s wide eyes. “It can also be you.” Her smile was chilling as fragments of the rock fell around her.

“I—I’M SORRY! PLEASE DON’T—”

“Good. We’re going to work with your back always on me. Got it? Never turn around to look at me. Don’t even think about it. And don’t make disgusting jokes—you know what I’ll do if you do.”

“Yes… everything you said.” Mineta obeyed like a frightened child. Sanae preferred this to his usual drooling and ogling whenever he saw her.

“What is your quirk?” she asked, keeping her tone calm. Mineta had turned his back as instructed.

“The balls on my head can stick to anything they touch.”

“Can you cancel the effect if someone touches them?”

“Yes.”

“Alright. Give me a lot of them—but make sure they don’t stick to me.”

Mineta transferred as many balls as he could from his head. Sanae made careful adjustments, and within moments, several purple balls floated strategically around the bomb. Anyone attempting to touch it would be immediately immobilized. Teamwork and strategy points? Maximized.

Sanae was confident she could handle the battle on her own, but she wanted the full score in every category.

“It starts now. Mineta-kun, stay here and watch the bomb. If anyone besides me comes near, try to hold them off and scream as loudly as you can. I have good hearing—I’ll hear you no matter how far.”

Buildings like these made things trickier, especially since she was instructed not to destroy them. She couldn’t end this in a single, Todoroki-style attack—but she had something up her sleeve. As a child, she had played hide-and-seek endlessly with her cousins, though she had always been terrible at finding them. She had once complained about it to Hanae, and Nee-san had told her to consider creating a wave of sound to detect positions.

“You were the best, Nee-san.” She thought, a sad smile brushing her lips.

A gentle ripple of air pressure pulsed through the building. It wasn’t perfect, but Sanae could distinguish humans within the structure. One was on the lowest floor, seemingly waiting for a signal to move up; another was on the third floor. She guessed the one on the third floor was stronger.

“Hey, Fujiwara! I knew you’d come looking for us,” Kaminari called out as soon as they met. “You’re strong, but no one else is here—so don’t try to fight me! My quirk is—”

Before he could finish, Sanae was behind him, striking the back of his neck. Kaminari crumpled to the ground, unconscious. She would learn about his quirk later.

Jiro attempted to retaliate, shaking the walls with her sound-based attacks. Sanae had to admit it was irritating—her acute hearing was both an advantage and a weakness. Jiro lasted longer than Kaminari, but as soon as Sanae regained her focus, she dispatched her with a precise strike to the back of the neck.

“Congratulations, Fujiwara-shoujo. You’ve earned the maximum points for this battle,” All Might greeted, his smile as wide as ever. 

Sanae walked in carrying both Kaminari and Jiro as though they weighed nothing. Mineta obediently walked ahead, still careful not to look at her.

“Thank you, All Might-san,” she said softly, offering a small smile.

“You were perfect there, Fujiwara-san,” Uraraka said, her eyes sparkling with admiration.

“You deserve to be called our best student,” Iida added seriously, his hands moving in precise gestures as he praised her.

“That was so cool, Fujiwara-san! I think you did even better than Todoroki-kun, even if not as fast. And you didn’t just isolate Mineta—you gave him an active role too,” Yaoyorozu said with a warm smile.

“Thank you, everyone,” she replied, smiling genuinely. “Now it’s your turn, Yaoyorozu-san. Good luck—I believe in you.”

Her black-haired friend looked slightly embarrassed at the encouragement, but a faint smile told Sanae she was pleased to have the support.

She stayed at the edge of the crowd, observing the students from a safe distance. Next to her stood a visibly shaken Bakugou, as if he’d seen a ghost. Should she speak to him? He might scream. Yet, strangely, no one else seemed to notice how unsettled he looked.

“Bakugou-kun?” Her voice cut through the haze, snapping him out of whatever had overtaken him. 

He turned, bloodshot eyes locking on her. Sanae tried, again, to reconcile the furious face before her with the boy she had met the other morning—but they seemed like entirely different people.

“Are you alright?” she asked softly. She braced herself, expecting an eruption.

“What—what the hell even is your quirk? What the hell are you!?”

He didn’t scream, but the brokenness in his voice was unmistakable. She recalled Midoriya mentioning that Bakugou hated hearing that someone might be stronger than him. Is this how it felt, she wondered.

“I’m Fujiwara Sanae,” she said gently, offering a small smile.

“I know that.” Well, thanks for remembering her name, she thought.

“My quirk allows me to alter any physics law I understand for any object I touch—or even myself,” she continued.

A silence fell between them, punctuated only by the distant sounds of Yaoyorozu’s battle. Sanae kept one eye on her friend while focusing on the storm of energy in front of her.

“You’re hella strong,” he whispered, low enough for only her to hear.

“Maybe,” she replied, thinking in terms of the students’ standards. By the world’s standard? She still had a long road ahead.

“You’re hella annoying—acting all modest when it’s obvious you know exactly what you are,” he spat out, the anger in his tone palpable. “Not that it matters—I’ll beat you. You, that ice guy, stupid Deku… I’ll beat everyone.”

Determined, rough, passionate, intense. Every ounce of it radiated from him. Sanae felt a curious warmth rise in her chest. Friendship? Probably not. Rivalry? Perhaps. A challenge? Most likely.

It was the first time someone had vowed to beat her, and the thrill was unlike anything Sanae had felt before. She had always been told she was the best, praised and admired—but never truly challenged. The thought that someone recognized her strength and wanted to surpass it made her pulse quicken. For the first time, she felt a spark of excitement, curiosity, and something like connection—a challenge she couldn’t wait to face.

“I’m looking forward to that, Bakugou-kun.~” 

“Stop talking like that!” His voice rose, drawing a few glances from nearby students. 

Sanae didn’t quite understand why he reacted that way, but she noticed a faint red tint to his face. The combination of anger and annoyance somehow made him… almost cute in her eyes.

Later, she walked with Yaoyorozu toward the meeting point for her friend’s driver. They discussed the afternoon’s events, analyzing what went well and what could have been better. Uraraka had asked Sanae to walk home together since they lived nearby, but in the end, the brunette stayed late at school to check on Midoriya in the infirmary. Sanae considered going with her but ultimately didn’t, only passing along a message for him at the end.

With what Bakugou told her earlier, she would need to make the most of her free time, training harder and studying more. So, of course, she didn’t head straight home. Instead, she stopped by the park where she had trained yesterday, ready to push herself further.

Notes:

I can only imagine Katsuki hating his life right now. Also yes Sanae noticed Katsuki wasn't nice to Izuku but like after that, there was rarely any occurence of where Katsuki was really mean to our MC.

Since she doesn't have the full picture, she won't dwell much into it.