Owarimonogatari – Ougi Formula Chapter 18

“The culprit was Komichi Tetsujou, right?”

Ougi-chan said out of the blue.

To this “unexpected” identity of the culprit, I was surprisingly unsurprised. My heart barely stirred. I was completely unperturbed. How come? Even though I should not have known.

I was just as Ougi-chan had said. Somewhere deep inside, I had known all along—that she was the one who was pulling the strings behind this situation. And that Sodachi Oikura had become her scapegoat—or rather, the victim of her actions.

“Shall we continue?”

“Yeah.” I consented. Originally, by the time the name of the culprit was revealed, there would be no need to talk any further. However, I had the obligation to listen to the end. As the narrator of this story, I must expose the truth behind this occasion.

“What made you think that Tetsujou was suspicious? To me, her situation isn’t much different from the rest of the students. Sure, it’s true that her name was mentioned many times throughout my narration, but wouldn’t you usually regard the students who refrained from participating as more suspicious? Well, my words are completely unbacked, though.”

“I’m not doubting her out of such a baseless argument, you know? What first triggered my suspicion was the number of people.”

“number of people?”

“38 people. That is the number of people introduced in Araragi-senpai’s story—I tried counting them. I’ve already double-checked, so I doubt I’ve miscounted. However, this is strange.”

“Strange. Why? It’s not an unreasonable number of students for a class.”

“That’s wrong.”

Ougi-chan spun, surveying the classroom. With incredible concentration, her eyes glanced from one vacant seat to another.

“Araragi-senpai. You mentioned that in this class, no matter the circumstances, you had constantly spent your time in isolation. Whenever group projects were assigned you were the third wheel—the sore thumb—the spare tire. But here’s where it gets strange. If there were 38 students in the class, whether there were two students, three students, or four students in a group, the remainder of students without a group would never result as one.”

(TN: 38÷2=18r2 and 38÷3= 12r2 and 38÷4=9r2, so Araragi-sama would never be alone with 38 students in his class.)

I was at a loss for words.

It was precisely as she said. It was a matter of the most basic mathematical calculations.

“I’m no genius when it comes to math, so Math level 3 or C would be a little too much for me, but I can at least do division. Then let’s try to find a number of students that leaves a remainder of 1 when we divide the students into groups. There’s barely any math to do, you know? We just have to find the common multiple of 2, 3, and 4, and then add 1.”


“The least common multiple of 2, 3, and 4 is 12\. 12 plus 1 is 13\. Oho, and we have miraculously found a number. However, a class of thirteen students is a bit too small after all, so let’s move on to the next smallest common multiple. 24\. Add 1 to 24 and we get 25\. That’s a pretty average class size across the nation, but Araragi-senpai had made it clear that only around half of the class participated in the study session. Seeing 19 out of 25 people is a bit out of question. Then let’s move onto the next smallest multiple—36—plus one—37\. I think this lies within the reasonable range of students, doesn’t it?”

“…Maybe some outsider blended in with the class? But Oikura declared that students unrelated to the case were forbidden entry into the class. Such a possibility shouldn’t—”

“have existed right? However, if we look at this predicament from a different angle, this could also mean that as long as they’re related to the incident, then it’s fine if they stay. For example—”

For example, the homeroom teacher.

Ougi-chan said, smiling unpleasantly.

“But there’s a term you have been constantly using throughout your entire narration, haven’t you. Once you entered the classroom, you uttered that all the members of Class 3-1 had been assembled. That’s right, rather than the complete ‘student’ attendance, you deliberately used the term ‘members’. In that case, the homeroom teacher would also be included in that number. Even if she were to participate in the class meeting, it would not feel out of place.”


“If we think back to it, while introducing series of 38 people, you used words like ‘student’, ‘boy’, ‘girl’, ‘uniform’, ‘classmate’, ‘freshman’, ‘high school student’, and et cetera. However, within the 38 introductions, only during one of them did you never express that they were a high school student. That person was—Tetsujou Komichi. Thus, with the fundamentals of mystery and math, we have determined that Tetsujou Komichi was the culprit through the process of elimination. But wait a second, wouldn’t it be bad for a student to address a teacher without adding a “Miss” before their surname? Hmm, but she was nicknamed “Jou” and you also addressed her without honorifics. Perhaps she was a teacher very intimate with her students and did not mind.”

Cracking a smile, Ougi-chan continued.

“Even for the softball club, she probably participated as the club advisor. Goodness, Araragi-senpai. It’s all because you had to go out of your way to use such misleading language. When you described her as ‘mature’, were you actually hinting at the fact that she was an actual adult?”

“…I had no such intention.”

“Haha, really?”


“Since we’re on the topic, when you had been escorted into the class room by the three girls, all of the seats were taken. However, you also mentioned that if you were to be nitpicky about it, Arikure-senpai’s, Kijikiri-senpai’s, Toune-senpai’s and Oikura-senpai’s seats were unoccupied. That’s strange, isn’t it? Wouldn’t it be weird if your seat wasn’t empty as well? Perhaps someone was sitting there. For instance, the homeroom teacher.

“That’s why it wasn’t as if Oikura forbid you from even taking your seat—there was no available seat for you to take in the first place.”

Ougi-chan said.

“Well, that’s just some supporting evidence. A trivial matter. So how was it? Did my theory that Tetsujou Komichi was not a student, but a member of school faculty completely miss the mark? Did I make any contradictions?”

“…you hit the bullseye. Correct—there was a total of thirty-seven students in Class 3-1. As a result, in addition to the supervisor, Tetsujou Komichi, the participants of the class meeting totaled up to thirty-eight.”

I said in return. I felt strangely compelled to rebut her reasoning—almost as though I was being accused of being the culprit.

“Even then, just proving Tetsujou as the teacher doesn’t justify your claims that she was the culprit. She sat in the seat of a student and proactively participated in the class discussion. That simply means she was a very friendly and warm-hearted teacher.”

“The peacemaker of the class, huh. You sure speak well of your former homeroom teacher, don’t you?”

Paying no heed to my remark, her face lit up with a smile again. I leaned forward in irritation.


“Naturally, even if Tetsujou-sensei had been absent from the meeting—even if her name was never once mentioned, I would have doubted the homeroom teacher. In the midst of the disorder, I wonder who was it that spoke up? To begin with, is it even possible for someone to know the questions before the test? Like.”

While I leaned forward, Ougi-chan pressed her body closer to me. She was too close. I faltered. How weak.

“It would be pretty difficult. Like sneaking into the faculty room? Hacking? Are those really the actions of someone who is committing these crimes for the pleasure?”

“…Sure, if you were a teacher, you would have been able to freely move in and out the faculty room, but to doubt—”

“Stop playing dumb, Araragi-senpai. This was also something mentioned in the midst of the confusion of the class conference—the fact that class 3-1’s homeroom teacher was also the math teacher. Komichi Tetsujou was the math teacher. If so, that means she didn’t know the questions beforehand. She was the one who made them.

Therefore there was no risk.

That was what Ougi-chan meant. She had really paid attention to the finest of details.

She was a superbly good listener.

“… but regardless of whether it’s ‘this case’ or ‘that case’, there’s no way she could have passed around the test questions. Tetsujou never participated in the study session, you know? Well, that’s because there’s really no reason for a teacher to participate in a study session… but a class meeting would be different. How would she leak information into the study session without being found out? Who could she entrust this task to?”

“Neither would she have to entrust it to anyone nor did anyone have to do it for her. Was Higuma was the one who mentioned it? He said that if the test questions had been leaked, something would have felt unnatural. It’s just an insight from his personal perspective, so I don’t know how reliable it is, but he makes a very valuable remark. In additon,—this is a major point—if they were to leak the test questions, why didn’t they just leak all the test questions? I don’t why they would only leak out a single portion of them.”

“To begin with, we’d have to know their motive for leaking the answers to know that.”

We will understand the reason afterward. In all consideration, the only logical argument seems to suggest that Tetsujou-sensei never leaked any information into the study group. The study group was a healthy environment where they taught each other and improved themselves. Just like Oikura wanted.”

“Then why did the nineteen people—”

“That’s easy. Tetsujou-sensei is the one who made the test question, you know? In that case, she can just make the questions to match the study questions.


I forced out an exclamation. I wasn’t surprised after all. I calmly took in the “unexpected truth” that Ougi-chan spoke of.

“Sunahama-senpai, who was in charge of day duty the day after, was lamenting over how she had to clean up after the study session, right? And then you said she had Tetsujou-sensei, Mebe-senpai, and Fukuishi-senpai to help her out. What do you think they had to clean up? Hey, hey, what about it Araragi-senpai? What do you think they had to clean up?”

“…throw away the candy wrappers, and maybe realigning the desks.”

“That’s not it, stupid!”

“…and erasing the blackboard, right?”

Reluctantly, I finished the thought.

That’s right. When holding a study session, a blackboard is indispensable. Basically, that means that the participants of the study session left most of its remains on the blackboard.

Naturally, the free space on a blackboard is limited, so questions were also erased to free up more space, which meant that not the entirety of the study session could be interpreted from the board but—

“A portion of the study session could be made out, huh.”

“Exactly. And if you knew the contents of the study session, then you could make the test questions to match it. Additionally, it was the day of the test, so if she was going to revise the test, she would only be able to do a portion.”

So the reason why the entirety of the study session was not captured was both because not all of it was written down and there wasn’t enough time.

“The math exam took two periods, so I guess she was revising the test problems while the physical examinations were happening… So we should consider the questions slipping into her subconscious while she erased them off the board as a reason for her high performance on the examination?”

“Yeah. I’m sure she realized this in the middle of the class meeting. That’s why she was so uneasy. If she said something carelessly, might have landed herself into the ‘study session’ side of the class. There were also people like Sunahama-senpai and Fukuishi-senpai who chose to ignore the questions on the board, so her ability to absorb that information also proves her innate ability.”

Well, yeah. Even if you knew the questions beforehand, it didn’t mean just anyone could solve them.

“That’s right. I’m sure Tetsujou-sensei also thought similarly, so when the class average catapulted, she was surprised as well. That all the participants except for Igami-senpai would achieve scores above 80… and on top of that, Oikura-senpai had organized a ‘criminal identification session’. She must have been so anxious—that her own crime would be exposed during the conference.”

“So much that she couldn’t even mediate between Oikura and me, huh.”

I leaned back. However, Ougi-chan leaned forward simultaneously. Stretching her body over the desk, she continued the conversation.

“On top of that anxiety, she was also playing an active role in the class meeting. And when push came to shove, she even helped guide the discussion. Even though there was no chance of being exposed in the first place. The fact that the teacher committed the crime is something that no one would ever come suspect. In mystery novel terms, it would be like the true culprit being the detective or investigator—a blind spot. Although that kind of plot has been long overused by now, no one actually suspected Tetsujou-sensei—am I right?”

“Yeah. No one.”

“Other than Araragi-senpai.”

“…No, if that counts as a realization, then you could probably say the same for everyone else in the room. I was just under the impression it was impossible.”

I mean wasn’t everyone relieved? That the process of majority rule ended at the sixth name? I mean, no matter how many names were called, the homeroom teacher’s name wasn’t written on the attendance record.

“Now let’s move onto, um, the incentive? The motivation behind the crime. The reason for her actions.”

“Ah… you said that I would know that later, but, Ougi-chan, you know that as well?”

“If a student was the culprit, this would be a meaningless crime to enact. Even if we were to assume it was purely for pleasure, it’s difficult to come up with a reason on the spot. That’s because if the class average rose, the culprit’s score would dim in comparison. The only merit in that course of actions would be for those who organized the study session—namely, Oikura. But in that case, not organizing a study session would have held more merit. You’ve also made the point that there was no need for her to organize it at all. However in the event that the class average rose, there is one other person who benefits from it. That’s the math teacher. The homeroom teacher for class 3-1\. Tetsujou-sensei. Her evaluation as a teacher would rise, you see? Basically, that was the incentive behind Tetsujou-sensei’s actions.”


Then wouldn’t it have been preferable for her to just hand out the exam in the middle of class? That way, none of us would have had to go through all—

“No, no. If she just passed out the test in the middle of class she’d be found out easily, wouldn’t she? This had to be done so that she wasn’t found out. But she went a bit overboard—by three questions to be exact. She should have held back and chose only one or two questions to switch out, but instead, she had underestimated the abilities of her students.”

That’s right. She was simultaneously making light of her own teaching ability. Her students had solved those questions without fail after all.

And then the outcome.

She lost an exceptional student.

“Is there anything I missed, Araragi-senpai?”

“No… there’s nothing.”

“I see. Then we should head back soon.”

To my curt response, Ougi-chan revealed a bright smile. At a moments notice, she backed away and stepped lightly towards the classroom door.

She set her hand on the handle.

“You can leave now, you know?”

She said.


in contrast, I sluggishly followed her steps. Glancing at my wristwatch, I found that it perfectly matched the clock on the wall. It was fifty-eight minutes past five. Like the way the last puzzle piece fell into place, the hands of both clocks finally fell into identical positions. Twice a day, even the clock frozen in time pointed to the right time.


The clock on the wall should have begun to move as well.

As if it was lagging behind.

Ougi-chan—and I found the answer after all.

The culprit was identified after all—and time continued to advance at its usual pace.

Soon, the last school bell will sound.

“…what do you mean it being fine to leave?”


“I mean, isn’t that a strange way to put it?… what do you mean?”

“Ah, were you unaware of it? Vampires can’t enter or a room or building without the permission of someone inside.”

“Ah… I’ve never experienced anything like that, though.”

“Well, it’s one modified by Oshino-san after all. But because it seems like you can enter buildings freely, I figured you might need permission to exit instead. So I thought I would try saying that ‘it’s fine to leave’. It’s just to ease my mind.”

“…that makes it sound like you were the one who confined me inside.”

“It’s just a misunderstanding. I would never do anything like that to Araragi-senpai. There’s no way I would.”

Ougi-chan explained, giggling to herself.

“You were seized by your own past. For two long years. Am I right?”


“It’s enthralling, though. The teacher they held so dearly as their symbol of ‘justice’ was the culprit of the academic dishonesty. Moreover, it was the intimate teacher who served as a peacemaker and earned the trust of her students. As betrayal seeped into Araragi-senpai’s memories, he put a lid on his heart. No matter how you looked at it, a student’s academic career was ruined. Perhaps Tetsujou-sensei also played a part in Oikura’s ability to become a senior as atonement for her actions?”

“Atonement? No. It was an excuse. An attempt to convince her that she was the better person.”

I said—in an unexpectedly sharp tone. In an attempt to gloss over my words, I pressed my hand against the door to push it open. In that moment, Ougi-chan laid a gentle hand over mine.

From this point on.

I will speak in all honesty.

So that nothing will be misunderstood.

“…what I plunged me into despair was—”

I have reclaimed the memories I tried so hard to forget. It was my recollection of the class meeting held in this classroom two years ago on July fifteenth.

And the process of majority rule.

The true reason for my despair over ‘justice’.

Neither was it because of the class meeting, nor the occurrence of majority rule.

It wasn’t even because of the truth.

Then let’s move on to the next suspect.

Seat number six.

Me—the person Oikura thought was the culprit.

“What plunged me into despair over ‘justice’ was—”

What plunged me into despair over ‘justice’ was—


“Because in the moment Oikura was selected as the culprit, our dear teacher Tetsujou-sensei’s hand was raised the highest.”


And the bell rang.

The door opened.

Come now, let’s go—the class meeting is over.

We can’t stay in school forever, you know?


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