Ishigami sat staring at a line of unhappy faces. Some of them were beyond unhappy—they wore looks of outright pain. A few had gone even further, and drooped in despondant resignation. One member of the dismal class—Morioka—hadn’t even glanced at the test sheet after Ishigami gave the go-ahead to start. He was staring vacantly out the window, head propped up on one hand. It was a nice day outside, with an endless expanse of blue sky stretched high over the school complex. Morioka was probably thinking about how he could be riding his motorcycle if he didn’t have to be in here, wasting time.
The school and most of the students were already out on spring break. There was just this one group of students, with one final, depressing hurdle to jump. Too many kids hadn’t passed even the make-up tests after finals and had been required to do remedial class work. Thirty of Ishigami’s students were in these special classes—a far larger number than for any other subject. And after they were done with the extra coursework, another test awaited them: the re-make-up test.
The head teacher had stopped by while Ishigami was writing up questions for the test, to make sure he didn’t make them too difficult.
“I don’t like saying this, but really at this point the tests are just a formality. We can’t let the students go on to the next grade with failing marks. And I know you don’t like doing all these extra tests, either, do you? Besides, we’ve had complaints that your tests were too difficult from the beginning. Just—make sure everyone passes, okay?”
Ishigami didn’t think his typical test questions were difficult. They were simple, in fact. There were no departures from the material he had covered in class. Anyone with half a brain, and a rudimentary understanding of mathematical principles, should have been able to solve them. Usually, all he did was change how the problems looked. Surely it would be too easy to use problems straight from the textbooks and practice sheets! Still, the students who simply tried to memorize answers and the ones who hadn’t paid any attention at all were at a loss when faced with basic challenges.
So this time Ishigami had done as the head teacher instructed. He had used representative questions straight from the students’ practice sheets. Anyone who had studied even a little should have had no problem.
Morioka gave a big yawn and looked at his watch. Then his eyes met Ishigami’s. Ishigami expected him to look away, but instead Morioka grimaced and held his hands up over his head in the shape of an X, as if to predict the mark that would be on this paper.
Ishigami tried grinning at him. Morioka looked surprised, then grinned back, and resumed looking out the window.
Ishigami remembered when Morioka had asked him what good differential and integral calculus was. Ishigami had used motorbike racing as an example, but he wasn’t sure if that got through to the boy. Morioka’s attitude didn’t annoy Ishigami. It was only natural to wonder why one had to study something. Once such questions were answered—well, then there was an objective, something to learn toward. And that could lead down the path toward an understanding of the true nature of mathematics.
Yet too many teachers refused to answer simple questions of relevance from their students. No, Ishigami thought, they probably aren’t able to answer them. They taught without really understanding their subjects, simply following a set curriculum, thinking only of coaxing a passing grade from the students so they could send them on their way to make room for next year’s flock. Questions like Morioka’s would have been nothing but an irritation to them.
What am I doing here? Ishigami wondered, not for the first time. Giving students tests just so they could earn points had nothing to do with the true meaning of mathematics. It didn’t mean anything. It wasn’t math, and it wasn’t even education.
Ishigami stood and took a deep breath. “Wherever you are on your test sheets, you can stop.” He looked over the classroom. “I want you to turn your papers over and write down what you’re thinking right now on the backs.”
Confusion washed across the faces of the students in the room. A mutter spread through the class. “What we’re thinking? What does that mean?”
“Specifically, I want you to write down what you think about math. No,” he amended, “just write anything about math at all. You’ll be graded on what you write.”
Every face in the room brightened.
“What grade are you going to give us?” a male student asked.
“Depends on what you write. If you can’t handle actual math, I hope you can at least say something about it,” Ishigami said, sitting back down in his chair.
Every student turned over his or her paper. Some, including Morioka, began to write immediately.
I’ll be able to pass them all now, thought Ishigami with some relief. There was no way to mark a blank answer sheet, but as long as they had each written something, he could assign grades as he saw fit. The head teacher might wonder a bit, but surely he couldn’t complain about Ishigami delivering the passing grades he’d specifically asked for.
The bell rang, indicating the end of the test period. A few of the students asked for a little more time, so Ishigami gave them an extra five minutes.
When it was done he collected the answer sheets and walked out of the classroom. The moment the door shut, he heard the room erupt into conversation. There were audible cries of relief.
Back at the teachers’ room, a man—one of the office assistants—was standing just inside the door, waiting for him.
“Mr. Ishigami? There’s someone here to see you.”
“To see me?”
The assistant walked up to him and whispered in his ear. “I think he’s a police detective.”
Ishigami sighed.
“What are you going to do?” the assistant asked, peering at him intently.
“What am I going to do? He’s waiting for me, isn’t he?”
“Yes, but I could tell him you’re occupied and send him home.”
Ishigami chuckled. “No need for that. Where is he?”
“The parent conference room.”
“I’ll be right there.” Stashing the test answer sheets in his bag, Ishigami made his way toward the conference room. He would have to grade them at home later.
The assistant started to follow him, but Ishigami waved him away, saying, “I’ll be fine on my own.” He knew well enough what the assistant was up to. The man wanted to know why the detective was there and had only suggested that they give the detective the brush-off in hopes that Ishigami would tell him what the visit was all about.
The man Ishigami had expected to see was waiting for him in the conference room: the detective named Kusanagi.
“Sorry to bother you here at school like this.” Kusanagi stood and bowed curtly.
“I’m not usually here over spring vacation. I’m surprised you found me.”
“Actually, I dropped by your apartment first, but it seemed you were out so I called the school. They said something about a make-up test? You have to give make-up tests during spring break?”
“It’s worse for the students, I assure you. And today wasn’t a make-up test. It was a re-make-up test.”
“You don’t say. Let me guess: you like putting pretty tough questions on your tests.”
“Why do you say that?” Ishigami asked, looking the detective in the eye.
“Just a feeling.”
“They’re not tough, though. I merely take advantage of the blind spots created when students assume too much. And they usually assume too much.”
“Blind spots?”
“For instance, I give them a question that looks like a geometry problem, but is in fact an algebra problem. If all they’ve done is memorize the problem sheets in their books—” Ishigami abruptly stopped talking and sat down across from the detective. “I’m sorry. I’m guessing you didn’t come here to talk about high school mathematics. So, why are you here?”
“Nothing much, really,” Kusanagi said, joining him at the table and pulling out his notepad. “I just wanted to ask you about that night again.”
“By ‘that night,’ you mean…?”
“The tenth of March,” Kusanagi said. “I believe you’re aware that’s when the incident occurred?”
“You mean the body they found by the Arakawa River? That one?”
“Not the Arakawa, the Old Edogawa,” Kusanagi corrected him without missing a beat. “You may remember me and my partner coming to ask you questions about Ms. Hanaoka? Asking if you’d noticed anything peculiar that night?”
“Yes, I remember. And I’m pretty sure I told you I didn’t recall anything out of the ordinary.”
“That’s right, you did. I was just hoping you could try to remember that evening in a little more detail for me.”
“How do you mean? It’s hard to remember something when nothing happened.” Ishigami let himself smile a bit.
“Right, but what I’m looking for—or what I was hoping to find—was something that maybe you didn’t pay particular attention to at the time, but might actually turn out to be a valuable piece of evidence for us. Maybe you can just tell me about that evening in as much detail as possible? Don’t worry if it has nothing to do with any incident.”
“All right. I suppose,” Ishigami said, scratching the back of his neck.
“I know it was a while ago now, so I brought something I thought might help you remember the day.” Kusanagi handed over a chart of Ishigami’s work schedule for the week of March tenth, showing a list of the classes he’d taught along with the school events schedule. He must have procured the information from the office. “Does anything here jog your memory?” the detective asked, smiling.
The moment he looked at the chart, Ishigami understood what the detective was up to. He wasn’t here about Yasuko Hanaoka, he was here to establish Ishigami’s alibi. Though Ishigami couldn’t say for certain why the police were suddenly turning their eyes in his direction, he suspected it had something to do with Manabu Yukawa’s strange behavior.
In any case, if the detective was here for an alibi, he’d better answer him. Ishigami settled himself in his chair and sat up straight. “I went home that night after the judo team finished practice, so it would have been around seven o’clock. I think I told you that before, too.”
“Indeed you did, indeed you did. So, you were in your apartment for the whole time after that?”
“Well, I think I probably was, yes,” Ishigami said, leaving his words purposely vague. He wanted to see how Kusanagi would respond.
“Did no one visit the apartment that night? Or call on the phone?”
Ishigami lifted an eyebrow. “Whose apartment do you mean? Ms. Hanaoka’s?”
“No, your apartment.”
“Mine?”
“I know you must be wondering what this has to do with our investigation. Believe me, we’re not investigating you. We’re simply trying to establish everything that happened in the general vicinity of Yasuko Hanaoka that night. That’s all.”
A pretty frail excuse, Ishigami thought, though he expected that the detective knew he was being obvious and that the man just didn’t care.
“I didn’t see anyone that night. I’m pretty sure nobody called, either. I rarely have visitors.”
“I see.”
“I’m sorry I don’t have more to tell you after you came all this way.”
“No, please, don’t worry about me. I’m sorry for taking your time. Oh, incidentally—” Kusanagi picked up Ishigami’s work schedule. “According to this, you took the morning of the eleventh off, only coming into work that afternoon. Did something happen?”
“You mean the next day? No, nothing happened. I just wasn’t feeling well, so I slept in. Third-quarter classes were almost completely over anyway, so I figured I could get away with it.”
“Did you see a doctor?”
“No, it wasn’t anything so serious. Which is why I ended up going in that afternoon.”
“Just now at the office I asked the assistant there, and he said that you rarely take time off, Mr. Ishigami. Just mornings sometimes. About once a month?”
“It’s how I use my vacation time, yes.”
“Right. The office told me you are often up late working on mathematics, and you take off the following morning, something like that?”
“That sounds like something I would have told the office, yes.”
“And this happens about once a month or so…” Kusanagi’s eyes dropped to the work schedule again. “But you took the morning off on the tenth, too—in other words, the day before. The office said they weren’t much surprised the first time, but when you took two mornings off in a row that got them. This was the first time that happened, was it?”
“I guess it might have been.” Ishigami put a hand to his forehead. He knew he had to answer carefully. “I didn’t have any particular reason for doing it that time, though. Like you said, I was up late the night before the tenth, and went to work in the afternoon. That night, I felt like I had a bit of a fever, and that’s why I was out the next morning as well.”
“But you recovered enough to come in after lunch?”
“That’s right.” Ishigami nodded.
“Right,” Kusanagi echoed, his eyes full of suspicion.
“Is something wrong?”
“No, I was just thinking, if you managed to go to school for the afternoon, you can’t have been too sick that morning. But then again, if they weren’t too sick, most people would have gone to work anyway. Especially if they’d missed their morning classes just the day before.” Kusanagi was openly doubting Ishigami now. He must’ve thought whatever information he might get out of the math teacher would be worth annoying him.
Ishigami smiled wryly, refusing to rise to the bait. “If you say so. I just remember having trouble getting out of bed that morning. But right before lunch I started feeling a lot better, so I decided to go in. Mostly because, as you pointed out, I had just taken the morning off the day before.”
All the while Ishigami talked, Kusanagi was staring him straight in the eye. The detective’s gaze was piercing and fierce—the gaze of someone who truly believed that when a suspect wasn’t telling the truth, it would show in his eyes.
“I see. Well, all that judo must keep you in good shape. Probably only takes you half a day to recover from a fever, eh? Wish I had your constitution. The fellow at the office said he’d never even heard of you calling in sick.”
“That’s hardly true. I catch colds, too, you know.”
“And you just happened to catch one on the night of the tenth.”
“What do you mean by that? I know that’s the night your murder took place, but it wasn’t a particularly special night for me.”
“Of course.” Kusanagi closed his notepad and stood. “Sorry for taking your time.”
“Again, I’m sorry I couldn’t be of more assistance.”
“Not at all. We’re just covering the bases.”
The two of them walked out of the conference room together. Ishigami saw the detective to the main entrance.
“Seen much of Yukawa lately?” Kusanagi asked as they walked.
“No, not at all,” Ishigami answered. “How about you? You talk to him now and then, right?”
“Not recently. I’ve been too busy. You know, the three of us should get together sometime. I hear from Yukawa that you enjoy a drink now and then?” He motioned with his hand as if tilting a glass.
“I’d be happy to, but shouldn’t that wait until you’ve solved this case of yours?”
“Probably, yes, but a man has to get out sometimes. I’ll give you a ring.”
“All right. I’ll be looking forward to it, then.”
“You do that,” the detective said, turning to walk out the door.
Ishigami returned to the hallway and watched him through a window. Kusanagi was talking on his cell phone as he walked out to the road. His expression hadn’t changed.
Ishigami thought about what his visit meant. They must have had a reason to turn their suspicions toward him. What would that be? He hadn’t sensed anything of the sort the last time he’d met Kusanagi.
Based on the questions he asked, Kusanagi was a still long way from the truth. He was basically shooting in the dark. Perhaps Ishigami’s lack of an alibi had given him a new direction. But if so, so be it. Ishigami had planned for this, too.
The problem was—
The image of Manabu Yukawa’s face flitted across his mind. How much of the truth had the physicist been able to sniff out? And how much of that truth did he really want to expose?
Ishigami remembered something Yasuko had told him the other day on the phone. Apparently, Yukawa had asked her what she thought of him—of Ishigami. And it sounded like he had known about Ishigami’s fondness for Yasuko.
The mathematician recalled his various discussions with Yukawa but couldn’t remember a single careless word or gesture that might have tipped him off. So how had his old friend noticed?
Ishigami turned and began to walk toward the teachers’ room. He ran into the office assistant in the hallway on the way there.
“The detective leave already?”
“Just now, yeah.”
“So aren’t you going home, Mr. Ishigami?”
“No, I remembered something I have to do first.”
Leaving the assistant to wonder what the detective had wanted, Ishigami returned quickly to the teachers’ room. Sitting down at his desk there, he reached into a box he kept beneath it and pulled out several files. These weren’t class files. They were part of the results of his work over the last several years on a particularly difficult mathematics problem.
He placed them in his bag with the test sheets and left the room.
“How many times do I have to tell you that in order to examine something you have to do more than just look at it? You can’t simply say you were satisfied with an experiment because you got the results you were expecting. I don’t care how you feel about the experiment. And not everything was really expected, was it? I want you to really look at the experiment and discover something in it that has meaning for you. Just—think a little more before you write, please?”
It was rare for Yukawa to be so obviously irritated. Shaking his head, he thrust the report back at the student who stood mute before him. The young man bowed his head and left the room.
“Don’t tell me you get angry, too?” Kusanagi remarked.
“I’m not angry. He wasn’t taking his work seriously, so I gave him a little direction, that’s all.” Yukawa stood and busied himself making a mug of instant coffee. “So, find anything out?”
“I looked into Ishigami’s alibi. Which is to say, I went and talked to him.”
“A frontal assault?” Yukawa turned from the sink, the large mug in his hand. “And? How did he react?”
“He claims he was at home for the whole night.”
Yukawa frowned and shook his head. “I asked you how he reacted. Not what he told you.”
“Well, he didn’t seem particularly flustered, if that’s what you mean. Then again, he was warned about my visit before he saw me, so he would have had a little time to get himself in order.”
“Did he seem surprised that you were asking about his alibi?”
“He didn’t come out and ask me why, no. But then again, I didn’t ask him all that directly, either.”
“Knowing him, he knew you’d be coming for his alibi sooner or later,” Yukawa said, half to himself. He took a sip of coffee. “So he was home that night?”
“Yeah. Had a fever, apparently, so he skipped his classes the following morning.” Kusanagi laid the work schedule he’d received from the school office on the table.
Yukawa walked over and sat. He picked up the schedule.
“The next morning … hmm.”
“After the murder, he would have needed time to take care of things.”
“What about the lady from the lunch shop? You know where she was that morning?”
“Of course. Yasuko Hanaoka went to work as usual on the eleventh. And, while we’re on the subject, her daughter went to school as usual, too. Neither of them was even late.”
Yukawa placed the work schedule back down on the table and crossed his arms. “By ‘time to take care of things,’ what exactly do you think he had to do?”
“Well, dispose of the murder weapon, for one thing.”
“It wouldn’t take him more than ten hours to do that.”
“Ten hours?”
“The murder took place on the night of the tenth. If he had to miss school the following morning, that means he needed more than ten hours to ‘take care of things,’ as you say.”
“Well, he would have needed time to sleep.”
“I doubt anyone could sleep if they had a murder to conceal. And if, after concealing it, they ended up without any time to sleep, they’d just go without. He’d have gone to work for sure, even if he had to prop his eyelids open to do it. Showing up on time but exhausted would raise far less suspicion than not coming in at all.”
“Then there must have been some reason he had to rest.”
“That’s what I’m trying to figure out,” Yukawa said, lifting his mug.
Kusanagi carefuly folded the work schedule on the table.
“There’s something I have to ask you. Why did you start to suspect Ishigami was involved? I’m just not sure how to proceed without knowing what piqued your interest.”
“That’s a strange thing for you to say. Didn’t you figure out, entirely on your own, that he was fond of Yasuko Hanaoka? Why should my opinion matter at all?”
“Well, it does. See, in order to report all this to my boss, I can’t just say I started to watch Ishigami based on a whim.”
“Can’t you say you were looking into people connected with Ms. Hanaoka, and the mathematician Ishigami’s name came up?”
“I did. And I looked into their relationship. The thing is, I haven’t been able to find a single scrap of evidence they’re closer than they are letting on.”
Mug still in hand, Yukawa began to laugh so hard his whole body shook. “I’m not surprised!”
“What? Why? What’s that supposed to mean?”
“Nothing much. It’s just I wasn’t expecting there to be anything between them at all. In fact, I guarantee you that no matter how hard you look, you won’t find even a trace of a relationship.”
“Well, thanks for your vote of confidence. You know my division chief is already losing interest in Ishigami. Pretty soon my hands will be tied as well. That’s why I need you to tell me why you’ve had your eye on him. Come on, Yukawa, you’ve had your fun. Why won’t you tell me?”
A serious look came across Yukawa’s face, and he set down his coffee. “I haven’t told you why because doing so would be meaningless. What I have to say wouldn’t help you all.”
“Why not let me be the judge of that?”
“Okay: the reason why I started to think he might have been involved is the same sort of reason you yourself have been talking about since you got here. Somehow I got the feeling that he might have a thing for Yasuko Hanaoka, so I thought I’d see if he had anything to do with the murder. Now, I’m guessing you want to know why I ‘had a feeling,’ and all I can say is, it was a hunch. Call it intuition. I’m not sure that anyone who didn’t understand Ishigami pretty well would be able to pick up on it. You’re always talking about a detective’s intuition, aren’t you? It’s something like that.”
“Well, this is unexpected. You’ve always made intuition sound like a dirty word.”
“I’m allowed to branch out now and then, aren’t I?”
“All right. Then at least tell me when it was you first noticed that Ishigami had a thing for her.”
“Sorry,” Yukawa replied immediately.
“C’mon!”
“It’s a matter of pride. Ishigami’s pride, I mean. It’s not the kind of thing I want to tell other people.”
Kusanagi sighed. Just then, there was a knock on the laboratory door, and another student stepped in tentatively and looked around.
“Over here,” Yukawa called out to him. “Sorry for calling you up like I did, but there was something I wanted to talk to you about with regard to your report the other day.”
“What might that be?” The student froze behind his glasses.
“Your report—it was well written. Just, there was one thing I wanted to check with you. I was wondering why you used solid-state physics to describe your process.”
The student looked bewildered for moment. “Wasn’t it a solid-state experiment…?”
Yukawa chuckled and shook his head. “Actually, the experiment is, in essence, based on elementary particle physics. I was hoping you’d consider that in your approach as well. Just because the problem seems like one of solid-state physics at first doesn’t mean that you shouldn’t consider other theories. Tunnel vision is no way to make it as a researcher. Your assumptions are your worst enemies. Trust them too much, and you’ll fail to see what’s right under your nose.”
“Right.” The student nodded.
“I’m giving you this advice because you do such good work. Thanks for dropping by.”
The student thanked him and left.
Yukawa turned his attention back to Kusanagi, only to see Kusanagi staring back at him.
“What? There something on my face?”
“No, I was just thinking you science types all seem to say the same things.”
“What do you mean?”
“When I visited him, Ishigami said something a lot like what you said just now.” Kusanagi told his friend about Ishigami’s mathematics test.
“Blind spots due to assumptions, eh? How like him.” Yukawa grinned. But the next moment, the physicist’s expression changed. Suddenly he stood, and clutching his head in his hands, he walked over to the window. He looked out and upward, toward the sky.
“Hey, Yukawa?”
But the physicist merely held up his hand for silence. Kusanagi shrugged and sat watching his friend.
“Impossible,” Yukawa muttered. “There’s no way he could’ve—”
“What? Could have what?” Kusanagi asked, unable to restrain himself any longer.
“Show me that paper you had. Ishigami’s work schedule.”
Kusanagi hurriedly produced the folded paper from his pocket. Yukawa took it. He stared at it for a moment, then quietly groaned. “I don’t believe it…”
“Don’t believe what, Yukawa? What are you talking about? Tell me!”
Yukawa thrust the schedule back toward Kusanagi. “Sorry, but I’m going to have to ask you to leave.”
“Huh? No way!” Kusanagi resisted. But when he saw the look on his friend’s face, he lost the next words he was going to say.
Yukawa’s expression was twisted with worry and pain. Kusanagi had never seen him look quite so miserable.
“Just go. I’m sorry,” Yukawa asked again, his voice like a moan.
Kusanagi stepped back from the table. There were a mountain of things he could have asked, but he realized the only thing he could do at that moment was leave.