The Devotion of Suspect X

EIGHT

From outside the gym door, Kusanagi could hear the squeaking of sneakers on polished hardwood, punctuated by what sounded like tiny percussive explosions. Familiar sounds.

He stopped in the doorway and looked inside. On the nearest tennis court he saw Yukawa poised on the near half of the court, racquet held at the ready, prepared for the next serve. The muscles in his thighs weren’t as toned as they had been back when the two of them were in school, but his form was as good as ever.

His opponent was a student. He was apparently very skilled, and he had deftly countered Yukawa’s usual devious attacks and answered his every move.

In one smooth motion, the younger man tossed the ball in the air and then smashed it into the corner. The game was over, and Yukawa sat down on the spot. He chuckled and said something to his victorious opponent. Then his eyes caught sight of Kusanagi. He called a thanks to the student, waved good-bye, pulled himself shakily to his feet, and, racquet in hand, headed over to the waiting detective.

“What is it now?”

Kusanagi took a half step back. “Hey, that’s my line. It was you who called me.”

There had been a call from Yukawa on the calls-received list on Kusanagi’s cell phone.

“Oh, that’s right. When I tried to get ahold of you my call went direct to voice mail, but it wasn’t important enough to leave a message. I figured you must be busy.”

“Actually, I had my phone turned off because I was watching a movie.”

“During business hours? You’re really letting your hair down.”

“I wish. I was checking into the mother and daughter’s alibi. Figured I might as well see what kind of movie the ladies went to see. After all, I can’t really tell if the suspect is telling the truth if I don’t know my facts.”

“Still, it’s hard to beat getting paid to watch movies.”

“That’s the irony of it. It’s no fun at all when you’re doing it for work. Anyway, I’m sorry I came all the way down here if it wasn’t important. I tried to find you at the lab, but they told me you were here.”

“Well, since you’re here anyway, how about getting something to eat? I do have to ask you something, after all.” Yukawa walked over to the door, where he slipped out of his gym sneakers and into his regular shoes.

“And what might that be?”

“It has to do with where you were this afternoon,” Yukawa said, walking.

“Where I was?”

Yukawa stopped and leveled his racquet at Kusanagi. “The movie theater.”

They stopped in at a bar near campus. It was a newer place, one that hadn’t been there when Kusanagi was at school. They sat down at a table at the back.

“The suspect says she went to the movies on the tenth of this month—the day Togashi was murdered. Now, the daughter told one of her friends at school about it on the twelfth,” Kusanagi said, pouring Yukawa a glass of beer from a bottle. “I just confirmed that with the friend. Which is why I went to see the movie—to see if what she said about the movie checked out.”

“Yes, yes, I’m sure you had every reason to be watching drivel on the public’s dollar. So what did the daughter’s friend have to say for herself?”

“Nothing helpful. According to her, there was nothing unusual about anything the daughter said. Her friend’s name is Mika Ueno. Mika told me she had seen the movie, too, so they had had a lot to talk about.”

“Odd that she would wait a day after seeing it,” Yukawa noted.

“Isn’t it? If she wanted to chat about it with her friends, why wouldn’t she do that the next day? So I started thinking, what if they really went to see that movie on the eleventh?”

“Is that possible?”

“Can’t rule it out. The suspect works until six o’clock, and if the daughter came home right after badminton practice, they could make the seven o’clock show. Which is what they allegedly did on the tenth.”

“Badminton? The daughter’s in the badminton club?”

“Yeah. I figured that out the first time I went to visit them. Saw her racquet in the apartment. Incidentally, the whole badminton thing bothers me, too. It’s a pretty intense sport, and even if she is in junior high, she should be bushed after practice.”

“Not if she’s a slacker like you who lets everyone else do the heavy lifting,” Yukawa commented, smearing some hot mustard on a rubbery cube of steamed konnyaku.

“Don’t try to derail the conversation with your little jokes. What I’m trying to say is—”

“It’s remarkable that a schoolgirl, worn out from badminton practice, would go off to the movies, then sing late into the night at a karaoke joint, right?”

Kusanagi blinked at his friend. That was exactly his point.

“Still, it’s not entirely inconceivable. She’s a healthy enough girl, right? And young.”

“That’s true. But she’s skinny—doesn’t look like she has much stamina.”

“I don’t know that that’s a valid assumption, and besides, maybe practice wasn’t so hard that day. And you confirmed they went to the karaoke place on the night of the tenth, didn’t you?”

“Yeah.”

“Well, what time did they go into the karaoke place?”

“9:40 P.M.”

“And you confirmed that the mom works at the lunch box store until six, right? If the crime was committed in Shinozaki, then allowing for a round trip, they had two hours to do the deed and still get to karaoke. I suppose it’s possible.” Yukawa folded his arms, chopsticks still in hand.

Kusanagi stared at him, wondering when he had told Yukawa that the suspect worked at a lunch box shop. “Tell me,” he said after a moment, “why are you so interested in this case all of a sudden? You never ask me how my other investigations are going.”

“I wouldn’t call it ‘interest,’ per se. It was just on my mind. I like this business of chipping away at ironclad alibis.”

“It’s less ironclad then simply hard to pin down—which is why we’re working on it.”

“But you have no evidence against her, nothing that would lead you to suspect her yet, right?”

“True enough. But the fact is, we have no one else worth suspecting right now. Togashi didn’t leave much of a trail. He didn’t have a lot of friends, but no real enemies either. That, and doesn’t it strike you as a little bit too convenient that they happened to go to the movies and karaoke on the night of the murder?”

“I see what you mean, but you need to make some logical decisions here. Maybe you should look at something other than the alibi?”

“Don’t feel you have to tell me how to do my job. We’re doing all the groundwork, believe me.” Kusanagi pulled a photocopy from the pocket of his coat where it hung on his chair and spread the paper out on the table. It was a drawing of a man’s face.

“What’s that?”

“An artist’s depiction of the victim when he was still alive. We have a few men around Shinozaki Station asking if anyone saw him.”

“That reminds me—you were saying some of the man’s clothing escaped burning? A navy jacket, gray sweater, and black pants, was it? Sounds like something just about anybody might wear.”

“Doesn’t it? Apparently they have a mountain of reports of people saying they saw someone a lot like him. We don’t know where to start.”

“So, nothing useful at all?”

“Not really. The closest thing we have to a useful tip is one woman who says she saw a suspicious-looking guy wearing clothes like that near the station. An office lady on her way home from work; she saw him loitering there. She called it in after seeing one of the posters we put up at Shinozaki.”

“It’s good to see the people here are being helpful. So why don’t you question her? Maybe you can get something more out of her.”

“We did, of course. The problem is, the man she saw doesn’t sound like our victim.”

“How so?”

“Well, first of all, the station she saw him at wasn’t Shinozaki, but Mizue—one station before it on the same line. That, and when we showed her the picture, she said his face looked rounder than the one in our illustration.”

“Rounder, huh?”

“One thing you come to realize as a police detective is that a lot of our work consists of barking up the wrong tree. It’s not like your world, where once the logic fits, you have your proof and you can call it a day.” Kusanagi busied himself with fishing for leftover chunks of potato with his chopsticks. He was expecting a snappy comeback, but Yukawa didn’t say anything. When he looked up he saw his friend staring off into space, his hands lightly clasped together.

Kusanagi had seen this look before: it was a sure sign that the physicist was deep in thought—though whether the sudden revery had anything to do with the matter at hand remained to be seen.

Gradually Yukawa’s eyes regained their focus. He looked at Kusanagi. “You said the man’s face was crushed?”

“Yep. His fingerprints were burned off, too. They must have been trying to keep us from identifying the body.”

“What did they use to crush the face?”

Kusanagi glanced around to make sure no one was eavesdropping, then he leaned across the table. “We haven’t found anything, but we suspect the killer used a hammer. Forensics thinks the face was struck several times to break the bones. The teeth and jaw were completely destroyed, too, making it impossible for us to check them against his dental records.”

“A hammer, huh?” Yukawa muttered, using the tips of his chopsticks to split a soft stewed daikon radish.

“What about it?” Kusanagi asked.

Yukawa put down his chopsticks and rested his elbows on the table. “If this woman from the lunch box shop was the killer, what exactly do you think she did that day? First, you’re assuming that she didn’t really go to that movie, right?”

“I’m not certain she did or didn’t go, if that’s what you’re asking.”

“Never mind what really happened. I just want to hear some deductive reasoning.” Yukawa made an encouraging motion with one hand while lifting his beer to his lips with the other.

Kusanagi frowned. “Well, it’s more conjecture than anything solid, but here’s what I think. The lunch box lady—let’s just call her Ms. A for short—well, Ms. A gets off work and leaves the shop after six. It takes her ten minutes to walk from there to Hamamatsu Station. It’s another twenty minutes from there on the subway to Shinozaki Station. She takes a bus or taxi from the station to someplace near the Old Edogawa River, which would put her near the scene of the crime at around seven o’clock.”

“And what’s the victim doing during this time?”

“The victim’s heading toward the scene, too. He’s going there to meet with Ms. A. But the victim comes from Shinozaki Station by bicycle.”

“Bicycle?”

“Yeah. There was a bicycle abandoned near where the body was found, and the prints on the bicycle matched those of the victim.”

“The prints? I thought you said his fingertips had been burned off?”

Kusanagi nodded. “After we figured out who the John Doe was, we got some useable prints. What I should have said was the prints on the bicycle matched those we found in the room where the victim was staying. Aha! I know what you’re getting at. You’re going to tell me that even if we could prove the man renting the room was the same one who used that bicycle, that doesn’t mean they were the victim, right? What if the man staying in the room was the real killer, and he used the bicycle? Plausible enough, I suppose. But we also found some hair in his room. It matched the hair on the victim’s body. We even did DNA analyses of both and they were a match.”

Yukawa chuckled. “No, I wasn’t going to suggest that the police had made a mistake identifying the body. I’m more concerned about the idea of him using this bicycle. Did the victim leave his bicycle at Shinozaki Station?”

“No, actually—”

Kusanagi went on to explain what he’d learned about the stolen bicycle. Yukawa’s eyes widened slightly behind his wireframe glasses.

“So the victim went out of his way to steal a bicycle at the station just to go to the scene of the crime? Why not take a bus or a taxi?”

“I don’t know why he stole the bike, but that’s what he must’ve done. The guy was unemployed, after all, without a whole lot of money to his name. He probably wanted to avoid paying the bus fare.”

Yukawa, looking unconvinced, crossed his arms and gave a faint snort. “Well, okay—however he did it, the victim went to meet with our Ms. A at the scene of the crime. Go on.”

“I figure they had planned some sort of rendezvous but Ms. A got there a little early and was hiding somewhere. When she saw the victim approach, she snuck up behind him, wrapped a rope around his neck, and strangled him to death.”

“Stop right there!” Yukawa raised both hands. “How tall was the victim?”

“One hundred and seventy centimeters plus change,” Kusanagi said, resisting the urge to curse. He knew what Yukawa was going to say next.

“And Ms. A?”

“About one sixty.”

“So he was over ten centimeters taller,” Yukawa said with a slight grin, resting his chin on his hand. “You see what I’m getting at here.”

“Sure, it’s hard to strangle someone taller than you. And from the angle of the marks on the victim’s neck, it’s pretty clear whoever strangled him was pulling upward. But the victim could have been sitting. Maybe he was still on the bicycle.”

“Well, I’m glad you had a sad excuse for your scenario ready.”

“Nothing sad about it,” Kusanagi said emphatically, bringing his fist down on the tabletop.

“So what happened next? She took off his clothes, smashed in his face with the hammer she also brought, and burned off his fingertips with a lighter? Then she set fire to his clothes, and fled the scene. That’s about it?”

“She still could’ve made it to Kinshicho by nine o’clock.”

“Theoretically, yes. But I can’t help thinking you’re grasping at straws. Don’t tell me that the entire department is backing your little scenario?”

Kusanagi’s mouth curled into a frown. He downed the rest of his beer and waved to the waitress for another round, then turned back to Yukawa. “Yeah, well, a lot of the men wonder if a woman really could have pulled it off.”

“As well they should. Even if she did catch him by surprise, it’s not easy to strangle a grown man who is fighting back. And believe me, he would have done everything in his power to stop her. Besides, it would be difficult for a woman of average size and strength to dispose of a grown man’s body after the deed was done. I’m sorry, but I have to join the crowd that thinks your theory is full of holes.”

“Yeah, I figured you’d say that. I don’t much believe it myself. I’m just saying it’s one of several possibilities.”

“Which suggests you have some other ideas. Well, don’t keep them all to yourself. Let’s hear another theory.”

“I’m not claiming that I’ve got much of anything right now. But the scenario I just gave you assumes that the man was killed near where he was found. It’s also possible he was killed somewhere else and then his corpse was dumped there. Truth be told, most of the department thinks that’s what happened. Regardless of whether Ms. A did it or not.”

“It does seem to be the more reasonable assumption. But it wasn’t the one you offered up first. Why?”

“Simple. If Ms. A was the killer, she couldn’t have done it someplace else. She doesn’t have a car or access to one. She can’t even drive. There was no way she could have transported the body to the riverbank.”

“I see. That strikes me as an important point.”

“And then there’s the matter of the bicycle. We could assume whoever left it there did so on purpose to make us think that the murder took place on the riverbank, but then there would have been no reason to go to the effort to put the victim’s fingerprints on it. Especially since they went to the trouble of burning fingertips off the body.”

“The bicycle is a mystery. For a number of reasons.” Yukawa tapped his fingers on the tabletop like he was playing the piano. Then he stopped and said, “Either way, isn’t it better to assume that a man probably did it?”

“That’s what most people at the department think. But I still think Ms. A was involved.”

“So Ms. A had a male accomplice?”

“We’re looking into people connected to her now. She used to be a hostess at a nightclub, after all. There have to be some men in her life.”

“An interesting assumption. I can hear the uproar from hostesses across the country already,” Yukawa said with a grin. He took a swallow of beer, then, a serious look returning to his face, asked to see the illustration again.

Kusanagi handed him the artist’s depiction of the victim. It was a rendering of Togashi as he might have appeared dressed in the clothes they’d found near the crime scene.

Yukawa stared at it intently. “Why did the killer feel the need to strip the body, I wonder?” he muttered.

“To help hide the victim’s identity. Same reason he crushed the face and got rid of the fingerprints.”

“Then why didn’t he take the clothes with him when he left? It’s only because he tried to burn them and failed that you were able to come up with that illustration there.”

“Well, he was probably in a hurry. Or he made a mistake.”

“I agree that you can tell someone’s identity from their wallet or driver’s license, but can you really identify someone from their clothes or shoes? It seems like the risk involved in taking the time to take off and burn his clothes would outweigh any benefits. Wouldn’t the killer want to get away as quick as he could?”

“What are you driving at? You think there’s another reason they stripped him?”

“I can’t say for sure. But if there was, then until you figure out that reason, you won’t be able to pin down your killer.” Yukawa traced a large question mark on the illustration with his fingertip.

The performance of the junior-year group 2 math class on the year-end exams was appalling. And group 2 wasn’t the only sad story; the entire junior class had done poorly. To Ishigami it seemed like the students were getting dumber by the year.

After he’d passed out the answers, the math teacher put up a schedule for make-up exams. The school had set a lowest acceptable score for each subject, and those students who didn’t reach it wouldn’t go on to the next grade. Of course, they prevented all but the most hopeless cases from failing and being held back a year by making them take as many make-up exams as they needed to pass.

Shouts of protest rose from the class when they saw the grades he’d given them. Ishigami ignored the outcry as usual, but one comment rose above the noise and reached his ears.

“Hey, Teach, aren’t there universities that don’t require a math test to get in?” one of the students was saying. “Why should us guys who are going to those schools have to pass math?”

Ishigami looked in the direction of the student, a boy named Morioka. He was leaning back in his chair, scratching his head and looking around at the other students for support. He was a short kid, but he filled the role of class crime boss—even Ishigami, who didn’t have this bunch for homeroom, knew his reputation. The boy already had a long history of warnings for riding to school on a motorbike, which was strictly forbidden.

“Are you going to art school, Morioka?” Ishigami asked.

“Well, I mean … if I do go to university, it’ll be one without a math exam for sure. Not that I plan on going. Besides, I’m not taking the optional math class next year, so what’s my grade this year matter? Hey, don’t get me wrong, I’m thinking about you, too, Teach. Can’t be much fun teaching with idiots like me in the class. So, I was thinking, maybe we could kind of come to an understanding about this. An agreement between adults, like.”

That last line got a laugh from the class. Ishigami chuckled wryly. “If you’re so worried on my account, then pass your make-up exam. It’s only differential and integral calculus. That can’t be too hard.”

Morioka scoffed loudly. He crossed his legs off to the side of his chair. “What good’s differential and integral calculus gonna do me? It’s a waste of time.”

Ishigami had turned to the blackboard to begin an explanation of some of the trickier problems on the year-end exam, but Morioka’s comment made him stop and turn around. This wasn’t the kind of thing he could let slide. “I hear you like motorbikes, Morioka. Ever watched a race?”

Morioka nodded, clearly taken aback by the sudden question.

“Well, do racers drive their bikes at a set speed? No, they’re constantly adjusting their speed based on the terrain, the way the wind’s blowing, their race strategy, and so on. They need to know in an instant where to hold back and where to accelerate in order to win. Do you follow?”

“Yeah, sure, I follow. But what’s that got to do with math?”

“Well, exactly how much they accelerate at a given time is the derivative of their speed at that exact moment. Furthermore, the distance they travel is the integral of their changing speed. In a race, the bikes all have to run roughly the same distance, so in determining who wins and who loses, the speed differential becomes very important. So you see, differential and integral calculus is very important.”

“Yeah,” Morioka said after a confused pause, “but a racer doesn’t have to think about all that. What do they care about differentials and integrals? They win by experience and instinct.”

“I’m sure they do. But that isn’t true for the support team for those racers. They run detailed simulations over and over to find the best places to accelerate—that’s how they work out a strategy. And in order to do that, they use differential and integral calculus. Even if they don’t know it, the computer software they’re using does.”

“So why not leave the mathematics to whoever’s making the software?”

“We could do that, but what if it was you who had to make the software, Morioka?”

Morioka leaned further back in his chair. “Me? Write software? I don’t think so.”

“Even if you don’t become a software engineer, someone else in this class might. That’s why we study mathematics. That’s why we have this class. You should know that what I’m teaching here is only the tip of the iceberg—a doorway into the world of mathematics. If you don’t even know where the door is, how can you ever expect to be able to walk through it? Of course, you don’t have to walk through it unless you want to. All I’m testing here is whether or not you know where the doorway is. I’m giving you choices.”

As he talked, Ishigami scanned the room. Every year there was someone who asked why they had to study math. Every year, he gave the same explanation. This time, since it was a student who liked motorbikes, he’d used the example of motorbike racing. Last year, it was an aspiring musician, so he talked about the math used in designing musical technology. But no matter the specifics of the discussion, which changed from year to year, it was all old hat for Ishigami.

When he returned to the teachers’ room after class, Ishigami found a note stuck to his desk. It was hastily scrawled, and it read, “Call Yukawa.” With a cell number written below, he recognized the handwriting as belonging to another one of the school’s math teachers.

What does Yukawa want? he wondered, swallowing to clear the sudden catch in his throat.

Cell phone in hand, he went out into the hallway. He dialed the number on the memo. Yukawa picked up after the first ring.

“Sorry to bother you during school hours.”

“Is it something urgent?”

“I guess you could call it urgent, yeah. Do you think we could meet today?”

“Today? Well, I have a few more things to take care of here. I suppose if it was after five o’clock…” He had just finished his sixth-period class, and all the students were in homeroom. Ishigami didn’t have a homeroom class of his own, so he could leave the keys to the judo dojo with another teacher and get out early if he had to.

“Great. I’ll meet you at the front gate at five, then. Sound good?”

“That’s fine—where are you now?”

“In the neighborhood. See you soon!”

“Right, see you.”

After Yukawa hung up, Ishigami clutched his cell phone with tense fingers, staring down at it. What could possibly be so urgent that it would drive the physicist to come see him here at school? Ishigami puzzled over it as he walked back to his desk.

By the time he had finished grading his few remaining exams and had gotten ready to leave it was already five. Ishigami walked out of the teachers’ room and cut across the schoolyard toward the front gate.

Yukawa was standing near the gate next to the crosswalk. His black coat fluttered in the wind. When he saw Ishigami, he waved and smiled. “Sorry to drag you out like this,” he called out cheerfully.

“I was just wondering what was so urgent that you came all the way out here to see me about it,” Ishigami said, his expression softening.

“Let’s talk while we walk.” Yukawa set off down Kiyosubashi Road.

“No, this way is faster,” Ishigami said, indicating a side road. “If we go straight through here it will get us right to my apartment building.”

“Yeah, but I want to go to that lunch box shop,” Yukawa explained.

“The lunch box shop? Why go there?” Ishigami asked, feeling the muscles in his face tighten.

“Why? To get a lunch box. Why else? I don’t think I’ll have time to get a proper dinner anywhere tonight, so I thought I might get something easy ahead of time. The lunches are good there, aren’t they? I’d hope so, seeing as how you buy them every day.”

“Oh … right. Off we go, then.” Ishigami turned toward Benten-tei.

They headed off in the direction of Kiyosu Bridge. As the walked along, a large truck rattled past them on the road.

“So,” Yukawa was saying, “I met with Kusanagi the other day—you remember, the detective that dropped in on you?”

Ishigami tensed, his premonition growing steadily worse.

“What’d he have to say?”

“Nothing big. Whenever he runs into a dead end, you see, he always comes whining to me. And never with the easy problems, either. Once he even wanted me to solve a poltergeist haunting. See what I mean?”

Yukawa began to tell him the story of the poltergeist haunting. It sounded interesting enough to Ishigami. But he knew that Yukawa hadn’t come all the way here to relate a would-be ghost story.

The math teacher was on the verge of asking his old friend what he had really come for when the sign for Benten-tei came into view. Another wave of unease washed over him. How would Yasuko react when she saw them? It was unusual under any circumstances for Ishigami to show up at this time of day, and if he came with a friend, she would be sure to suspect the worst. He just hoped she had the sense to act naturally.

Yukawa stepped up to the sliding glass door to Benten-tei, opened it, and went inside. Ishigami followed, somewhat hesitantly. He saw Yasuko behind the counter, in the middle of helping another customer.

“Welcome!” she said brightly to Yukawa. Then she turned to look at Ishigami. A look of bewilderment came into her eyes, and her smile froze on her face.

“Did my friend do something?” Yukawa asked.

“No—nothing,” Yasuko shook her head, still smiling uncomfortably. “He’s my neighbor. He always buys his lunch here…”

“So I’m told. I’m here on his recommendation.”

“Thank you, then,” Yasuko said, nodding politely.

“We were classmates back in university,” Yukawa went on, turning to Ishigami. “I was just over at his place the other day.”

“Oh, right.” Yasuko smiled and nodded again.

“Oh, he told you?”

“Yes, in passing.”

Yukawa nodded, smiling. “So, what do you recommend? No, what does he usually buy?”

“Mr. Ishigami almost always gets the special, but I’m afraid we’re sold out…”

“That’s too bad. Let’s see, then. They all look so good…”

While Yukawa selected a boxed lunch, Ishigami stood looking out through the sliding glass door. He wondered if the detectives were watching from somewhere nearby. If possible, he didn’t want them to see him being friendly with Yasuko.

Then another thought occurred to him, and he gave Yukawa a sidelong glance. Could Yukawa be trusted? Did he need to be on his guard around this old friend? If he’s friends with Kusanagi, anything he sees here might eventually wind up back with the police.

Yukawa had finally decided on a lunch box. Yasuko had just gone back with his order when the glass door slid open again and a man in a dark brown jacket stepped into the shop. Ishigami glanced behind him as casually as he could. He felt his jaw clench involuntarily.

It was the man he had seen dropping Yasuko off the other day in front of their apartment building. From beneath his umbrella, Ishigami had watched them talking together. He had gotten the impression that they were old friends—or something more.

The man didn’t seem to notice Ishigami. He was waiting for Yasuko to reappear. When she came back to the front and saw him, her eyes opened in surprise. The man merely nodded, smiling, with a look that said, We’ll talk after you’ve dealt with these customers.

Who is he? Ishigami wondered. When did he show up, and how did he get so close to Yasuko Hanaoka? Ishigami vividly remembered the look on Yasuko’s face when she had stepped out of the taxi the night before. He had never seen her looking so full of life. Her face hadn’t been the face of a mother or an employee at a lunch box shop. It had been her true face, he thought. A woman’s face.

A face she wore for this man, and would never wear for Ishigami—

Ishigami’s gaze darted between the mystery man and Yasuko. He thought he could feel the atmosphere shift between them. A feeling of anxiety clutched at the math teacher’s chest.

Yukawa’s lunch box was ready. He paid, took the bag, and turned to Ishigami. “Thanks for waiting.”

They left Benten-tei and went down to the Sumida River at the stairs by Kiyosu Bridge. They began to walk along the river.

“So who was that guy?” Yukawa asked.

“Huh?”

“The guy that came into the shop. It looked like you recognized him.”

Internally, Ishigami cursed his old friend’s powers of observation. “Really? Can’t say that I did,” he replied, striving to maintain his composure.

“Oh, well, never mind then.” Yukawa said.

“So what is the urgent business all about, anyway? Don’t tell me you came all this way just to buy a lunch box?”

“Oh, right. I hadn’t gotten to why I came, had I?” Yukawa frowned. “Like I said before, that Detective Kusanagi has a habit of bringing me all of his annoying loose ends. Anyway, this time he came because he found out I knew you, and you’re her neighbor. It turns out he has a … well, a rather unpleasant request.”

“What’s that?”

“To put it bluntly, the police are still investigating the murder of your neighbor’s ex-husband, and they have suspicions about your neighbor. Unfortunately, they haven’t got a shred of evidence linking her to the crime. So, they’d like to keep tabs on her, watch what she does—you know, observe. But there are limits to how far they can take that. Which is where we come to you.”

“Wait, they don’t want me to watch her for them, do they?”

Yukawa scratched the back of his head sheepishly. “Er, well, yes, actually they do. It’s not like they want you to observe her all the time, twenty-four seven. They just want you to keep an eye on the place next door, and let them know if you notice anything. I know, it’s a serious imposition, but that’s how they are.”

“So that’s why you came out here to talk to me?”

“Well, I expect the police will make a more formal request soon enough. They just wanted me to feel you out about it first. Personally, I wouldn’t care if you said no—in fact, I almost think you should, but I thought I owed my detective friend at least a preliminary chat with you.”

Yukawa looked sincerely put upon. Secretly, though, Ishigami wondered if the story was really true. Would the police really go to a civilian with a request like that?

“Is that why you wanted to go to Benten-tei, too?”

“Honestly, yes. I wanted to see this suspect for myself. And I gotta say, now that I have, I don’t think she’s capable of killing someone.”

Ishigami was about to tell him that he agreed, but he held back. Instead, he said, “Well, they say you shouldn’t judge a book by its cover.”

“True enough. So, what do you say? How would you answer if the police asked you to spy for them?”

Ishigami shook his head. “Honestly, I’d rather not get involved. I’m not in the habit of prying into other people’s lives, and besides, I barely have the time. It might not look it, but I’m rather a busy man.”

“So I thought. Look, I’ll just tell Kusanagi what you said. That should put an end to the whole idea. Sorry if I made you uncomfortable at all.”

“No, not a bit.”

They were approaching Shin-Ohashi Bridge. They could already see the homeless people’s shanties along the riverside.

“So the murder happened on March tenth, I think he said,” Yukawa said. “Kusanagi mentioned you came home kind of early that day?”

“Yeah. I didn’t have anything scheduled that night. I think I got back around seven—I believe that’s what I told him.”

“After which you holed up in your room, doing battle with those mathematical problems of yours?”

“Something like that.”

As he talked, Ishigami wondered if Yukawa was actually trying to see if he had an alibi. If that was the case, then he already suspected Ishigami of being involved.

“Which reminds me, I have no idea if you have any other hobbies. I mean something other than math.”

Ishigami snorted. “Hobbies? Not really. Math is about all I do.”

“What you do to blow off steam, then? Do you like going for drives?” Yukawa pantomimed gripping a steering wheel.

“No, no. Even if I wanted to, I couldn’t. I don’t own a car.”

“But you have a driver’s license?”

“Is that a surprise?”

“Not particularly. You’re not so busy that you couldn’t find the time to go to driving school, are you?”

“I got it right after I found out I wasn’t getting a university job. I figured it might be of help in finding work. Of course, it ended up not helping at all,” Ishigami said with a sidelong glance at Yukawa. “What, are you trying to figure out whether I could drive a car?”

Yukawa blinked. “No. Why would I?”

“Given your questions, I just thought you might be.”

“Well I didn’t mean anything by it. I was just wondering if you like to go for drives. Or, more to the point, if you had anything you like to discuss other than mathematics once in a while.”

“Other than mathematics and murder mysteries, you mean.”

Yukawa laughed. “Well said.”

They passed beneath Shin-Ohashi Bridge. The man with gray hair pulled into a ponytail was boiling something in a pot over a makeshift burner. He had a small oil can sitting next to him. A few of the other homeless were out and about.

As they made their way up the stairs by the bridge, Yukawa turned to Ishigami and said, “Well, I’d better be getting back home. Sorry for troubling you with the whole investigation thing.”

“Just apologize to Detective Kusanagi for me. I’m sorry I couldn’t help him.”

“I don’t think there’s any need to apologize. And, I hope you don’t mind if I drop in again?”

“No, I don’t mind.”

“Great. We can drink sake and talk math.”

“You mean talk math and murder.”

Yukawa shrugged and wrinkled his brow. “Maybe so. Though I did come up with a new problem for you. Maybe something you can think about in your spare time?”

“That being?”

“Which is harder: devising an unsolvable problem, or solving that problem? And it’s not an empty question. Unlike the Clay Mathematics Institute prize people, I guarantee this puzzle has an answer. Interesting, no?”

“Very interesting,” Ishigami said, trying to read Yukawa’s expression. “I’ll think about it.”

Yukawa nodded, then turned and walked back toward the main road.