* * *

  “I don’t think she had anything to do with it,” Kishitani said in a low voice as the two detectives walked away from apartment 204.

  “Hard to say.”

  “I think that’s great that they go out to karaoke together. It’s not often you have a mother and daughter who get along so well.” It was clear from his tone that Kishitani did not consider Yasuko Hanaoka a suspect.

  As they walked down the hall they became aware of a man coming up the stairs toward them. He was middle-aged and heavyset. The two detectives stopped and let him pass. The man continued on to apartment 203, unlocked the door, and went inside.

  Kusanagi and Kishitani glanced at each other, then turned around.

  The plate next to the door of 203 read “Ishigami.” They rang the doorbell, and the man they had just seen opened the door. He had taken off his coat, revealing a sweater and slacks beneath.

  The man’s face was a blank as he looked at Kusanagi and Kishitani. In Kusanagi’s experience, almost everyone viewed him with suspicion at first, if not alarm, but this man’s face revealed absolutely nothing.

  “Sorry to disturb you this late. I was wondering if you could help us,” Kusanagi said with a friendly smile, showing the man his police badge.

  Still, the man’s face didn’t twitch a muscle. Kusanagi took a step forward. “It’ll only take a few minutes. We’d like to ask you some questions.” Thinking that perhaps the man hadn’t been able to see his badge, he held it out closer.

  “What’s this about?” the man asked without even glancing at the badge in Kusanagi’s hand. He seemed to know already that they were detectives.

  Kusanagi took a photograph from his jacket pocket. It was a picture of Togashi from when he had been a used-car salesman.

  “This is photo from a few years ago, but—have you seen anyone resembling this man around here recently?”

  The man stared intently at the photograph for a moment, then looked up at Kusanagi. “Can’t say I know him.”

  “Right, I’m sure you don’t. But, I was wondering if you had seen anyone who looked like him?”

  “Where?”

  “Well, for example, somewhere in the local area?”

  The man squinted again at the photograph. This is a dead end, thought Kusanagi.

  “Sorry, never seen him,” the man said. “I don’t really remember the faces of people I pass on the street, anyway.”

  “Yes, of course,” Kusanagi said, already regretting having come back to question the man. But, since he was here, he might as well be thorough about it. “Might I ask, do you always come home at this time?”

  “I suppose it depends on the day. Sometimes I’m late with the team.”

  “Team?”

  “I supervise a judo club. I’m responsible for closing up the dojo at the end of the day.”

  “Oh, you’re a schoolteacher, then?”

  “Yes, high school,” the man replied, and he told them the name of the school where he worked.

  “I see. Well, then, I’m sorry to have bothered you. You must have had a long day,” Kusanagi apologized, lowering his head.

  It was then that he noticed the mathematics textbooks piled up in the entranceway. Oh, great, he thought, a lump growing in his stomach, a math teacher. Math had been Kusanagi’s worst subject in school.

  “Ah, I was wondering—” he said, trying to shake off the feeling. “Your name here on the plate by the door … do these characters read ‘Ishigami’?”

  “That’s right, I’m Ishigami.”

  “Mr. Ishigami, I was wondering if you remember what time you came home on the tenth of March?”

  “The tenth of March? Why, did something happen?”

  “No, nothing to do with you, sir. We’re just gathering what information we can about events in the local area that day.”

  “I see, well, March 10, huh?” Ishigami stared briefly into the distance before returning his gaze to Kusanagi. “I’m pretty sure I came home directly that day. I would say around seven o’clock.”

  “Anything unusual happen next door that evening?”

  “Next door?”

  “Yes, um, Ms. Hanaoka’s place?” Kusanagi asked, lowering his voice.

  “Did something happen to Ms. Hanaoka?”

  “No, nothing. We’re just gathering information.”

  A curious look crept over Ishigami’s face. He was probably starting to imagine what could possibly have happened to the mother and daughter living next door. From the look of his apartment, Mr. Ishigami was single.

  “I don’t recall anything unusual, no,” Ishigami replied.

  “No loud noises, or talking?”

  “Hmm.” Ishigami scratched his neck. “Sorry, nothing comes to mind.”

  “I see. Are you friends with Ms. Hanaoka by any chance?”

  “Well, she lives next door, so we meet each other now and then and say hello. But that’s about all.”

  “I see. Thanks, and we’re sorry to have bothered you.”

  “Not at all,” Ishigami said, nodding and reaching for the door. Kusanagi saw that he was lifting his mail from the box that hung on the inside of the door. The detective’s eyes went wide for moment when he saw the words “Imperial University” written on one of the letters.

  “Erm,” Kusanagi said hesitantly. “Did you graduate from Imperial University?”

  “Huh?” Ishigami started, his eyes opening a little wider. Then he, too, noticed the address on the letter in his hand. “Oh, this? Must be an alumni letter. Does whatever you’re investigating have anything to do with the university?”

  “No, I had a friend from there is all.”

  “Oh, yes, I see.”

  “Er, sorry for the trouble.” Kusanagi bowed curtly, turned, and departed.

  When the detectives had left the apartment building behind, Kishitani spoke up suddenly. “Wait, sir—didn’t you go to Imperial University? Why didn’t you tell that guy?”

  “No reason, really. Just didn’t want to start anything, is all. I’m sure he was from the science department, and frankly, my bunch didn’t get along with the fellows over there.”

  “You have a thing about the sciences, don’t you?” Kishitani said, grinning. “Do I detect an inferiority complex?”

  “I’d be fine if someone didn’t keep rubbing my face in it,” Kusanagi muttered, the image of Manabu Yukawa—the friend the half-jokingly, called “Detective Galileo”—rising in his mind.

  * * *

  After the detectives had been gone a good ten minutes, Ishigami stepped out into the hallway outside his apartment. He glanced next door. The light was on. He turned and went down the stairs.

  It was quite a walk to the nearest public phone where he had a reasonable chance of not being observed. He didn’t own a cell phone, and he couldn’t use the landline in his own apartment.

  As he walked, he went back over the details of his conversation with the police. He was sure he hadn’t given them a single reason to suspect he was involved in any way. But there was always a chance, however slight. If the police suspected Yasuko, they would have to figure that a man had been involved in disposing of the body. They might start looking for someone connected to the Hanaokas, a man who would be willing to dirty his hands for them. They might even consider investigating the mathematics teacher who lived next door.

  Ishigami knew he had to avoid going to their apartment, of course. He had been avoiding any direct contact. That was why he didn’t call from his own house. The investigators might see from the phone records that he had made frequent calls to Yasuko Hanaoka and find it suspicious.

  But what about Benten-tei?

  He still hadn’t made up his mind about that. All things being equal, he should probably avoid the place for a while. But the police might come around asking questions. The owners might tell them about how the mathematician who lived next to Yasuko came by there every day to buy lunch. Wouldn’t they find it odd if he stopped coming right after the
day of the murder? Shouldn’t he keep going there as usual so as not to raise suspicions?

  Ishigami didn’t trust his own capacity to come up with a logical answer to this question, because he knew that, in his heart, he wanted to keep going to Benten-tei. That lunchbox shop was his connection to Yasuko. If he didn’t go there, he would never see her at all.

  He arrived at the public phone and inserted a telephone card. The card had been a gift from another teacher—the front showed a picture of the teacher’s newborn baby.

  The number he dialed was for Yasuko’s cell phone. They might have put a tap on her home phone, after all. The police claimed they didn’t wiretap citizens, but he didn’t trust that one bit.

  “Yes?” came Yasuko’s voice over the line. She would have already guessed that it was he, because of the public number. He had told her he would contact her this way.

  “It’s me, Ishigami.”

  “Oh, yes.”

  “The police came to my apartment a few minutes ago. I’m guessing they dropped by your place as well.”

  “Yes, a little while ago.”

  “What did they want to know?”

  Ishigami listened to every word Yasuko said, organized it in his head, analyzed it, and committed it to memory. It seemed that, for the time being, the police didn’t directly suspect Yasuko. They had probably just been following procedure when they asked after her whereabouts. They might have someone check out her story, but it probably wouldn’t be a high priority.

  But if they found out that Togashi had visited on the tenth, that he had come to see Yasuko, they wouldn’t be so friendly the next time they turned up. And the first thing they were bound to check out would be her statement that she hadn’t seen Togashi recently. Luckily, he had already prepared her for that eventuality.

  “Did the detectives see your daughter?”

  “No, Misato was in the back room.”

  “I see. Still, they will probably want to question her before long. You know what to do if that happens, right?”

  “Yes, you were very clear. I think she’ll be okay.”

  “I don’t mean to repeat myself, but remember, there’s no need to make an act of it. She just needs to answer the questions they ask as mechanically as possible.”

  “Yes, I told her that.”

  “Did you show the police your ticket stubs?”

  “No, I didn’t. You told me I didn’t have to show them unless they asked for them specifically.”

  “Then that’s fine. By the way, where did you put the stubs?”

  “In a kitchen drawer.”

  “Put them inside the theater pamphlet. Nobody goes out of their way to store ticket stubs. They might suspect something if you have them in your drawer.”

  “Okay, I’ll take them out.”

  “By the way…” Ishigami swallowed. He tightened his grip on the receiver. “The owners at Benten-tei … do they know about me going there to buy my lunch?”

  “What…?” Yasuko asked, momentarily taken aback.

  “What I’m asking is, do the people who run the store where you work know that your neighbor comes there frequently to buy lunches? This is rather important, so please be honest.”

  “Well, yes, actually. The owners were saying they were happy you were such a reliable regular.”

  “And they know that I’m your neighbor?”

  “Yes … is that bad?”

  “No, I’ll worry about that. You just do as we discussed. All right?”

  “Yes.”

  “Right,” Ishigami said, turning to set down the receiver.

  “Oh, um, Mr. Ishigami?” Yasuko’s voice came softly.

  “Yes?”

  “Thank you. Thank you for everything. We’re in your debt.”

  “No…” Ishigami paused. “Don’t mention it,” he said, and he hung up the phone.

  When Yasuko said “Thank you,” he had felt a tingle rush through his body. Now his face was flushed, and he welcomed the night breeze on his skin. He was even sweating a little.

  Ishigami headed home, elated. But his high didn’t last long when he remembered what she had said about Benten-tei.

  He realized that he had made a mistake when talking to the detectives. When they asked how well he knew Yasuko, he had only told them that they said hello when they chanced to meet. He should also have told them about the lunchbox shop.

  * * *

  “Did you confirm Yasuko Hanaoka’s alibi?”

  Mamiya had called Kusanagi and Kishitani over to his desk. He was clipping his nails.

  “The karaoke box checked out,” Kusanagi reported. “The person at the desk there knew her face. And they were in the book, from nine forty for an hour and a half.”

  “What about before that?”

  “Considering the time, they probably caught the seven o’clock show at the theater. It ended at nine ten. If they went to eat ramen after that, their story holds,” Kusanagi said, looking over his notes.

  “I didn’t ask if their story held, I asked if you checked it out.”

  Kusanagi closed his notebook. His shoulders sagged. “Just the karaoke box.”

  “You call that doing your job, Detective?” Mamiya asked, glaring up at him.

  “C’mon, Chief. You know it’s almost impossible to check out alibis in theaters and ramen shops.”

  One ear listening to Kusanagi, Mamiya pulled out a business card and threw it on the desk. The card read “Club Marian.” It gave an address in Kinshicho.

  “What’s that?”

  “The place where Ms. Yasuko used to work. Togashi dropped in there on the fifth of March.”

  “Five days before he was murdered.”

  “Apparently, he was asking about Yasuko. Anyway, I think that’s more than enough for even you to figure out what I’m getting at.” Mamiya pointed to the door behind the two detectives. “I want you to go and check out that alibi, every bit of it. If anything doesn’t fit, I want you to go back and talk to this Yasuko again.”

  FIVE

  A small pole about thirty centimeters long stuck up from a square box on the lab table. There was a ring, only a few centimeters across, encircling the base of the pole. The strange item would have looked a bit like a carnival ring-toss game were it not for the cord snaking out of the side of the box and the single toggle switch on top.

  “What the heck’s this?” Kusanagi muttered, bending down to stare at the device.

  “I wouldn’t touch that if I were you,” warned Kishitani beside him.

  “Nah, I’m sure it’s fine. If this thing were dangerous, he never would’ve left it lying out here like this.” Kusanagi flicked the switch. The moment he did so, the ring around the pole began to float upward.

  Kusanagi gaped. The ring was hovering in midair, wobbling slightly.

  “Try pushing the ring down,” came a voice from behind him.

  Kusanagi looked around as Yukawa walked into the room, a file folder cradled in his arms.

  “Welcome back. Class?” Kusanagi asked as he turned back to the floating ring. Reaching out gingerly, he tried to push it down with his fingertips. A second later he yanked back his hand. “Yowch! That thing’s hot!”

  “It’s true, I’m not in the habit of leaving dangerous objects lying about. I do, however, assume a basic knowledge of physics.” Yukawa strolled over to the table and flicked off the switch. “This device is only high school–level physics, as a matter of fact.”

  “Well, I didn’t take physics in high school,” Kusanagi said, blowing on his fingertips. Kishitani laughed immoderately.

  “Who’s your friend?” Yukawa asked with a raised eyebrow.

  The smile vanished from Kishitani’s face and he bowed curtly. “Kishitani. I work with Detective Kusanagi. I’ve heard a lot about you, Professor. You’ve helped us out with a lot of cases, haven’t you? They call you Detective Galileo down at the station.”

  Yukawa frowned and waved his hand. “Don’t call me that. I don’t help out bec
ause I enjoy it, you know. I just couldn’t bear listening to Detective Kusanagi’s faulty attempts at reasoning on a certain occasion, and I made the mistake of correcting him. I’d be wary of spending too much time with him, if I were you. You might catch whatever he has that’s hardened his brain into a rock.”

  Kishitani guffawed, earning him a glare from his superior.

  “You laugh too much,” Kusanagi grumbled. “Besides,” he said, turning to Yukawa, “you know you enjoy trying to solve our cases.”

  “What’s there to enjoy? Do you know how much valuable research time I’ve squandered on your account? I certainly hope you haven’t brought me another of your annoying, so-called ‘unsolvable’ puzzles today?”

  “No, you’re off the hook for now. We just happened to be in the area, so we dropped in.”

  “Ah, that’s a relief.” Yukawa walked over to a nearby sink, filled a kettle with water, and set it on a gas burner—the start of his usual instant coffee ritual. “So, did you resolve the murder along the Old Edogawa River?” he asked, measuring coffee powder into a cup.

  “How did you know we were working on that case?”

  “Simple deduction. It was on the news the same night you took a call while in my lab. And from the look on your face, I would further deduce that the investigation isn’t going so well.”

  Kusanagi gestured dismissively. “Oh, I wouldn’t say it’s going all that badly. We have a few suspects now. It’s just getting started.”

  “Oh? Suspects?” Yukawa asked over his shoulder, not sounding particularly interested.

  “Actually,” Kishitani chipped in, “I don’t think we’re heading in the right direction, myself.”

  Yukawa lifted an eyebrow at him. “You object to the direction the investigation is taking?”

  “Well, I wouldn’t call it an objection…”

  “I’d prefer you didn’t call it anything,” Kusanagi said with a scowl.

  “Sorry, sir.”

  “Why apologize?” Yukawa asked, clearly starting to enjoy himself. “You follow orders, yet you have your own opinion—sounds perfectly reasonable to me. Proper, even. Without people to question the status quo, how can we ever hope to arrive at truly rational decisions?”