Yasuko was confused. At first, she had thought she knew what the professor was driving at, but now she wasn’t so sure. Whatever it was, she had a feeling that something unpleasant was waiting for her in his words.

  And yet everything he had said so far was true; he had simply revealed another side of the truth, one she hadn’t considered closely until this moment. Yasuko didn’t know what Ishigami had been up to all this time—not really. And she had indeed found it strange that the detectives had been treating her with kid gloves. Not only that, but on the three occasions they had come to question her they had never even come close to guessing what had actually happened.

  And Yukawa knew why—

  She saw him check his watch.

  “It pains me to have to tell you these things,” he said at length, his face tightening in a grimace. “Because I know that Ishigami wouldn’t want me to. I’m sure he’d rather you didn’t know the truth no matter what happened. Not for his sake, but for yours. Because if you knew, you would have to live bearing even more pain than you already do. Yet I have to tell you. I feel like I would be doing him a disservice as a friend if I didn’t make you aware of how much love he has for you, how he has gambled his very life for you. Even if it’s against his wishes, I can’t bear having you not know.”

  Yasuko’s heart was racing. Her breathing had grown shallow; she felt as if she might faint.

  “I’m not sure what you’re trying to say.” She meant to speak forcefully, but her voice came out weak and trembling. “If … If you have something to tell me, please do.”

  “He killed that man, the one that was found by the Old Edogawa.” Yukawa took a deep breath. “Ishigami was the killer. Not you, or your daughter. He’s not turning himself in for a crime he didn’t commit. He’s guilty of murder.”

  Yasuko gaped, not comprehending what she was hearing.

  “However,” Yukawa added, “that body did not belong to Shinji Togashi. That was not your ex-husband. He was a complete stranger made to appear to be your ex-husband.”

  Yasuko knitted her brow in disbelief, but when she saw the physicist’s eyes blinking with sorrow, the tears gathering on the lenses of his glasses, suddenly she understood. She gasped, darting a hand to her mouth, almost yelling in surprise. The blood drained from her face.

  “Looks like you finally understand what I’m trying to tell you,” Yukawa said softly. “Yes. In order to protect you, Ishigami committed murder—on March 10. The day after Shinji Togashi was killed.”

  Yasuko felt her head spinning. She swayed dizzily, struggling to remain upright on the bench. Her hands and legs had gone cold; her skin prickled as if with a thousand thorns.

  * * *

  Even from a distance, it was clear to Kusanagi that Yukawa had told the woman the truth. Her face had gone completely pale. Unsurprising, Kusanagi thought. He didn’t know anyone who wouldn’t be shocked by the story, least of all someone so directly involved.

  Kusanagi still didn’t entirely believe it himself. He had practically scoffed when Yukawa had told him his theory on the way there. Not that he could imagine why his friend would joke about such things—it just seemed like such an unrealistic story.

  “That’s impossible,” Kusanagi had said. “He killed someone else to cover up Yasuko Hanaoka’s crime? Who would do something so stupid? And for that matter, who did he kill?”

  Yukawa had looked even sadder at that question and had shaken his head. “I don’t know what his name was. But I know where he was from.”

  “What do you mean by that?”

  “There are people in this world who could disappear overnight and no one would bother looking for them, or worry where they had gone. I’ll bet no one even filed a missing persons report. Whoever it was most likely had no contact with their family anymore, if their family is even alive.” Yukawa had pointed back along the riverbank down the path where they had just been walking. “You saw them back there.”

  Kusanagi hadn’t understood what Yukawa was saying at first. But as he looked back down the riverbank, a light had flashed on in his head. “The homeless!”

  Yukawa hadn’t nodded. He had only said, “Did you notice the fellow collecting those empty cans? He knows everything about the people living in his community. I talked to him the other day, and he told me there was this guy who had joined them only a month before. Not a friend, just someone who had chosen to live there with them. He hadn’t built a shack of his own yet, and still had an aversion to sleeping on cardboard. The Can Man told me that everyone was like that at first—it’s hard to give up your pride—but in the end, they all broke. Anyhow, this new arrival disappeared one day, without so much as a word of parting. The Can Man wondered what had happened to him, but that was all. Some of the other people living there must’ve noticed, too, but no one talked about it. It’s not unusual in their world for people to just go missing like that.

  “Incidentally,” Yukawa had continued, “this man disappeared on or around March 10. He was about fifty years old. He’d put on a little weight, but was otherwise of average build.”

  The body on the Old Edogawa had been found on March 11.

  “I’m not sure exactly how it happened, but Ishigami must have learned of Yasuko Hanaoka’s crime, and he’d decided to help her conceal it. He realized that it wouldn’t be enough to simply dispose of the body. If the police should find and identify it, they would inevitably come knocking on her door. And once the questioning started, he wasn’t sure how long she and her daughter could continue pretending they didn’t know anything about it. So, he decided on a different plan: he would kill someone else and then make the corpse look like Shinji Togashi. Then he would slowly reveal to the police when and how the victim had been slain. The more the investigation progressed, the less suspicion would fall on Yasuko Hanaoka. Why should it? She didn’t kill that man by the river. That wasn’t evidence of the murder of Shinji Togashi. You were on an entirely separate case and you didn’t even know it.”

  It had been hard to believe that the story Yukawa was telling him could be true. Kusanagi had shaken his head the whole time he was listening to it.

  “I think the solution only occurred to Ishigami because he often walked along the river here. He’d had plenty of time to consider the homeless who lived there and their lives. Why were they living at all? Were they just killing time, waiting there for the day when they would eventually die? When they died, would anyone notice? Would anyone care? That’s what I imagine him thinking.”

  “So because of that he thought it would be all right to kill one of them?” Kusanagi had asked.

  “Certainly not ‘all right.’ But when he was putting his plan together, I’m certain he wouldn’t have forgotten them or their particular circumstances. Remember what I told you. He’s a man capable of doing anything as long as it makes logical sense.”

  “And murder is logical?”

  “A murdered body was the piece he needed to complete his puzzle.”

  The story was, frankly, unbelievable. And hearing Yukawa deliver it, almost as if he was giving a lecture to his students, had made Kusanagi wonder about his friend.

  “On the morning after Yasuko Hanaoka killed Shinji Togashi, Ishigami made contact with a homeless man. I’m not sure exactly what transpired between them, but it’s pretty safe to say he offered the man a job. His job description was to first go to the room Shinji Togashi had been renting and hang out there until evening. Ishigami had spent the night before removing all traces of Shinji Togashi’s presence from the room. The only fingerprints and hair that would be left in the room would belong to the homeless man. That night, the man was to go to a place indicated by Ishigami, wearing clothes he had given him.”

  “Shinozaki Station?” Kusanagi had asked, but Yukawa had shaken his head.

  “No. Probably the stop before that. Mizue.”

  “Why Mizue?”

  “Ishigami stole a bicycle from Shinozaki station and went to meet the man at Mizue Station. It’
s highly likely that Ishigami had left another bicycle there for himself. The two of them rode together to the banks along the Old Edogawa River, where Ishigami killed the man. He smashed his face to hide the fact that he wasn’t Shinji Togashi. Technically, he didn’t have to burn off the man’s fingerprints, because he had already planted them in Togashi’s rented room, which would have led the police to believe that it was Togashi’s body anyway. Yet if he had crushed the man’s face and not removed his fingerprints, leaving the job half done as it were, it would have raised suspicion. His hand was forced by his fear that it might take too long for the police to discover the body’s identity. Which is why he left fingerprints on the bicycle. For the same reason he left the man’s clothes only half burned.”

  “But I don’t see the reason why he had to steal a new bicycle for all that.”

  “Ishigami stole a new bicycle to hedge his bets.”

  “What bets?”

  “Ishigami needed to make sure that the police correctly ascertained the time of the homeless man’s murder. He knew the autopsy would reveal a relatively accurate time of death, but he was afraid the body might not get discovered in time, which would make an accurate time of death much harder to determine. If the span of the possible time of death extended to the evening of the day before, in other words, the evening of March 9, that would be very bad for his plan because that was the evening when Togashi actually was killed. Neither Yasuko Hanaoka nor her daughter had an alibi for then. To prevent that from happening, he needed proof that the bicycle had been stolen on or after the tenth. Which is why he chose the one he did—a bicycle that most likely had been left there for less than a day, so the owner would be able to determine roughly when it had been stolen.”

  “So the bike came in handy in more than one way for him,” Kusanagi said, smacking himself on the forehead with his own fist.

  “I heard that when the bicycle was found both tires were flat. Ishigami did that to prevent someone else from riding off with it. He did everything he could to make sure the Hanaoka’s alibi would stand.”

  “But why provide them with such a weak alibi, then? We still haven’t found decisive evidence that they really were at that movie theater.”

  “Yet you haven’t been able to find evidence they weren’t there either, have you?” Yukawa had pointed out. “A weak alibi that nevertheless stands up under pressure. That was the trap he laid for you, don’t you see? If he had given them an ironclad alibi, the police would have had to point their suspicions elsewhere. They might even suspect a bait and switch. Someone might even get the bright idea that the victim they’d found wasn’t really Shinji Togashi. Ishigami was afraid of that, so he made everything point to Yasuko Hanaoka as the killer, and Shinji Togashi as the victim. Once the police took the bait, they were hooked.”

  Kusanagi had groaned. It was just as Yukawa had said. Once they’d determined that the body was likely Shinji Togashi’s, they started to suspect Yasuko. Why? Because her alibi was flimsy. So they continued suspecting her, which meant they’d never suspected that the body wasn’t that of her ex-husband.

  “What a frightening man,” Kusanagi had whispered. And Yukawa had agreed. “It was something you said that led me to the true nature of his scheme, actually.”

  “Something I said?”

  “Remember what Ishigami told you about his method of designing mathematics exams? About coming at the test-taker from a blind spot created by their own assumptions? Like making an algebra problem look like a geometry problem?”

  “Yeah? What about it?”

  “It’s the same pattern. He made a trick body look like a trick alibi.”

  Kusanagi had practically yelped.

  “Remember afterward, when you showed me Ishigami’s work schedule from his school? He’d taken the morning of the tenth as well as the morning of the eleventh off from work. That’s what tipped me off to the fact that the incident Ishigami really wanted to hide had taken place not the night of the tenth, but the night of the ninth.”

  That incident was the murder of Shinji Togashi at the hands of Yasuko Hanaoka.

  Everything Yukawa had said fit the case precisely. In fact, everything the physicist had been obsessing over—from the stolen bicycle to the half-burned clothes—had turned out to be vital pieces of the puzzle. Kusanagi had to admit that he, along with every other detective that had looked into the case, had been caught in a labyrinth of Ishigami’s design.

  Yet it all still seemed too unreal to be true. Killing a person to hide a murder—who would think of something like that? Of course, that’s the point. He didn’t want us to think of it.

  “There’s another side to his setup,” Yukawa said then, as though he could read Kusanagi’s thoughts. “Ishigami planned to turn himself in in Yasuko’s place should things fall apart. But if he were really taking her place of his own free will, there was always the danger that his resolve might waver. He might even break under repeated police questioning and cough up the truth. I doubt he feels any such threat to his resolve now, though. All he has to do is claim that he was the killer, which, of course, is quite true. He is a murderer, and deserves to be in prison. In exchange for paying his debt to society, he gets to protect, utterly and forever, the person whom he loves with all his heart.”

  “So when did Ishigami realize the jig was up?”

  “I told him as much, in a way that only he would understand. What I told you earlier, about there being no useless cog in our society—how only a cog can determine how it is used—you know what I meant by that, don’t you?”

  “You’re talking about our nameless victim Ishigami used as the final piece in his puzzle.”

  “What Ishigami did is unforgivable. He should have turned himself in. And that was why I talked to him about the cogs. I just didn’t guess he would go about it in quite the way he did. To protect her by making himself out to be a stalker—that was when I realized how deep his plan went.”

  “So where is Shinji Togashi’s body?”

  “I have no idea. Ishigami must have disposed of it in some fashion. Perhaps some prefectural police department has found him already, or maybe they haven’t.”

  “Prefectural? You mean somewhere outside of our jurisdiction?”

  “He would avoid this area, yes. He didn’t want the murder of Shinji Togashi being linked to his own crime if he could possibly avoid it.”

  “So that’s why you were looking at newspapers in the library. You were checking to see if another unidentified body had been found.”

  “And I found nothing where the corpse matched Togashi’s description. Though I’m sure he’ll turn up sooner or later. I doubt he was all that thorough in hiding it. There would be no danger of that body being identified as Shinji Togashi, after all.”

  “Well, I’d better start looking then,” Kusanagi said, but Yukawa shook his head.

  “You promised. Remember? I’ve been talking to you as a friend, not a detective. If you choose to act on this information in your official capacity, then that’s all we are. A detective and his informant.”

  Yukawa’s eyes were dead serious. No arguing with him.

  “I’m going to throw the ball in her court. See what she does,” Yukawa had said then, pointing toward Benten-tei. “I seriously doubt she knows the truth of what happened. She doesn’t know the sacrifice Ishigami’s made. I’ll tell her. Wait and see what she decides to do. I’m sure Ishigami wants her to be happily ignorant of everything. But I cannot stand for that. I think she needs to know.”

  “And you think she’ll turn herself in when she hears what you have to say?”

  “No idea. I don’t really think she should turn herself in, myself, given the circumstances. When I think of what Ishigami would want, I’m inclined to say she should go free.”

  “Well, if Yasuko Hanaoka doesn’t eventually turn herself in, I’m going to have to start a new investigation. Even if it means the end of our friendship.”

  “I understand.”

&nb
sp; So Kusanagi had stood there, smoking cigarette after cigarette, watching his friend talk to Yasuko Hanaoka. Now Yasuko’s head was slumped forward. She barely shifted on the bench during the whole time Yukawa spoke to her. Now the physicist’s lips were moving, but his expression never changed. Still, Kusanagi could feel the tension in the air around the two of them even from where he was standing at the entrance to the park.

  At last Yukawa stood up from the bench. He bowed curtly in Yasuko’s direction, then walked toward the detective. Yasuko remained sitting on the bench, slumped half over, unmoving.

  “Thanks for waiting,” Yukawa said.

  “You tell her everything?”

  “Yep.”

  “She say what she’s going to do?”

  “No. It was pretty much just me talking. I didn’t ask what she was going to do, nor did I tell her what she ought to do. It’s up to her now.”

  “Well, like I said before, if she doesn’t turn herself in—”

  “I know,” Yukawa said as he began to walk away. Kusanagi walked with him, matching his stride. “You don’t have to say it. More importantly, I have a favor to ask of you.”

  “You want to see Ishigami?”

  Yukawa’s eyes opened a little wider at that. “How’d you guess?”

  “How long have we been friends?”

  “Oh, quite some time.” Yukawa shook his head, a lonely smile on his lips. “Quite some time.”

  NINETEEN

  Yasuko sat motionless on the bench. She felt the weight of everything she’d been told like a physical sensation, heavier than she could imagine, so heavy it shocked every inch of her body. So heavy it felt like it might crush her heart.

  How could he go so far?