Ishigami called to mind the detective named Kusanagi. He seemed like a personable man. Soft-spoken, not too imposing. But if he was a detective in Homicide, that meant he had the requisite information-gathering skills. He wasn’t the kind to scare a witness into revealing something, but the sort who casually drew the truth out of them. He had noticed the letter from Imperial University in Ishigami’s mail, too, which meant he was observant. And all of this made Kusanagi someone who required caution.
“Did you ask him about anything else?”
“That was the only thing I asked. But Misato…”
Ishigami’s grip tightened on the receiver. “They went to her school?”
“Yes, I only just heard about it myself. They caught up with her on the way home after classes. I think it was the same two detectives that came here.”
“Is Misato there now?”
“Yes, hold on.”
Misato was on the phone immediately. She must have been standing right next to her mother. “Hello?”
“What did the detectives ask you?”
“They showed me his picture, asked if he’d been by the apartment…”
“Togashi. You told them he hadn’t, right?”
“Yeah.”
“What else did they want to know?”
“They wanted to know about the movie. If I’d really gone on the tenth or not. They thought maybe we’d got the date wrong. I told them I knew it was then, absolutely.”
“What did the detectives say then?”
“They wanted to know if I’d told any of my friends about the movie, or texted them.”
“And?”
“I told them I didn’t text anybody, but I did tell a friend. Then they wanted to know who my friends were.”
“Did you tell them?”
“I only gave them Mika’s name.”
“Mika’s the girl you told about the movie on the twelfth, correct?”
“Yeah, that’s right.”
“Good. You did good. Did the detectives want to know anything else?”
“Nothing big. They wanted to know if I was enjoying school, how badminton practice was, that kind of stuff. I wonder how they knew I was on the badminton team? I didn’t have my racquet with me.”
Ishigami surmised that Kusanagi had seen her racquet when he visited the Hanaokas’ apartment. This detective was turning out to be formidable.
Yasuko got back on the phone and asked, “Well, what should we do?” Her voice sounded faint on the other end of the line.
“Nothing, for now. This isn’t a problem,” Ishigami said with conviction. He wanted to put her at ease. “Everything is going according to my calculations. I should expect that the detectives will be back again soon. Just follow my instructions and everything will be all right.”
“Thank you, Mr. Ishigami … you know I don’t have anyone to turn to but you.”
“That’s all right. Good luck. This will soon be over. I’ll speak with you again tomorrow.”
Ishigami hung up the phone and took out his phone card, already slightly regretting his final words. He shouldn’t have told her it would be over soon. Just how long was “soon”? He shouldn’t be saying things that couldn’t be quantified like that.
However, it was true that events were developing according to plan. He had known they would find out eventually that Togashi had been looking for Yasuko—that was why Ishigami had made the effort to establish an alibi. He had also expected the police to question that alibi.
And he had expected that the police would try to make contact with Misato. They must have hoped she would be the weak link in the chain, a way to take apart the alibi in the absence of any witnesses. Ishigami had taken several steps to prevent that from happening, but he thought now that it would behoove him to check once more and make sure he hadn’t overlooked anything.
Ishigami returned to his apartment, his mind racing, only to find a man standing in front of his door—a tall fellow, unfamiliar, wearing a thin, black jacket. He must have heard Ishigami coming up the steps, for he was facing toward him. His wire-rim glasses glittered.
At first, Ishigami thought it was another detective. But then he realized that no, that was wrong. The man’s shoes were in perfect condition, as good as brand-new.
He approached, warily, and the man spoke. “Ishigami?”
Ishigami looked up at the stranger’s face. The man was smiling. It was a smile he remembered.
Ishigami took a deep breath, and his eyes went wide as the memories came vividly back to him from a twenty-year distance.
“Manabu Yukawa.”
SIX
The classroom felt deserted that day, as always. The room was large enough to seat a hundred students, but there were only twenty or so there now. Most of them were in the back row so that they could slip out after attendance had been taken or work on some project of their own during the lecture.
Very few undergraduates wanted to be mathematicians. In fact, Ishigami was probably the only one in his entire class. And this course, with its lectures on the historical background of applied physics, was not a popular one.
Even Ishigami wasn’t all that interested in the lectures, but he sat in the second chair from the left edge in the front row. He always sat there, or in the closest available position, in every room, at every lecture. He avoided sitting in the middle because he thought it would help him maintain objectivity. Even the most brilliant professor could sometimes err and say something inaccurate, after all.
It was usually lonely at the front of the classroom, but on this particular day someone was sitting in the seat directly behind him. Ishigami wasn’t paying his visitor any attention. He had important things to do before the lecturer arrived. He took out his notebook and began scribbling formulas.
“Ah, an adherent of Erdős, I see,” said a voice from behind.
At first, Ishigami didn’t realize the comment was directed at him. But after a moment the words sank in and his attention lifted from his work—not because he wanted to start a conversation, but out of excitement at hearing someone other than himself mention the name “Erdős.” He looked around.
It was a fellow student, a young man with shoulder-length hair, cheek propped up on one hand, his shirt hanging open at the neck. Ishigami had seen him around. He was a physics major, but beyond that, Ishigami knew nothing about him.
Surely he can’t be the one who spoke, Ishigami was thinking, when the long-haired student, still propping up one cheek, remarked, “I’m afraid you’re going to hit your limits working with just a pencil and paper—of course, you’re welcome to try. Might get something out of it.”
Ishigami was surprised that his voice was the same one he’d heard a moment earlier. “You know what I’m doing?”
“Sorry—I just happened to glance over your shoulder. I didn’t mean to pry,” the other replied, pointing at Ishigami’s desk.
Ishigami’s eyes went back to his notebook. He had written out some formulas, but it was only a part of the whole, the beginnings of a solution. If this guy knew what he was doing just from this, then he must have worked on the problem himself.
“You’ve worked on this, too?” Ishigami asked.
The long-haired student let his hand fall down to the desktop. He grinned and shrugged. “Nah. I try to avoid doing anything unnecessary. I’m in physics, you know. We just use the theorems you mathematicians come up with. I’ll leave working out the proofs to you.”
“But you do understand what it—what this—means?” Ishigami asked, gesturing at his notebook page.