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Yukawa met his gaze. Facing him straight on like this, Ishigami could sense the strength behind the physicist’s eyes.

“Wait, are you really angry? I’ve upset you.”

“This is ridiculous,” Ishigami muttered, setting off again. He began climbing the stairs that led up toward Kiyosu Bridge.

“Clothes they think belonged to the victim were found a short distance away from the body,” Yukawa said, following a pace behind. “They were half-burned, in an oil can. They think the murderer did it. When I heard that, I wondered why the murderer didn’t do a better job and burn the clothes completely. The police seem to think it was because he wanted to leave the scene as quickly as possible, but that leads one to wonder why he wouldn’t have just taken the clothes with him to burn someplace else when he had more time. Or maybe he thought they would burn more quickly than they did? Once I started thinking about it, it bothered me. So I tried burning some clothes myself.”

Ishigami stopped again. “You burned your clothes?”

“In an oil can, yes. A jacket, a sweater, some pants, shoes … oh, and underwear. Bought them at a used-clothes shop. I was surprised how much it cost! See, unlike mathematicians, we physicists aren’t satisfied with something until we’ve performed the experiment ourselves.”

“And your results?”

“They burned pretty well, actually, and put off a lot of toxic fumes,” Yukawa told him. “There was nothing left. It didn’t take long at all. Maybe five minutes, tops.”

“And so?”

“So why didn’t the murderer wait those five minutes?”

Ishigami shrugged. He climbed the stairs leading back to the street and, at the top of the stairs, he turned left on Kiyosubashi Road—the opposite direction from the way to Benten-tei.

“Not buying lunch today?” Yukawa asked, as he’d expected.

“I told you I don’t go there every day,” Ishigami retorted, frowning.

“I was just worried about your lunch, that’s all,” Yukawa said, quickening his pace to walk beside him. “They also found a bicycle near the body, you know. Turns out it had been stolen from Shinozaki Station. The suspected victim’s fingerprints were on it.”

“What of it?”

“Kind of surprising to have a criminal who goes so far as to crush the victim’s face, yet forgets to wipe his bicycle for fingerprints. Pretty stupid, really, unless he left his fingerprints on the bicycle on purpose. But why would he do that?”

“I’m sure you’re about to tell me.”

“Maybe in order to link the bicycle to the victim. Clearly, it was better for the criminal for the police to draw that conclusion.”

“Why’s that?”

“Because the criminal wanted the police to assume that the victim had ridden that bicycle from Shinozaki Station himself. And for that, he couldn’t use just any old bicycle.”

“So there was something special about the bicycle they found?”

“I wouldn’t say ‘special.’ It was your typical morning commuter bike. With one exception: it was brand-new.”

Ishigami felt every pore on his body open. It was getting more difficult for him to breathe steadily.

Someone called out, “Good morning!” and he started at the sound. A female student was passing them on her bicycle. She nodded toward Ishigami.

“Oh, hey, morning,” he hurriedly called back.

“That’s impressive. I didn’t think students said hello to their teachers anymore,” Yukawa commented.

“Hardly any do. So why did this bicycle have to be brand-new?”

“If you’re going to steal a bicycle, why not steal a new one—that’s what the police seem to think. But our thief didn’t care about that. He cared about when the bicycle had been left at the station.”

“Because…?”

“The thief had no use for a bicycle that might have been left by the station for days. And he wanted the owner to report the theft. That’s why the bicycle had to be new. Owners of brand-new bicycles don’t usually leave them out on the street for very long and are more likely to go to the police when their bicycle goes missing. Neither of these things was absolutely necessary for the thief to create his camouflage, but either would help, so he chose the course of action most likely to yield positive results.”

“Hmph.”

Ishigami refrained from commenting on Yukawa’s conjecture. He walked on, looking only at the street in front of them. They were nearing the school. The sidewalk was filling up with students.

“Well, this is certainly an interesting story, and I’d like to hear more,” he said, stopping and turning to face Yukawa. “But maybe you’ll let me be for now? I don’t want the students prying.”

“Absolutely. I think I’ve said pretty much what I had to say, in any case.”

“It was interesting,” Ishigami said. “I recall you posing a question to me before. You asked which was more difficult, formulating an unsolvable problem, or solving that problem. Remember?”

“I do. And I have an answer for you. It’s more difficult to create the problem than to solve it. All the person trying to solve the problem has to do is always respect the problem’s creator.”

“I see. What about the P = NP problem, then? The question of whether or not it’s as easy to determine the accuracy of another person’s results as it is to solve the problem yourself.”

Yukawa favored him with a suspicious look, unsure of where Ishigami was leading.

“You’ve given me your answer,” Ishigami went on, pointing a finger at Yukawa’s chest. “Now it’s time for you to hear someone else’s solution.”

“Ishigami…”

“Good day.” The mathematician turned his back on Yukawa and strode into the school, tote bag clutched tightly in his arms.

It’s over, he thought. The physicist had seen through everything.

*   *   *

Misato sat in uncomfortable silence, eating her apricot pudding. Yasuko wondered once again whether it would have been better just to have left her at home.

“You get enough to eat, Misato?” Kudo was asking. He had been fretting over her all evening.

Misato nodded, mechanically sticking the spoon into her mouth, without even a glance in his direction.

You can drag a teenager to a good restaurant, but you can’t make her enjoy it.

They had come to a Chinese place in Ginza for dinner. Kudo had insisted that Yasuko bring her daughter, and so she had dragged Misato along, despite the girl’s protests. In the end, Yasuko had convinced her to come by telling her that it would seem unnatural for them to avoid going out—that it might make the police suspicious.

But now that she saw how worried Kudo was, she regretted it. All through dinner, he had tried a variety of approaches to get the girl to talk, but he had failed to get more than a few terse words out of her all night.

Misato finished her dessert and turned to her mother. “I’m going to the bathroom.”

“Oh. Okay.”

Yasuko waited for Misato to leave, then turned to Kudo, clasping her hands together. “I’m so sorry.”

“Huh? About what?” He looked genuinely surprised, though Yasuko knew it was an act.

“She’s really shy, that’s all. And I think she has issues with older men.”

Kudo smiled. “Don’t worry. I didn’t imagine we’d be great friends by evening’s end. I was just like her when I was a teenager. I’m happy just to have gotten to meet her today.”

“Thanks, you’re too kind.”

Kudo nodded. He fished in the pocket of his jacket, which hung on the back of his chair, and pulled out a cigarette and lighter. He had refrained from smoking during dinner on account of Misato.