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“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.

NINE

They had eaten the last of the shrimp, and the wine bottle was empty. Yasuko drank the last sip of wine from her glass and breathed a sigh of contentment. She couldn’t remember the last time she had been out for real Italian food.

“Something more to drink?” Kudo asked her, a line of red showing beneath his eyes.

“I’m fine, thanks. Why don’t you order something?”

“No, I’ll pass. Save it for dessert.” He smiled and dabbed at his mouth with a napkin.

Yasuko had gone out to dinner with Kudo several times back when she was a hostess. Whether the meal was French or Italian, he had never stopped at the first bottle of wine.

“Drinking less these days?”

Kudo nodded thoughtfully. “I suppose I am. Less than before, at any rate. Maybe I’m getting old.”

“There’s nothing wrong with moderation. You have to take care of yourself.”

“Thanks.” Kudo laughed.

He had called her cell phone earlier that day to ask her out to dinner. At first, she hesitated, but then she accepted. The murder investigation had given her pause. It felt wrong, somehow, to go out to dinner at a time like this. Wrong for her, and especially for her daughter, who was surely even more frightened by the whole thing than she was. There was also the matter of Ishigami, and his help in covering up Togashi’s death. She wondered how long his assistance would remain unconditional.

Then again, she thought, maybe it was precisely at times like these that she should do her best to act normal. If she didn’t have a particular reason not to go, wouldn’t it be “normal” to accept an old friend’s offer to go to dinner? It would be more unnatural for her to refuse, and if word of it reached Sayoko, then she might grow suspicious.

Whatever the line of reasoning she came up with to rationalize it to herself, Yasuko knew it was all a pretense. The real reason she had accepted Kudo’s offer was that she’d wanted to see him again.

She wasn’t sure if she had romantic feelings for him. In fact, before he had showed up the other day, she had scarcely thought of him in the last year. She was fond of him, that was true, but at present, it went no further.

Yet she couldn’t deny that after he had invited her out, she had felt elated—an elation very similar to what she remembered feeling when making a date to meet a lover. She had even felt her body warming. Heart aflutter, she had asked Sayoko if she could get out of work early.

It was possible that all she really wanted was an escape from the worrying that had become a constant in her life. Or perhaps she wanted once again to be treated like a woman, to feel those things she had not felt in so long.

Regardless of the reasons, Yasuko didn’t regret accepting Kudo’s invitation. Though she couldn’t help feeling like she was sneaking away from something else she should have been doing, it was undeniable that she was having fun.

“What did your daughter do for dinner tonight?” Kudo asked, taking a sip of coffee.

“I left her a message telling her she could order out. I’m guessing pizza—it’s her favorite by far.”

“Hmph. Poor girl. Eating pizza while we’re here with this feast.”

“I don’t know. I think she prefers watching TV and eating pizza to a place like this. She’s not fond of formal dining—or anything else where you have to act proper.”

Kudo nodded, frowning. He scratched at the side of his nose. “That may be, that may be. I doubt she’d like to share a meal with some strange old man, either. But maybe next time I could take the both of you out to something simpler. A sushi-go-round, perhaps?”

“Thanks. But you don’t have to worry on our account.”

“It’s not worrying. I’d like to meet her—your daughter.” Kudo raised his eyes shyly from his coffee.

When he had first invited her out, he’d insisted that she bring her daughter along. And Yasuko had been sure of his sincerity, which made her happy.

Yet she had known at once that she couldn’t bring Misato. It was true that the girl didn’t like places like the restaurant Kudo had chosen. That, and Yasuko didn’t want her daughter to have to deal with people at a time like this. If the conversation had chanced to drift to the murder, she didn’t know whether Misato would be able to keep her cool. She also didn’t want her daughter to see her mother as she was now—a single woman out with a man.

“What about you, Kudo? Is it all right for you to skip out on dinner with your family?”

“What about me, indeed.” Kudo set down his coffee cup and rested his elbows on the table. “Actually, one of the reasons I invited you out to dinner today was to talk about that.”

Yasuko lifted an eyebrow, looking into his eyes.

“That is to say—actually, I’m single now.”

Yasuko gasped out loud.

“My wife got cancer. Pancreatic. She had surgery, but it was too little, too late. She passed away last summer. She was young, but once it started it went quickly. It was over in blink of an eye.”

He spoke evenly, which had the effect of making his story sound almost unreal to Yasuko’s ears. For several seconds, she merely sat there, staring at him.

“Really?” she finally managed.

“I wouldn’t joke about something like that,” he replied with a wry smile.

“No, of course you wouldn’t. I just don’t know what to say—” She looked down at the table, then bit her lip before looking back up. “I … I’m sorry for your loss. It must have been difficult.”