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Yukawa chuckled. “No, I wasn’t going to suggest that the police had made a mistake identifying the body. I’m more concerned about the idea of him using this bicycle. Did the victim leave his bicycle at Shinozaki Station?”

“No, actually—”

Kusanagi went on to explain what he’d learned about the stolen bicycle. Yukawa’s eyes widened slightly behind his wireframe glasses.

“So the victim went out of his way to steal a bicycle at the station just to go to the scene of the crime? Why not take a bus or a taxi?”

“I don’t know why he stole the bike, but that’s what he must’ve done. The guy was unemployed, after all, without a whole lot of money to his name. He probably wanted to avoid paying the bus fare.”

Yukawa, looking unconvinced, crossed his arms and gave a faint snort. “Well, okay—however he did it, the victim went to meet with our Ms. A at the scene of the crime. Go on.”

“I figure they had planned some sort of rendezvous but Ms. A got there a little early and was hiding somewhere. When she saw the victim approach, she snuck up behind him, wrapped a rope around his neck, and strangled him to death.”

“Stop right there!” Yukawa raised both hands. “How tall was the victim?”

“One hundred and seventy centimeters plus change,” Kusanagi said, resisting the urge to curse. He knew what Yukawa was going to say next.

“And Ms. A?”

“About one sixty.”

“So he was over ten centimeters taller,” Yukawa said with a slight grin, resting his chin on his hand. “You see what I’m getting at here.”

“Sure, it’s hard to strangle someone taller than you. And from the angle of the marks on the victim’s neck, it’s pretty clear whoever strangled him was pulling upward. But the victim could have been sitting. Maybe he was still on the bicycle.”

“Well, I’m glad you had a sad excuse for your scenario ready.”

“Nothing sad about it,” Kusanagi said emphatically, bringing his fist down on the tabletop.

“So what happened next? She took off his clothes, smashed in his face with the hammer she also brought, and burned off his fingertips with a lighter? Then she set fire to his clothes, and fled the scene. That’s about it?”

“She still could’ve made it to Kinshicho by nine o’clock.”

“Theoretically, yes. But I can’t help thinking you’re grasping at straws. Don’t tell me that the entire department is backing your little scenario?”

Kusanagi’s mouth curled into a frown. He downed the rest of his beer and waved to the waitress for another round, then turned back to Yukawa. “Yeah, well, a lot of the men wonder if a woman really could have pulled it off.”

“As well they should. Even if she did catch him by surprise, it’s not easy to strangle a grown man who is fighting back. And believe me, he would have done everything in his power to stop her. Besides, it would be difficult for a woman of average size and strength to dispose of a grown man’s body after the deed was done. I’m sorry, but I have to join the crowd that thinks your theory is full of holes.”

“Yeah, I figured you’d say that. I don’t much believe it myself. I’m just saying it’s one of several possibilities.”

“Which suggests you have some other ideas. Well, don’t keep them all to yourself. Let’s hear another theory.”

“I’m not claiming that I’ve got much of anything right now. But the scenario I just gave you assumes that the man was killed near where he was found. It’s also possible he was killed somewhere else and then his corpse was dumped there. Truth be told, most of the department thinks that’s what happened. Regardless of whether Ms. A did it or not.”

“It does seem to be the more reasonable assumption. But it wasn’t the one you offered up first. Why?”

“Simple. If Ms. A was the killer, she couldn’t have done it someplace else. She doesn’t have a car or access to one. She can’t even drive. There was no way she could have transported the body to the riverbank.”

“I see. That strikes me as an important point.”

“And then there’s the matter of the bicycle. We could assume whoever left it there did so on purpose to make us think that the murder took place on the riverbank, but then there would have been no reason to go to the effort to put the victim’s fingerprints on it. Especially since they went to the trouble of burning fingertips off the body.”

“The bicycle is a mystery. For a number of reasons.” Yukawa tapped his fingers on the tabletop like he was playing the piano. Then he stopped and said, “Either way, isn’t it better to assume that a man probably did it?”

“That’s what most people at the department think. But I still think Ms. A was involved.”

“So Ms. A had a male accomplice?”

“We’re looking into people connected to her now. She used to be a hostess at a nightclub, after all. There have to be some men in her life.”

“An interesting assumption. I can hear the uproar from hostesses across the country already,” Yukawa said with a grin. He took a swallow of beer, then, a serious look returning to his face, asked to see the illustration again.

Kusanagi handed him the artist’s depiction of the victim. It was a rendering of Togashi as he might have appeared dressed in the clothes they’d found near the crime scene.

Yukawa stared at it intently. “Why did the killer feel the need to strip the body, I wonder?” he muttered.

“To help hide the victim’s identity. Same reason he crushed the face and got rid of the fingerprints.”

“Then why didn’t he take the clothes with him when he left? It’s only because he tried to burn them and failed that you were able to come up with that illustration there.”

“Well, he was probably in a hurry. Or he made a mistake.”

“I agree that you can tell someone’s identity from their wallet or driver’s license, but can you really identify someone from their clothes or shoes? It seems like the risk involved in taking the time to take off and burn his clothes would outweigh any benefits. Wouldn’t the killer want to get away as quick as he could?”

“What are you driving at? You think there’s another reason they stripped him?”

“I can’t say for sure. But if there was, then until you figure out that reason, you won’t be able to pin down your killer.” Yukawa traced a large question mark on the illustration with his fingertip.

*   *   *

The performance of the junior-year group 2 math class on the year-end exams was appalling. And group 2 wasn’t the only sad story; the entire junior class had done poorly. To Ishigami it seemed like the students were getting dumber by the year.

After he’d passed out the answers, the math teacher put up a schedule for make-up exams. The school had set a lowest acceptable score for each subject, and those students who didn’t reach it wouldn’t go on to the next grade. Of course, they prevented all but the most hopeless cases from failing and being held back a year by making them take as many make-up exams as they needed to pass.

Shouts of protest rose from the class when they saw the grades he’d given them. Ishigami ignored the outcry as usual, but one comment rose above the noise and reached his ears.