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‘There’s no particular need to thank me. I merely gave the advice that any scientist would in that situation.’ Yukawa sat down across from the detective. There was a chessboard on the workstation between them; he picked up the white knight and began toying with it. ‘So they found the arsenous acid.’

‘We had them run a full analysis. The acid in the filtration system was almost certainly that used to kill Yoshitaka Mashiba.’

Yukawa nodded, returning the piece to the chessboard. ‘Did they say in which part of the system they found the poison?’

‘It was near the water outlet, not in the filter itself. Forensics thinks the killer inserted the poison into the joint that connects the filtration system with the water hose running up from the main line.’

‘I see.’

‘The only problem,’ Utsumi continued, ‘is that they can’t figure out how the killer did it. So how was it done? We’ve got the results from Spring-8 you wanted. Surely you can reveal the trick now.’

Yukawa rolled up the sleeves of his white lab coat and crossed his arms. ‘Forensics couldn’t figure it out?’

‘They say there’s only one possible method: you would have to remove the hose from the filtration system, put the poison in, then reattach it. But that would leave certain telltale signs – marks on the hose or whatever – which they didn’t find.’

‘And you have to know exactly how it was done?’

‘Of course. If we can’t prove how the crime was committed, it doesn’t matter if we have a suspect.’

‘Even though you found the poison?’

‘We won’t have a chance in court if we don’t know how the crime was committed. The defence will claim police error.’

‘Oh?’

‘They’ll say that there’s a possibility that some of the arsenous acid in the coffee made its way to the filtration system after the fact. We are talking about trace molecules here.’

Yukawa sat back in his chair, nodding his head slowly. ‘They might make that argument, it’s true. And if the prosecution couldn’t provide a means of insertion, the court would have to listen to the defence.’

‘Which is why we really need you to explain how it was done. Please. Forensics wants to know, too. Some of them even wanted to come with me to hear it from you firsthand.’

‘Well, that won’t do. I can’t have police tromping through my lab.’

‘Which is why I came by myself. Well, and Detective Kusanagi’s coming later on.’

‘Speaking of which, shouldn’t we wait for him to get here? I don’t want to have to repeat my explanation. Also, there’s one last thing I need to check first.’ Yukawa lifted an index finger. ‘In your department’s opinion – no, actually, your personal opinion is fine – what was the motive for the murder of Yoshitaka Mashiba?’

‘Well, I think romantic troubles would pretty much sum it up.’

Yukawa frowned. ‘Isn’t that a rather abstract motive on which to rest your case? Try telling me who loved whom, who hated the victim enough to kill him, and why.’

‘Well, it’s all conjecture at this point …’

‘Fine. Like I said, all I’m looking for is your personal opinion.’

Utsumi nodded; she lowered her eyes, collecting her thoughts.

Steam bubbled from the coffeemaker. Yukawa stood and retrieved two coffee mugs from the sink.

‘Well,’ Utsumi said as he began to pour the coffee, ‘I think Ayane Mashiba did it. Her motive was that she felt her husband had betrayed her – not just because he asked her for a divorce when he decided she couldn’t bear him children, but also because he had started seeing another woman. That’s what pushed her to murder.’

‘Do you think she made up her mind the night of the party at the Mashiba house?’ Yukawa asked.

‘She probably made her final decision that night, yes. But I think it’s likely she had started harbouring murderous intentions a little earlier than that. She knew about Yoshitaka and Hiromi Wakayama. She also had intimations of Hiromi’s pregnancy. Yoshitaka’s declaration was the final straw.’

Yukawa returned to the table, holding a coffee cup in each hand. He placed one in front of Utsumi. ‘What about this woman, Junko Tsukui? Did she have nothing to do with the murder, then? Isn’t Kusanagi out there right now questioning people about that?’

The likelihood of a personal connection between Junko Tsukui and Ayane Mashiba was the first thing Utsumi had mentioned to Yukawa when she got to the lab.

‘I wouldn’t say there’s no connection. It’s likely that the arsenous acid used in this murder was the same that Ms Tsukui used to kill herself. If Ayane was close to her, she would’ve had an opportunity to get the poison from her.’

Yukawa raised his cup and his eyebrow at Utsumi. ‘And then?’

‘Excuse me?’

‘Is that all Junko Tsukui had to do with it? She just provided the poison? Her death doesn’t factor into the motive at all?’

‘Well, it’s hard to say …’

Yukawa smiled thinly and sipped his coffee. ‘Then it’s hard for me to tell you the trick.’

‘What?! Why?’

‘Because telling you would be far too dangerous. You haven’t yet figured out what this case is really about.’

‘And you have?’

‘More precisely than you.’

Utsumi was glaring at Yukawa, both hands clenched around her mug, when they heard a knock at the door.

‘Good timing! Maybe Kusanagi can shed a little light on the subject,’ the professor said, rising to his feet.

TWENTY-EIGHT

As soon as Kusanagi walked into the room, Yukawa asked how the latest questioning had gone. After a moment’s hesitation, the senior detective told them what he’d heard from Ikai.

‘Yoshitaka Mashiba talked to her first. Which pretty much dismantles your theory, Utsumi,’ Kusanagi said, with a sidelong glance at the junior detective. ‘I mean, the idea that Ayane used the party as a way to get close to him.’

‘It was less a theory than it was a possibility.’

‘Okay. Well then, it’s no longer a possibility. So what do you think happened now?’ He turned to look at her directly.

Yukawa offered Kusanagi a mug of coffee. The detective nodded in thanks.

‘What do you think?’ Yukawa asked his friend. ‘If we accept what Mr Ikai told you at face value, then the couple first met at that party. Which would make the fact that Mr Mashiba’s ex was Ayane’s friend a simple coincidence. How does that sit with you?’

Kusanagi sipped his coffee, sorting out his thoughts. He opened his mouth to speak, then hesitated, tapping his fingers on the tabletop.

Yukawa grinned. ‘So you don’t believe the lawyer?’

‘Ikai’s not lying,’ Kusanagi said at last. ‘But there’s no proof that what he saw was the truth.’

‘Go on.’

Kusanagi took a breath before saying, ‘It could have been an act.’

‘A performance?’

‘Yes. Intended to give the impression that it was their first meeting … in order to hide the fact that they had a relationship before the party. Ikai was brought along so that there would be a witness. A mobile phone case on a bar leading to true love is a little too perfect.’

‘Perfect indeed,’ Yukawa said, a spark in his eye. ‘And I happen to agree with you. Let’s see what the lady thinks.’ He turned to Utsumi.

She nodded. ‘It makes sense. But why go through all that trouble?’

‘That’s the rub, isn’t it? Why put on an act?’ Yukawa looked at Kusanagi. ‘What do you think they were up to?’

‘It’s simple. They were trying to hide the truth.’

‘And what truth is that?’

‘The truth of how they actually met. Which would have been through Junko Tsukui. A fact which they didn’t want getting out, what with her being Mashiba’s former girlfriend, and dead besides. They needed to create a situation where they could meet again, for the first time, under different circumstances: the party.’