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Yukawa snapped his fingers. ‘An excellent theory. Unas -sail able, really. So let’s talk about how they really met. More to the point, when they fell in love. Was it before or after Tsukui committed suicide?’

Utsumi took a deep breath, straightening in her chair before she looked towards Yukawa. ‘Do you think Ms Tsukui committed suicide after Mr Mashiba started seeing Ayane?’

‘It makes sense. Imagine her, betrayed by both her lover and her friend. That would be quite a shock.’

Kusanagi felt his heart sinking into darker depths. What Yukawa was suggesting did indeed make sense. That scenario had occurred to him as well while he was in the middle of his chat with Ikai.

‘That certainly clears up the point of that party,’ Utsumi said. ‘With Mr Ikai there to testify that the two had met for the first time while he was watching, they would be able to deny any connection between their relationship and Junko Tsukui’s suicide.’

‘See? Now we’re getting somewhere,’ Yukawa said, a satisfied look on his face.

‘Should we confront Mrs Mashiba about it?’ Utsumi wondered out loud, looking towards Kusanagi.

‘Confront her how?’

‘What if we showed her the picture book, the one with the tapestry in it? Doesn’t that prove they knew each other?’

Kusanagi shook his head. ‘All she’d have to say is, “Sorry, no idea”.’

‘But …’

‘She’s been hiding her friendship with Yoshitaka’s ex – even the fact that she knew he had an ex at all. If all we do is bring her some picture books, we won’t get anywhere. We’d simply be tipping our hand.’

‘I have to agree with Kusanagi,’ Yukawa said, stepping over to the chessboard and picking up a black pawn. ‘If you’re going for checkmate, better do it in one move, or you’ll have a stalemate on your hands.’

Kusanagi looked at the physicist. ‘So – she did it.’

Yukawa remained at the chessboard. ‘This next part is the most important. Now that we know a little more about Mrs Mashiba’s past, how does that knowledge relate to the case at hand? Is the arsenous acid really the only connection?’

‘Maybe,’ Utsumi said thoughtfully, ‘Mrs Mashiba couldn’t forgive her husband for leaving her especially because of what their relationship had done to her friend?’

‘I could see that,’ Yukawa said, nodding.

‘No,’ Kusanagi said, ‘that’s not how she would think about it. She betrayed her friend and stole her man – just as her assistant betrayed her and stole her husband.’

‘Karma, then? So she would just resign herself to her fate?’ Yukawa said. ‘No hatred towards her husband or his lover – is that what you’re trying to say?’

‘Not exactly …’

‘I think there’s a question both of you need to ask.’ The physicist turned away from the chess set, catching both detectives with his stare. ‘Why do you think Yoshitaka Mashiba switched from Junko Tsukui to Ayane?’

‘I don’t know,’ Utsumi said, ‘probably just a change of heart—’ She put her hand to her mouth. ‘Oh. No, that’s not it, is it?’

‘It’s not,’ Kusanagi said. ‘He left her because she didn’t give him a child. Remember, Mashiba was ready to marry any woman who’d get pregnant for him. If it looked like she couldn’t, he would switch.’

‘That fits with everything we’ve heard thus far,’ Yukawa agreed. ‘So the question is, did Ayane know his reason at the time? Did she think Yoshitaka left Junko and chose her because he thought she would bear him children?’

‘Well …’ Kusanagi fell silent.

‘I doubt it,’ Utsumi said crisply. ‘What woman would want to be chosen like that? If she realized it at all, it was just before they got married – when they arranged to split up if she couldn’t get pregnant within a year.’

‘That’s what I think, too,’ Yukawa said. ‘So let’s talk about motive again. You mentioned that Mr Mashiba’s betrayal was the motive, Utsumi, but was what he did really a betrayal? After one year, there was no pregnancy, so he asked for divorce and hooked up with another woman – wasn’t he just living up to the agreement they made?’

‘That’s true; but emotionally speaking, how could she accept that?’

Yukawa smiled. ‘So let’s phrase it a different way: if we assume that Ayane was the killer, then her motive was that she didn’t want to honour her own promise. Correct?’

‘I guess you could say that.’

‘What are you driving at?’ Kusanagi asked his friend.

‘Try to imagine how Ayane was feeling just before she got married. What were her intentions when she made that agreement with Yoshitaka? Was she optimistic that she could get pregnant within the year? Or had she decided that, even if she didn’t get pregnant, her husband wouldn’t follow through on his end of the deal?’

‘Both, I’d say,’ Utsumi answered.

‘Okay. Let me ask you this, then: if she thought there was a chance she might get pregnant, wouldn’t she have gone to the hospital?’

‘Hospital?’ Utsumi furrowed her brow.

‘According to what you’ve told me, not once during the year did Ayane undergo infertility treatment. With a promise like the one this couple had made, I would have expected her to start visiting a gynaecologist within a few months of the wedding.’

‘According to what Mrs Mashiba told Hiromi Wakayama, they hadn’t tried infertility treatments because those take too long.’

‘That would be Mr Mashiba’s thinking. Why bother with all that time and money when it would be quicker to simply find a new wife? But what about Ayane’s perspective? Wouldn’t she want to try anything, even if it meant grasping at straws?’

‘Yeah, sure,’ Kusanagi muttered.

‘So why didn’t she go to the hospital? Therein lies the key to this case.’ Yukawa adjusted his glasses with one finger. ‘Think about it. She had time, she had money. So why wouldn’t she go?’

Kusanagi thought. He tried to put himself in Ayane’s shoes, but no answer was forthcoming.

Suddenly, Utsumi stood. ‘Maybe she didn’t go because she knew there was no point.’

‘No point? What do you mean?’ Kusanagi asked.

‘What if she knew any treatments would be pointless?’

‘Exactly,’ Yukawa said. ‘She knew going to the hospital would do nothing for her. That’s why she didn’t go. It’s the most logical explanation.’

‘So … she knew she was completely infertile,’ Utsumi said.

‘She was over thirty. Surely she’d had at least one gynaecological exam by that age. Maybe she had been told earlier that she couldn’t have children. If so, not only would there be no point in going to the hospital, there would also be the danger that if she did go, her husband might learn the results.’

‘Wait a second. You’re saying that she made that bargain with her future husband even though she knew she couldn’t have children?’ Kusanagi asked.

‘That’s what I’m saying. Her only hope was that her husband wouldn’t follow through on his threat. Of course, he did, with flying colours. So, she decided to kill him. Now, let me ask you – when did she first contemplate killing Yoshitaka Mashiba?’

‘When she found out about him and Hiromi—’

‘No, that’s not it.’ Utsumi cut Kusanagi off. ‘If she had planned on killing her husband if he kept the promise, then she made up her mind when she made the promise.’

‘That’s the answer I was waiting for,’ Yukawa said, his face taking on a sudden sober intensity. ‘Essentially, Ayane predicted that, within a year’s time, she would have reason to kill her husband. Which meant it was possible for her to prepare the means to kill him in advance.’