Salvation of a Saint

NINETEEN

Utsumi was at the Meguro Police Station writing a report when Kusanagi and Kishitani marched into the room, familiar scowls on their faces.

‘The old man go home already?’ Kusanagi asked when he saw her.

‘No, I think the chief’s over in Investigations.’

Kusanagi left without another word, leaving Kishitani behind.

‘Looks like he’s in a bad mood,’ Utsumi said.

Kishitani shrugged. ‘We finally managed to track down Yoshitaka Mashiba’s old flame.’

‘Really? Isn’t that a good thing?’

‘Well, we hit a little snag when we went to follow up.’ He dropped into a folding chair and related the story of the beetroot alien and its illustrator to a surprised Utsumi. ‘We ended up going to the publisher,’ he concluded, ‘and we got a photograph of her to show to that waitress at the tea café, who confirmed her as Yoshitaka’s ex-girlfriend. Which nicely wraps up that chapter, and leaves Kusanagi’s former-lover theory dead in the water.’

‘No wonder he’s grumpy.’

‘I’m a little disappointed myself,’ Kishitani said. ‘We do the run-around all day only to end up with this. Talk about exhausting.’ He yawned and stretched.

Just then Utsumi’s phone rang. It was Yukawa.

‘Hello again,’ she said into the receiver. ‘Didn’t I just talk to you earlier today?’

‘Where are you now?’ Yukawa asked.

‘Meguro station, why?’

‘I’ve been thinking about things, and realized I need you. Can you meet?’

‘Again? Sure, no problem. But what’s up?’

‘I’ll tell you when I see you. You pick the place,’ Yukawa said. He sounded uncharacteristically excited.

‘Okay, well, I could just go to the university—’

‘No, I’ve already left. I’m headed towards you, actually. Just pick a place somewhere in between.’

She gave him the name of a nearby twenty-four-hour restaurant, and he hung up. Utsumi placed her half-written report in her bag and grabbed her jacket.

‘Was that Galileo?’ Kishitani asked.

‘Yes. He said he needed to talk to me about something.’

‘I hope he figures out the poisoning trick so we can solve this case and go home. Take notes, if you don’t mind. Sometimes his explanations can be a little dense.’

‘I know,’ Utsumi said as she headed out of the room.

She was drinking tea when Yukawa hurried into the restaurant. He sat down across from her and ordered a hot chocolate.

‘No coffee?’

‘No, the two cups earlier were enough,’ Yukawa said, with a slight frown. ‘Sorry for dragging you out like this.’

‘It’s not a problem. So what’s this about?’

‘Right …’ He glanced down at the table once before looking back up at her. ‘First, I need to know if you still suspect Mrs Mashiba.’

‘Huh? Well, yes, I do. I suspect her.’

‘Right,’ Yukawa said again, reaching inside his jacket to pull out a folded piece of paper. He placed it on the table. ‘Read this.’

Utsumi picked up the paper, unfolded it, and began to read, her eyes narrowing. ‘What is this?’

‘Something I want you to look into. In detail.’

‘And this will solve the mystery?’

Yukawa blinked and gave a little sigh. ‘No, probably not. But this will at least prove it’s unsolvable. Think of it as a kind of way to cover the bases.’

‘What do you mean?’

‘After you left my laboratory today, I started thinking. If we hypothesize that Mrs Mashiba poisoned the coffee, then the question is: How did she do it? The answer is: I have no idea. My conclusion was that this is a problem without a solution – save one.’

‘Save one? So there is a solution.’

‘Yes, but it’s an imaginary solution.’

‘You lost me.’

‘An imaginary solution is one that, while theoretically possible, is practically impossible. There appears to be only one method by which a wife in Hokkaido can poison her husband in Tokyo. However, the chances that she pulled it off are infinitely close to zero. You see? The trick is doable, but pulling it off isn’t.’

Utsumi shook her head. ‘I’m not sure I do see, actually. So this homework you’ve given me is to prove that the trick is impossible? Why?’

‘Sometimes it’s as important to prove there is no answer to a question as it is to answer it.’

‘Except I’m looking for answers, Professor. I’d much rather be getting to the truth of what happened than engaging in theoretical exercises, if you don’t mind. That’s my job.’

Yukawa fell silent. His hot chocolate arrived. After a moment he lifted the cup and took a sip. ‘Of course,’ he muttered at last. ‘You’re right.’

‘Professor …’

The physicist reached out and retrieved the piece of paper off the table. ‘It’s a habit we scientists get into,’ he said. ‘Even if the solution to a problem is imaginary, we can’t rest until we look into it. But, of course, you’re a detective, not a scientist. You can’t be wasting your valuable time proving something’s impossible.’

He neatly refolded the paper and placed it in his jacket pocket. The edges of his mouth curled upward into a smile. ‘Forget I said anything.’

‘Why don’t you tell me what this impossible trick was?’ Utsumi said. ‘Then I can decide for myself whether or not it’s really impossible. Based on that, I can look into whatever you wanted me to check.’

‘I can’t do that,’ Yukawa replied.

‘Why not?’

‘If you knew what the trick was, it would colour your opinion, rendering you unable to conduct your research objectively. And, if you’re not going to look into it anyway, there’s no need for you to know the trick. Either way, I can’t tell you.’

Yukawa reached for the bill, but Utsumi grabbed it before he could pick it up. ‘It’s on me,’ she said.

‘Unthinkable,’ Yukawa said. ‘I made you come out here.’

Utsumi held out her other hand. ‘Give me that paper. I’ll look into it for you.’

‘But it’s an imaginary solution.’

‘I don’t care. If it’s the only solution we’ve got, I want to know what it is.’

Yukawa sighed and produced the paper. Utsumi peered at it briefly before putting it in her bag. ‘So … if it turns out that the answer isn’t “imaginary”, as you call it, after all, we have a chance at solving the mystery.’

‘Maybe,’ Yukawa muttered noncommittally as he pushed up his glasses with one finger.

‘We don’t have a chance?’

‘If it’s not imaginary,’ the physicist said, a keen glimmer in his eye, ‘then you still won’t be able to solve it. Neither will I. It’s the perfect crime.’