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Kusanagi took the book and examined it. It was titled It Can Rain Tomorrow, and it apparently chronicled the adventures of a teruterubozu – a diminutive tissue-paper ghost created by children wishing for good weather. The illustrator’s name was listed as Sumire Ucho – Violet Butterfly, Kusanagi thought. If that’s not a pen name, I don’t know what is.

‘Is this illustrator still connected with your company?’

‘No, not since she made those first illustrations. The company holds all the rights to the character.’

‘Did you ever meet her personally?’

‘I didn’t, I’m afraid. Like I said, we had to keep her existence a secret. Only the CEO and a few other people ever saw her. The contract talks and everything were handled directly by the CEO.’

‘By Mr Mashiba?’

‘Yes. I think he was the beetroot alien’s biggest fan,’ Ms Yamamoto said, staring at the detective.

Kusanagi let his eyes drop back down to the book. There was a little ‘About the Author’ section, but no mention of her real name or age.

Still, it was clear that this woman fitted the bill. Kusanagi lifted the book in one hand. ‘Do you mind if I borrow this?’

‘Not at all,’ the receptionist replied, glancing at her watch. ‘I should be getting back. I’ve told you everything I know. I hope it helps.’

‘Tremendously. Thank you,’ Kusanagi said, inclining his head.

Once she had left, Kusanagi handed the book to his partner. ‘Give the publisher a ring, would you?’

‘Think she’s the one?’

‘There’s a chance. At the very least, we know there was something between this illustrator and Yoshitaka Mashiba.’

‘You sound confident.’

‘It was the look on Ms Yamamoto’s face that sold me. She suspected before today that something was up between those two.’

‘Then why do you think she didn’t say anything before now? The officers we sent to the company earlier asked everybody for information about Mr Mashiba’s female friends.’

‘Maybe she was too unsure to say anything at the time. We didn’t exactly ask her to tell us about the ex-CEO’s lovers, either. We just asked about the illustrator, and she put two and two together, and realized there was something to her hunch.’

‘Interesting. I’m sorry I called her a robot.’

‘You can make up for it by getting on the phone with that publisher now.’

Kishitani pulled out his mobile phone and stepped out of the lounge, book tucked under his arm. Kusanagi watched him make the call in the building lobby. He drank his coffee. It had gone completely cold.

Kishitani returned, a glum look on his face.

‘Couldn’t get hold of anybody?’

‘No, I did.’

‘But they’d never heard of Ms Ucho?’

‘No, they had.’

‘So what’s with the long face?’

Kishitani opened his notebook. ‘Her real name is Junko Tsukui. This book here was published four years ago. It’s out of print now.’

‘You get a number for her?’

‘She doesn’t have a number.’ Kishitani looked up from his notebook. ‘She’s dead.’

‘What? When?’

‘Two years ago, at her home. She committed suicide.’

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.’