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“You’ve got to be kidding. You weren’t joking when you said you were goofing off, were you?” Naho put money on the table for her banana juice. She didn’t want Kaga to pay for her.

“It’s hot again today,” murmured Kaga, looking out the window. “Look. All the businessmen walking up this way from the Ningyocho subway station — see how they’ve got their jackets off and their shirtsleeves rolled up?”

“What the heck do I care?” Naho said sharply. She could no longer bother to be polite.

“You see? Here comes another one. He’s taken his jacket off and slung it over his shoulder. Poor chap.”

“Why shouldn’t he, in this heat?”

“It’s cooler than it was earlier, though. See? Here’s a guy who’s kept his jacket on.”

Sure enough, a rather stout man strolled by with his suit perfectly in place.

“Are you trying to tell me something?” Naho couldn’t keep the note of irritation out her voice.

“Take a good look. What do you see? Most of the men walking from right to left — in other words, from the Ningyocho neighborhood to Hamacho, the next neighborhood over — have taken their jackets off. With the men walking from left to right, it’s the opposite: they’ve all got their jackets on.”

Naho swiveled around in her seat to inspect the street.

A gaggle of businessmen passed by, going from right to left. Naho’s jaw dropped. Kaga was right: nearly all of them had their jackets off.

“It’s true,” she murmured under breath.

“Interesting, eh?” said Kaga.

“But why? Is it just a coincidence?”

“You shouldn’t dismiss something like this as a coincidence. That’s too easy. You should assume there’s a reason for it.”

“Do you know what that reason is, Detective Kaga?”

“Perhaps I do.” Kaga smirked.

“What are you grinning for? Why are you so pleased with yourself?”

“I’m not being conceited. To be honest, once I’ve told you the reason, I doubt you’ll be very impressed. A lot of office workers walk along this street, but most of them work for firms with offices in Hamacho. Okay, so here’s my question. The time now is half past five. What sort of people would you expect to find walking from right to left, in other words from Ningyocho toward Hamacho, at this time of day?”

“Well, given what time it is...,” said Naho thoughtfully, as she stared at yet another businessman walking by in his shirtsleeves, “they must be on their way back to their offices.”

“Right. In other words, these are the people who’ve been out of the office all day. They work outside, probably in sales or service, stuff like that. The people who are going from left to right are the opposite: they’ve been in the office all day. Because they’ve been in an air-conditioned office most of the day — in contrast to their colleagues who are all hot and bothered from running around outside — they’re a little on the chilly side if anything. That’s why they’re wearing their jackets. Plus by this time in the afternoon, the temperature has gone down quite a lot. Take a closer look at the people coming from the direction of Hamacho. On the whole, they’re on the older side. My guess is they’re quite senior and their jobs don’t involve much running around outside the office. That also helps explain why they get to leave at five thirty on the dot.”

As she listened to Kaga’s explanation, Naho inspected the men walking down the street. There was the occasional exception, but all in all she had to admit that the detective’s theory was very plausible.

“Wow... I think you’re right. I’ve lived here my whole life, but I never noticed that until you pointed it out.”

“Well, it doesn’t have much practical value.”

Naho nodded, then suddenly looked at Kaga wide-eyed.

“Does this have any connection to the murder?”

Kaga picked up the check from the table.

“You remember me asking you what Mr. Takura was wearing?”

Naho blinked in acknowledgment.

“He looked smart and had his jacket on...”

“But Mr. Takura is one of those people who are out and about all day. He told us that he went to visit you after going to the victim’s apartment in Kodenmacho. That would have involved quite a lot of walking. Given the circumstances, he did well to have his jacket on and look so neat and tidy.”

“I see what you mean... Of course, he could just have been toughing it out.”

“That’s a possibility, sure. Still, I think that’s where we may find the answer to the riddle of the missing thirty minutes.” Kagawa got up and walked over to the cash register to pay.

“Hang on. What are you implying?”

“I can’t tell you any more yet. I need to unravel that riddle first,” said Kaga, as they left the café.

4

Over dinner, Naho relayed what Detective Kaga had told her. Getting Satoko to grasp the concept of the missing thirty minutes was quite a struggle. Naho had to write out a timeline of Takura’s movements before her grandmother could understand.

“Huh,” snorted Satoko, her head cocked to one side. “I don’t think those thirty minutes matter much, one way or the other.”

“Thirty minutes is long enough for someone to have committed the murder. That’s why the police are taking it so seriously.”

“Then the police are idiots. First of all, would Mr. Takura do something like that? Of course not. He’d never do anything so horrible. He’s not that kind of person. He always keeps his promises, always does his best to understand other people’s points of view. People as considerate as he are rare nowadays. I mean, he came around the minute I got out of hospital—”

Naho interrupted Satoko with a dismissive wave of the hand.

“We all know that Mr. Takura’s a nice guy. There’s no point going on about it. The important thing is to figure out a way to prove to the police that he didn’t do it.”

“That’s exactly what I’m saying. We need to tell the police loud and clear. The only reason they could possibly suspect Mr. Takura is because they have no idea what kind of man he is.”

“I’m wasting my time,” muttered Naho under her breath. She looked over at Fumitaka, her father. He was sitting in silence, a solemn expression on his face.

“What are you thinking, Dad?”

“Huh? Oh, I was wondering if Mr. Takura really said those things.”

“What things?”

“You know, about how he dropped in on you here after going to Kodenmacho and before going back to the head office, then heading home after that.”

“That’s what Detective Kaga told me he said.”

“Hmm. I wonder...” murmured Fumitaka, deep in thought.

“What’s wrong, Dad?”

“Oh, I don’t know.”

“That Detective Kaga is a handsome young fellow,” declared Satoko, as she prepared a pot of tea. “He’s got the perfect face for a samurai drama on TV. He’s clever-looking, too.”

“I think he is clever. He pointed out something very interesting to me.” Naho then told Satoko about Kaga’s observation regarding how the businessmen walking along Amazake Alley were dressed.

“Gosh, he’s right!” exclaimed Satoko wonderingly. “That would never have occurred to me.”

“Anyway, that set Detective Kaga wondering why Mr. Takura still had his jacket on when he came to see us on that day. He thought it might be connected to that thirty-minute gap.”

“How?”

“He doesn’t yet know.”

“Well, he’s got some eccentric ideas. Who knows, perhaps that makes him a better detective.”