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This, Floyd realised, was exactly one of those times.

“You’re right,” he said. “If only one of those strange kids had shown up, I guess I’d have thought nothing of it.”

“The central defect of the human mind,” Custine said, “is its unfortunate habit of seeing patterns where none exist. Of course, that is also its chief asset.”

“But sometimes a very dangerous one.”

Custine stood up, wiping his palms on his trousers. “Don’t feel bad about it, Floyd. It happens to the best of us. And there’s never any harm in asking questions.”

Custine gathered his tools, hat and coat and together they walked down two flights of stairs and knocked on Blanchard’s door. Floyd delivered a sanitised version of events: yes, it seemed likely to him that Susan White had been murdered; it even seemed likely to him that she had been something other than an innocent American tourist.

“A spy?” Blanchard asked.

“Too soon to say,” Floyd answered. “There are still leads we need to look into. But you’ll hear from us as soon as we have something concrete.”

“I spoke to one of the other tenants. It seems you have been asking questions about a little girl.”

“Just ruling out any possible witnesses,” Floyd said.

“What could a little girl possibly have to do with this?”

“Probably nothing at all,” Custine interjected, before Floyd was tempted to expound his unlikely theories to Blanchard.

“Very well,” Blanchard said, eyeing the two of them. “I must emphasize how important it is to me that you find Susan’s killer. I feel that she will not sleep soundly until the matter is resolved.”

He said it as if he meant Susan White, but he was looking at the photograph of his dead wife.

They drove back through thick Thursday-afternoon traffic, taking avenue de Choisy north to place d’Italie and then cutting through a darkening rat’s maze of side streets until they were on boulevard Raspail. Floyd turned the radio dial, searching for jazz, but all he got was traditional French accordion music. It was the new thing now. Traditional was in; jazz out. Chatelier himself had called jazz morally corrupting, as if the music itself was a kind of narcotic that had to be wiped from the streets.

Accordion music always made Floyd feel seasick. He turned off the wireless.

“There’s something I need to ask,” Custine said.

“Say it.”

“There’s a possibility we haven’t really discussed. It concerns the old man.”

“Go on.”

“Do you think it’s possible he killed her?”

Floyd thought about it for a moment, then shook his head. “Makes no sense, André. If the police weren’t interested, why would he risk re-opening that can of worms?”

“Human nature being what it is, anything’s possible. What if he has a secret need to be discovered? Once the police abandoned their inquiry, he’d have had no choice but to call in private detectives.”

“All the evidence we’ve seen so far points away from Blanchard.”

“But we know he had access to her rooms. He’s the one person who has keys for every room. What if she did have a lover, and Blanchard found out about it?”

“Explain the wireless, or the smashed typewriter, or the box of papers.”

“Perhaps he’s playing some kind of double-bluff game with us, strewing our path with misleading clues while hoping we have the sense to see through them and—”

“Is this the way they teach you to think at the Quai?”

“I’m just saying that we shouldn’t exclude the possibility. He seems like a nice enough old gentleman, but the worst ones generally do.”

“I think you’ve been sitting in that room for too long, André.”

“Perhaps,” Custine said. “Still, a little suspicion never goes amiss in this line of work.”

Floyd turned the car on to boulevard Saint-Germain. “I agree that we can’t rule it out, all the other evidence notwithstanding. I’ll even admit that the thought had crossed my mind.”

“Well, then.”

“But I still don’t believe he killed her. That said, if you feel you need to explore the possibility… well, I’m sure you can nose around the problem without being too tactless. Ask him again about the police not taking up the case. Ask him if he knew of anyone who might have been jealous of the time he spent with the girl.”

“I’ll be the very model of discretion,” Custine said.

“You’d better be. If he loses his temper and throws us off the case, we’re going to have to start looking for new premises in a less salubrious part of town.”

“I didn’t think there was a less salubrious part of town.”

“My point exactly,” Floyd replied.

He parked the Mathis. Nothing new in his pigeonhole; no bills or mysterious letters from long-lost girlfriends. That, he supposed, had to count as a kind of good luck.

But the elevator had broken down again, jammed somewhere up on the fourth floor. The engineer from the elevator company was sitting on the lowest flight of stairs, smoking a cigarette and studying the racing pages. He was a small, shrewlike man with pomaded hair who always smelled of carbolic soap. He nodded at Floyd and Custine as they tramped past.

“Busy, Maurice?” Floyd asked.

“Waiting for a new part from head office, Monsieur Floyd.” He shrugged expressively. “With the traffic the way it is today, could be hours before they get here.”

“Don’t break a sweat,” Floyd said.

Maurice saluted them and went back to his newspaper.

Entering their office, Custine put away his tools, washed his face and hands and changed his shirt and then set about making tea. Floyd sat at his desk, pulled the telephone across and called the Paris operator to request an international call to Berlin. He gave her the number of Kaspar Metals, reading from the letter in the tin, and waited for the connection to be made.

After a while, the operator’s voice came back on again. “I’m sorry, monsieur. That number must be wrong.”

Floyd gave her the number again, but there had been no mistake. “You mean no one picks up the telephone?”

“No,” she said. “The line is totally dead.”

Floyd thanked her and returned the receiver to its cradle. One more dead lead, then. He drummed his fingers and then dialled Marguerite’s number in Montparnasse.

“Floyd,” Greta said, answering.

“How are things?”

“She’s resting.”

“Can I see you this evening?”

“I suppose so.”

“Easy on the enthusiasm, kid.”

She sighed. “I’m sorry, Floyd. It’s just that I may not be in the best of moods.”

“Then you could use some cheering up.”

“And you’re the man for the job, I take it?”

“Custine and I have been working hard on the case. I think we all need a treat tonight. How about I take the three of us out to dinner, and we finish off the evening in Le Perroquet Pourpre?

“I suppose I can make it,” she said, not sounding at all sure of herself. “Sophie’s in tonight, studying, so I could ask her to look after Marguerite—”

“That’s the spirit. I’ll drive over in an hour. Spruce yourself up—we’re hitting the bright lights tonight.”

“I’ll do my best,” she said.

Custine and Floyd drank tea and discussed the case, making sure they’d shared all the essential observations, comparing notes on their interviews with the tenants. While they talked, a scratchy old Bluebird pressing of Sidney Bechet playing “Blues in Thirds” spun on Floyd’s phonograph.