“This is an interesting combination,” Carolynsaid, inspecting her sandwich. “Corned beef, pastrami, turkey and—”

“Smoked whitefish.”

“And cole slaw and Russian dressing, all on a seeded roll. Nice. I don’t think I ever had it before. Is it named for anybody?”

“They call it the Pyotr Kropotkin,” I said. “Don’t ask me why. Normally it comes on rye bread, but I thought—”

“Much better on a roll. Where’s your sandwich, Bernie?”

“I’m just having coffee,” I said. “I’ve got a lunch date in an hour.”

“You didn’t have to bring me a sandwich, Bern. You could have just called and I’d have gone somewhere on my own. But I’m glad you came by, because I never got out of the house yesterday. It’s a funny thing, but every time I spend four or five hours at Pandora’s or the Fat Cat, I’m a complete wreck the next day.”

“I wonder why that is.”

“Well, the rooms are very smoky,” she said. “A lot of the regulars smoke, and the ventilation’s not good at all.”

“That must be it.”

“And in the course of a long evening I’ll almost always have a piece of pie or a candy bar, something sweet like that. And you know how I’m subject to sugar hangovers.”

“I know.”

“So I spent the day at home. I reread a Kinsey Millhone. The one about the high school kid who has an affair with his gym teacher’s wife, and then she gets him to kill her husband. I just gave away the ending, so I hope it’s one you already read.”

“ ‘T’ Is for Sympathy? I read it when it first came out.”

“You remember the scene where Kinsey’s shooting baskets with the girls’ gym teacher?” She rolled her eyes. “Case closed, Bern. So how’d it go yesterday? You sell any books?”

“Well, it’s a long story,” I said.

“Wow,” she said. “Its real complicated, isn’t it? Did you know the dead guy would turn out to be Luke?”

“I knew there had to be a connection,” I said. “There were too many ‘just-happeneds’ from the beginning. When a corpse just happened to be in the apartment Doll Cooper just happened to mention, I figured he wasn’t some guy who dropped in to wash his hands. Besides, he looked familiar.”

“I remember you saying that.”

“I thought I might have seen him around the neighborhood, but I’d seen him more recently than that, and not from a distance, either. He was the harlequin.”

“Huh?”

“On Joan Nugent’s easel. A bell went off when Doll talked about posing for Mrs. Nugent. I immediately thought of the harlequin, but all I could remember for certain about him was that he looked sad.”

“You’d look sad, too, with a bullet hole in your forehead.”

“The harlequin looked sad,” I said, “but beyond that I couldn’t picture what he looked like. When they’re dressed like that all you see is the costume.”

“So you went back for a second look.”

“I went back for the baseball cards,” I said, “or whatever Doll was hoping to find in Luke’s apartment.”

“And you didn’t want her along when you went in.”

“No, I figured one’s company and two’s a crowd. From Luke’s place it was easy enough to go back to the Nugents’. I was already in the building, and I knew the locks wouldn’t be a problem.”

“Except for the one in the bathroom.”

“That was still bothering me,” I admitted. “The fact that it was clearly impossible. There were two scenarios I could come up with and neither of them made any sense. One, he broke into the apartment, took off all his clothes, locked himself in the bathroom, twisted his arm into a knot to shoot himself in the middle of the forehead, and then ate the gun.”

“Couldn’t he have dropped it and fallen on it?”

“Sure, why not? Or he could have opened the window, stuck the gun on a ledge, closed the window, then slumped down in the tub and expired. The thing is, nothing about suicide makes sense, even if you manage to figure out a way he could have done it.”

“So that leaves murder.”

“And that was impossible, too, because the door’s locked from the inside. Whoever killed him had to leave the bathroom through the door.”

“What about the window?”

“Forget the window. The idea of some Human Fly slipping through that tiny bathroom window and rappelling down the side of the building—well, I’d rather believe he shot himself and then ate the gun for dessert. No, the murderer went out the door, but the door was locked.”

“The murderer was a ghost?”

“Either that or there was some way to get around the lock. The more I thought about it, the more I figured that had to be the answer. The last time I flushed the toilet for Raffles, I thought about installing one of those pet ports. You know, you put some sort of hinged flap at the bottom of the door, and that way an animal can get in and out even if the doors closed. If I had one of those, I wouldn’t have to remember to leave the bathroom door open.”

“Did the Nugents have one of those?”

“No.”

“Because I can’t believe a cat killed him, Bernie. I draw the line at that.”

“No,” I said, “although a dog or cat could have moved the gun so that a suicide would wind up looking like murder. But they don’t have any pets, and it wouldn’t matter if they did because there was no pet port in the bathroom door in the first place. But there had to be something, and then I just happened to think of the light switch.”

“Just happened.”

“What triggered it,” I said, “was flicking a switch in my own bathroom. The light didn’t go on.”

“Because it was a dummy switch?”

“No, because the bulb had burned out.”

“How many burglars did it take to change it?”

“Just one, but while I was changing it I remembered the switch at the Nugent apartment. Now it’s not unusual to have a switch that no longer turns anything on or off. A lot of people remove ceiling fixtures when they redecorate, and it’s easier to leave the switch plate than plaster over the hole in the wall. Still, I got to wondering what I’d find underneath the switch plate.”

“And what you found was a hole in the wall.”

“Right.”

“And that meant somebody could shoot Luke Santangelo, go out the door, pull it shut, unscrew the switch plate, reach in through the opening, and lock the door.”

“Barely,” I said. “If my arm had been any shorter I couldn’t have reached. And if it had been any fatter it wouldn’t have gotten through.”

“So we can look for somebody with long skinny arms. But why would anybody go through all that? I don’t get it.”

“Neither do I.”

“So that it would look like suicide? But if you were gonna fake a locked-room suicide, wouldn’t you leave the gun behind?”

“Ah, zair you have eet,” I said. “No matter how clevair ze criminal, he makes ze leetle mistake.”

“But—”

“It doesn’t make sense,” I agreed, “but so what? It’s not my problem.”

“It’s not?”

I shook my head. “I’m glad I found out about the dummy switch plate, because the impossible-crime element bothered me. I wanted to know how it was done. But I don’t have to know why it was done, or by whom.”

“Or what Luke was doing in that apartment.”

“None of that. I put a couple of pieces of jewelry in the tub with him, and I rifled some drawers in the bedroom and took some other jewelry away with me. That was to give the cops an easy answer to some of those questions. He was committing a burglary, he had a partner, the partner killed him. And no, I don’t think that’s what happened, but I don’t honestly care what happened.”

“You don’t?”

“I’ve got enough things to worry about,” I said. “Like making sure they drop the charges against me. And finding a way to keep from losing the store.”

“The store,” she said. “I forgot about that, with everything that’s been going on. Bernie, your problems are over!”

“They are?”

“You’ve got the cards, haven’t you? All you have to do is give them to Borden Stoppelgard in exchange for a long-term extension of your lease. Wasn’t that the deal he offered you?”