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It was a heavy machine, about waist height, but it moved readily enough on its casters. There was nothing underneath it. There was no shredded paper in the white plastic bag in the bottom half. A dirt smudge on the beige metal top suggested nothing in particular. When I pushed the On button the machine gnashed its many teeth but nothing came out.

Staples and Bray had been watching me, and now Staples came over to say, “Something?”

“I’m not sure.” I frowned at him, frowned at the room, at all its lumber yard banality.

“You’re onto something.” Staples was staring at me as though I were an egg and he’d just heard cracking sounds.

I said, “Kaklov and the receptionist and the guard all went upstairs at twelve. They all came down together at one?”

“Right.”

“Kaklov came in here, and the other two stayed outside. That was at one o’clock. When was the body found?”

“Three-thirty. A phone call from outside came through for Kaklov, the receptionist buzzed, there wasn’t any answer, she knocked on the door, she and the guard talked it over, and finally the guard broke the door in.”

“Between one and three-thirty, did Kaklov have any visitors?”

“No.”

“Any other phone calls?”

“No.”

Bray had also come over, and now he said, “The preliminary medical report says he’d been dead at least a couple of hours when he was examined. Meaning probably before two.”

I said, “Or as close to one o’clock as the assassin could make it.”

“Looks that way.”

I frowned at the room. The answer was in here somewhere. I felt I could almost reach out and touch it. I said, “The assassin came in during lunch and hid in the bathroom. Kaklov came in at one o’clock, locked the door, and the assassin killed him. The guard broke the door down at three-thirty, and Kaklov was in here alone.” Looking back at Bray, I said, “What about after they found the body? Any time when there wasn’t anyone around?”

But Bray shook his head. “There’s a special police detachment a block from here,” he said. “For the UN. There were officers on the scene within five minutes, and both the receptionist and the guard swear they stayed right in that office the whole time.”

“I was afraid that was the answer.” I leaned against the paneled wall, folding my arms and looking around this damn bland enigmatic room. I said, “I find myself thinking of the Sherlock Holmes dictum: ‘When you have eliminated the impossible, whatever remains, however improbable, must be the truth.’ So what are the impossibilities here?”

Bray said, “The whole thing is impossible. This isn’t the kind of case I like.”

“No, let’s think about it.” I looked over at the desk again, where the killing had taken place. “The assassin getting in was possible. The assassin committing the crime was possible.”

“The assassin getting out again,” Bray said. “That’s impossible.”

“So we eliminate that.” Smiling as though I knew what I was doing, I said, “In approved Sherlock Holmes style, we eliminate the impossible. The assassin did not get out. So where does that leave us?”

“Up a tree,” suggested Staples.

“Up a—” Then it hit me. “Of course!”

They both stared at me. Half-whispering, Staples said, “You’ve got it?”

“Of course I’ve got it. If the assassin didn’t get out of this room, Fred, then he’s still here.

Bray said, “If you mean suicide, Kaklov did it himself, it won’t work. A man can’t strangle himself, not that way.”

“No, there was a killer,” I agreed. “But the point is, he’s still in this room. That’s what the dirt on the paper shredder is all about.”

“Dirt on the paper shredder?” Staples went over to frown at it. “Yeah, you’re right. So what?”

“Think, Fred. Think about the dirt on the bathroom floor.”

“Smudged footprints.” He transferred his bewildered frown from the paper shredder to me. “He stood on the paper shredder?”

“Certainly. Don’t you know where he is?” I pointed up. “He’s in the ceiling.”

I was right, of course. Dropped ceilings are constructed of a metal gridwork hung by wires from the beams of the original ceiling. The two-foot by four-foot fiberboard rectangles simply lie in this grid, and can be pushed up and out of the way. A space of a foot or more is left below the old ceiling, to leave room for the fluorescent light fixtures and for the fiberboard pieces to be slipped up over the grid.

The gridwork isn’t very strong, and wouldn’t normally support the weight of a man, but this was a special case. First, the killer had brought in two six-foot lengths of thin lumber and placed them diagonally across the grid, spreading the weight. Second, the killer wasn’t a man but a woman, a slender twentyish girl who couldn’t have weighed over a hundred pounds.

A hundred very nasty pounds, I might say. When Fred Staples, following my suggestion, climbed up on the paper shredder, lifted the nearest section of fiberboard and stuck his head in between the ceilings to look, she kicked him in the face. He gave a yelp and came catapulting off the shredder and into my arms, the fiberboard rectangle bouncing and careening around us, while at the same time the girl came through another ceiling section and landed feet first on Al Bray’s head.

Both cops were yelling, I was falling down from the weight of Fred Staples, and Al Bray was being beaten to the ground by the furious knees, heels, elbows, fists and forehead of the woman wrapped around his neck. She was dressed all in black — shoes, slacks, sweater — and she’d descended more like a demon than a human being.

“Stop her!” Bray yelled from the floor, and I wriggled out from under Staples just in time to snap my fingers around her near ankle as she scurried for the door.

I learned to regret that. She turned back the way a cat does when its hind leg is grabbed. The first thing she did was leave three long fingernail gashes on my right wrist, and the second thing she did was leave four long fingernail gashes on my left cheek. Then Bray arrived, and hit her very very hard with his fist on the side of her head, just above the ear. (He later explained that in all head-punching the target should be an area covered by hair, to minimize visible bruises later. Every trade has its expertise.)

The girl fell down when Bray hit her, and he immediately stepped on her long hair, so she couldn’t get up again. When she snapped her head around to bite his ankle he rested his other foot on her throat and said, “Think it over.”

She thought it over, glaring up at everybody, and while she was thinking Fred Staples put her wrists in handcuffs behind her back. They stood her up then, and frisked her in a thorough blunt irritable way that had nothing of sex in it at all.

Meantime, my wrist and face were both beginning to sting. I licked my wrist, but couldn’t do much about my face. I also went to the nearest vinyl divan and sat down, feeling a bit shaky.

The girl had suddenly become very vocal. She shouted a lot of fierce things, undoubtedly of a political nature, burning with passion and historical ignorance, but since this Nathan Halizing was being done in that k-k-k language I took to be Visarian I remained ignorant of her specific quarrel with the late Mr. Kaklov. Al Bray rapped her with a knuckle in the hair a couple of times and she subsided, but continued muttering and glaring at everybody.

Bray and a uniformed cop then took the girl away, and Fred Staples came over to me with a handkerchief extended in his right hand. “What’s that for?” I said. “I’m not crying.”

“No, you’re bleeding.”

“I’m what?” Grabbing the handkerchief, I pressed it to the stinging side of my face, and it came away with diagonal red lines on it. “That’s my blood!”