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“Now that you mention it,” said Sheilan, “there’s a very close resemblance between the Problem of the Hermetically Sealed Room and the Problem of the Ironclad Alibi. No, I’m not talking about Margaret Kimball – not, for that matter, any of your trio of magician-suspects.”

“Do you mean there’s someone else? A fourth magician?”

“Precisely. A fourth magician who has played the Invisible Man much better than Dave Hooker and completely eluded your hawk-like instincts. Someone who had a better motive for murder than Margaret Kimball, Dave Hooker, and Leo Gurney all rolled into one. Someone who is apparently safe from suspicion-”

“Bailey!” breathed Doran. “The one person-”

“Bailey!” Sheilan let out a snort. “Let’s not be fantastic! He and the desk clerk alibi each other. No, the person I am referring to is safe from suspicion for a very convincing reason – he happens to be dead. That’s right, the person I’m talking about is Charles Kimball.”

“I see,” said Doran slowly.

“No, I’m afraid you don’t,” said Sheilan, “It’s a complicated business. Charles Kimball is dead, but he is still the only murderer we have to deal with. Jerry, you’ve been holding this puzzle upside down.

“Suppose I take it from the beginning and reconstruct. Didn’t it strike you as strange that Kimball should carry a gun with a silencer? If he were carrying a gun for protection against a person or persons unspecified, surely he’d want noise, wouldn’t he? He’d have nothing to hide; on the contrary, he’d want people to hear the shots and come running to help him, wherever and whenever he was attacked. No, the silencer indicated a guiltier purpose.”

“I see what you mean,” said Doran. “You mean Kimball was going to commit a murder.”

“Exactly,” said Sheilan, “and all that abracadabra with the elevator was arranged by Kimball – to give himself an alibi. But that alibi backfired and presented you with an impossible situation.

“The person Kimball was planning to murder was obviously the man he suspected of being his wife’s lover-Leo Gurney. He had no way of knowing, of course, that Dave Hooker was really the culprit, and that he was planning to kill the wrong man.”

“But if that was the case,” said Doran, “why didn’t he wait for confirmation from Bailey?”

“Two reasons. First, because it would look better for Kimball if the murder took place before he received confirmation from Bailey. That was why he instructed Bailey to avoid making contact with him before the time set for the appointment. Who would suspect that a man would hire a detective to investigate his wife’s infidelity and then murder the lover even before the investigator made his report? The second reason is more important: Bailey wasn’t hired as a detective at all; he was hired as part of the murder plan – because Kimball needed an unsuspecting, unimpeachable witness for his alibi.

“Kimball knew he would be suspected immediately if Gurney were found murdered, so he set about creating a foolproof alibi. He did it the same way he would create an illusion for his show, making full use of his talents as an acrobat and escape artist.

“The crux of your impossible situation, you see, is that you were looking at it the wrong way. It was a closed circle with no way for a murderer to get in, but the circle could be broken if the ‘victim’ got out.

“The plan was probably suggested to him when he saw that the elevator door on the eleventh floor was directly across from his room. His first step was to hire Bailey and arrange for him to be waiting in the lobby on the morning of the murder. Then he acquired a gun and waited. The telltale symptoms of nervousness which were so widely misinterpreted were just that – the nervousness of a man about to engage in the most dangerous of enterprises-committing a murder.

“When he came back to the hotel last night, he did two things. First, he picked the padlock on the trap door and left it open, arranging the lock so that it would appear as usual to any ordinary inspection. Then, before he went to bed, he set his watch ahead about fifteen minutes.

“He got up early this morning and deliberately awakened his wife so that she would testify that she’d been with him from, say, 6:30 to 7:02. He asked her to hand him the watch so that the false time would be fixed in her mind. Kimball actually left the room a good ten minutes before seven, not a few minutes after.

“He was certain she would be sufficiently curious about his hints of ‘secrets’ to follow him to the elevator door and try to get some idea of where he was going. And so she watched the indicator and saw that he went straight down to the lobby.

“Or rather, the car traveled straight down. The escape panel was already open; all Kimball had to do was climb through and stay perched on top of the car. The car reached the lobby, but it seemed to arrive empty, and Bailey, the carefully planted witness, noticed nothing.

“In the meantime, Kimball stepped from the roof of the car up to the second floor – a short enough distance-forced the outer door in the manner you indicated was possible, and got out. Then he simply turned around, pushed the button for the elevator again, and rode back up to the ninth floor to complete his plan. On the way up he erased any traces of the deception by setting his watch back and padlocking the trap door again.

“The rest was simple. He picked the lock of Gurney’s door, stepped inside, intending to put a bullet through Gurney’s head. It was still early in the morning and Kimball, expecting his victim would still be asleep, did not even consider the possibility of encountering resistance. By the time he’d get back to the elevator and ride down to meet Bailey, no more than ten minutes would have elapsed.

“Bailey would be waiting with the evidence which presumably would confirm his suspicions of Gurney. Kimball could then play the outraged husband and ask Bailey to accompany him to Gurney’s room and stage a confrontation.

“And what would they find in Gurney’s room? Gurney with a bullet in his head. To Bailey’s professional eye it would be clear that Gurney had been killed only minutes before. And Kimball would have an indisputable alibi. From 6:30 to 7:02 he had been with his wife in their room. At 7:02 he had left his wife and ridden straight down to meet Bailey, who would then supply him with the rest of his alibi. In short, it would be an illusion-exactly the kind of production by which Kimball made his living and on which he would be perfectly willing to stake his life. If the illusion succeeded, he would have gotten away with murder.

“But, unfortunately for Kimball, the magician paid more attention to the mechanics of the illusion than to the mechanics of the murder itself. What must have happened when Kimball got to Leo Gurney’s room seems clear enough. Kimball went there to kill Gurney, but because of stupidity, jitters, or just plain bad luck the attempt backfired and Kimball died instead.

“We can infer that, for some reason or other, Leo Gurney was not asleep when Kimball got to his room; if he had been, he would be dead now, not Kimball. And it certainly seems likely, judging from his record, that Gurney was a man who knew how to protect himself, that he would be able to get the gun away from his attacker before he had a chance to fire. Then again, it would be very much in character for a man like Gurney to carry some sort of weapon – a switchblade knife, say, that could cause a wound like the one which killed Kimball.

“So Kimball is disarmed, but he is still determined. He attacks with his bare hands, overcomes Gurney – a much smaller man – and begins to choke the life out of him. Gurney manages to pull out his knife, and using his right hand he hacks twice at Kimball’s left arm in an attempt to dislodge his grip. Then, in desperation, and as they are struggling, Gurney aims to kill, burying the blade in his opponent’s back. Kimball died instantly.