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Ellery grinned a little. “I have been working on presumptions and more or less feeble deductions, as you can see; yet if you put together all the scattered, flimsy facts which I have outlined in the past ten minutes, I think you will see that common sense simply cries out that the blade was used for shaving, that it was broken, and that it was taken away. We find no evidence that the blade might have been used for anything but its legitimate purpose; and this only strengthens the contention. Let me leave this line of thought temporarily and go to another, altogether different, and in its way one of the most significant in the entire investigation.”

There was a surreptitious rustling of bodies in hard chairs, a quick intake of breath. The eyes on Ellery did not waver.

“It may come to you,” he said in a quiet, merciless voice, “that more than one person could have been implicated in this affair; that, perhaps, if Miss Carmody did not put away her shoes and hat — disregarding the damning evidence of the cigarets — she still might have been present; for another — a man — could have disposed of the shoes and hat while she stood by or did something else. I shall disprove that with the most gratifying expedition.”

He put his palms flat on the desk, leaned slightly forward. “Who, ladies and gentlemen, had rightful access to this apartment? Answer: The five possessors of the keys. That is — Mr. French, Mrs. French, Miss Carmody, Miss Marion French, and Mr. Weaver. The master key in O’Flaherty’s desk was closely guarded, and no one could have got it without either his knowledge or the knowledge of the day man, O’Shane. And no such knowledge exists, which makes it plain that the master key in no way enters our calculations.

“Of the six keys in esse, as it were, we are now able to account for five. Mrs. French’s is missing. All the others are absolutely accounted for as having been exclusively in the possession of their owners. Mrs. French’s key has been sought for by the combined cunning of the detective force. It is still missing. In other words, it is not on these premises, despite the fact that O’Flaherty positively avers that Mrs. French had it in her possession when she entered the store Monday night.

“I told you at the beginning of this impromptu demonstration that the murderer probably took that key. Now I tell you not only that he took it, but that he had to take it.

“We have one confirmation in fact that the criminal wanted a key. On Monday afternoon, some time after Miss Carmody left the French house furtively, Miss Underhill, the housekeeper, received a telephone call. The caller claimed to be Miss Carmody. The caller asked Miss Underhill to have Miss Carmody’s key to the apartment ready, that a messenger would be sent for it at once. Yet only the very same morning, Miss Carmody had told Miss Underhill that she had lost her key, she thought, and asked Miss Underhill to secure one of the other keys and make a duplicate for her!

“Miss Underhill doubts that the caller was Miss Carmody. She is ready to swear that someone stood by the telephone at the other end and prompted the caller’s reply when Miss Underhill reminded the caller about the lost key and the morning instructions. The caller then hung up in some confusion...

“What is the inference? Surely that the caller was not Miss Carmody, but a hireling or accomplice of the murderer, who prompted the call in order to secure a key to the apartment!”

Ellery drew a long breath. “I leave you for the moment to your own cogitations on the interesting inflections this incident raises... Now let me conduct you through a logical maze to another conclusion — the one with which I began this branch of my thesis.

“Why did the murderer want a key? Obviously, to secure a means of access to the apartment. He could not get in except through the agency of a second person who possessed a key, if he had not one himself. Presumably he expected to be admitted to the apartment by Mrs. French, but in the careful planning of the crime the possession of a key for himself might conceivably be important, and this explains the call and the projected ‘messenger.’ But to the case in point!

“The criminal killed Mrs. French in the apartment. Now that he had a corpse and knew that he must take it down into the window-room, for the various reasons I have given, he pulled up with a sudden thought. He knew that the door to the apartment had a spring lock that snapped shut. He had no key, having failed in his effort to get hold of Bernice Carmody’s. He must carry the body out of the apartment. Yet he had much to do in the apartment afterward — clean up the evidences of blood, ‘plant’ the shoes and hat, the banque game and cigarets. As a matter of fact, even if he cleaned up the room and ‘planted’ the false evidence before he took the body down, he still needed means of reentry into the apartment. He had to pussyfoot through the store for the felt, the glue, and other paraphernalia needed to fix the book-ends. How was he to get back into the apartment? He also meant to sleep in the apartment, apparently — again, how was he to get back? You see, whether he took the body downstairs before or after he cleaned up, he still needed a means of reentry to the apartment...

“His first thought must have been to insert something between the door and the floor to keep the springed door from clicking shut. But what about the watchmen? He must have thought: ‘The watchmen make rounds through this corridor by the hour. They will be sure to notice a partly open door and investigate.’ No, the door had to be closed. But... a thought! Mrs. French had a key, her own key — the one by which she herself entered the apartment. He would use that. We can picture him opening her bag while she lay, bleeding and dead, across the desk, finding the key, putting it into his own pocket, picking up the corpse and leaving the apartment, now certain of a means of reentering it when he was through with his grisly task.

“But” — and Ellery smiled grimly — “he had to bring the key back upstairs with him, obviously, to get into the apartment again. Therefore we didn’t find it on the body. True, he might have gone upstairs, done his cleaning up, and then taken the key downstairs again. But — of course that’s inane — how would be get back again? Besides, the danger he would encounter — taking still another chance of being detected on the main floor getting into the window... It was dangerous enough the first time, but that was inescapable. No, he probably figured that the best thing he could do would be to pocket the key and dispose of it when he left the building in the morning. True, he might have left it in the apartment, on the card-table for example. But the fact that it isn’t in the apartment shows that he took it away with him — he had two alternatives and chose one of them.

“We find then—” Ellery paused for the merest instant — “that our criminal committed the murder without accomplices.

“I see doubt on some faces. But surely it is quite clear. If he had an accomplice, he wouldn’t have been forced to take the key at all!.. He would have carried the body downstairs, and his accomplice would have remained in the apartment to open the door for him when he was finished downstairs. Don’t you see? The very fact that he had to take the key shows that it was a one-man job. I might be confronted with the objection: ‘Well, it could have been two people at that, because both might have carried the body downstairs.’ To that I reply with certainty, ‘No!’ because it would have involved a double risk — two people would have been easier to detect by a watchman than one. This crime is well thought out — the author of it would never have taken this unnecessary chance of discovery.”