“As you are now at liberty,” Mr. Reece pronounced, “perhaps you will be good enough to come down to the library, where we will not be disturbed. I shall be glad to learn what steps you propose to take.”

Hazelmere, to Alleyn’s satisfaction, produced his own line of imperturbability and said blandly that the library would no doubt be very convenient. Mr. Reece, then pointedly addressing himself to Alleyn, said that luncheon had been postponed until two o’clock and would be in the nature of a cold buffet to which the guests would help themselves when so inclined. It was now one-twenty.

“In the meantime,” Mr. Reece magnificently continued, “I will take it as a favor if you will extend my already deep obligation to you by joining us in the library.”

Alleyn thought there would be nothing Hazelmere would enjoy less than having him, Alleyn, on the sideline, a silent observer of his investigatory techniques.

He said that he had promised to look in on Troy. He added (truthfully) that she suffered from occasional attacks of migraine and (less truthfully) that one had threatened this morning. Mr. Reece expressed wooden regrets and hoped to see him as soon as it was convenient. Alleyn felt as if they were both repeating memorized bits of dialogue from some dreary play.

Mr. Reece said: “Shall we?” to Hazelmere and led the way out of the studio. Hazelmere turned in the doorway, and Alleyn rapidly indicated that he was returning to the bedroom. The Inspector stuck up his vast thumb and followed Mr. Reece to the stairs.

Alleyn shut the door and Dr. Carmichael, who had continued his now familiar role of self-obliteration, rose up and asked if Hazelmere really meant to carry out the Plan.

“Yes, he does, and I hope to God he’ll do himself no harm by it.”

“Not for the want of warning.”

“No. But it was I who concocted it.”

“What’s the first step?”

“We’ve got to fix Maria asking for, or being given unasked, permission to lay out the body. Hazelmere had better set it up that she’ll be told when she may do it.”

“Suppose she’s gone off the idea?”

“That’s a sickening prospect, isn’t it? But we’re hoping the opportunity it offers will do the trick. I’m going along now to get those two chaps onto it.”

Dr. Carmichael said, “Alleyn, if you can spare a moment, would you be very kind and go over the business about the keys? I know it, but I’d like to be reminded.”

“All right. There are at least four keys to the bedroom. Maria had one, which I took possession of, the Sommita another, and young Bartholomew the third. Mrs. Bacon had the fourth. When Reece and the Sommita went upstairs after the concert they found Maria waiting. If the door had been locked she had let herself in with her own key. The Sommita threw a violent temperament, gave them what for, kicked them out, and locked the door after them. They have both said individually that they distinctly heard the key turn in the lock. Maria returned later with a hot drink, let herself in with her own key, and found her mistress murdered. There was no sight anywhere on any surface or on the floor or on the body, of the Sommita’s key. I found it subsequently in her evening bag neatly disposed and wrapped at the bottom of a drawer. Reece is sure she didn’t have the bag when they took her upstairs. The people who fussed round her in her dressing room say she hadn’t got it with her and indeed in that rig it would have been an incongruous object for her to carry — even offstage. Equally it’s impossible to imagine her at the height of one of her towering rages, getting the key from wherever it was, putting it in the lock in the fraction of time between Reece or Maria, closing the door behind them and them both hearing the turn of the lock. And then meticulously getting out her evening bag, putting her key in it, and placing it in the drawer. It even was enclosed in one of those soft cloth bags women use to prevent gold mesh from catching in the fabric of things like stockings. That’s the story of the keys.”

“Yes. That’s right. That’s what I thought,” said Dr. Carmichael uneasily.

“What’s the matter?”

“It’s just — rather an unpleasant thought.”

“About the third key?”

“Yes!”

“Rupert Bartholomew had it. Maria came to his room, very late in the night, and said I’d sent her for it.”

“Did she, by God!”

“He gave it to her. Bert, asleep in the chairs across the doorway, woke up to find Maria trying to stretch across him and put the key in the lock.”

“She must have been dotty. What did she think she’d do? Open the door and swarm over his sleeping body?”

“Open the door, yes. It opens inwards. And chuck the key into the room. She was hell-bent on our finding it there. Close the door, which would remain unlocked: she couldn’t do anything about that. And when, as is probable, Bert wakes, throw a hysterical scene with all the pious drama about praying for the soul of the Sommita and laying her out.”

“Actually what did happen?”

“Bert woke up to find her generous personal equipment dangling over him. She panicked, dropped the key on him, and bolted. He collected it and gave it to me. So she is still keyless.”

“Could you ever prove all these theories?”

“If the plan works.”

“Maria, eh?” said Dr. Carmichael. “Well, of course, she does look — I mean to say—”

“We’ve got to remember,” Alleyn said, “that from the time Maria and Reece left the room and went downstairs and he joined his guests for dinner, Maria was in the staff sitting room perparing the hot drink. Mrs. Bacon and Marco and others of the staff can be called to prove it.”

Carmichael stared at him. “An alibi?” he said. “For Maria? That’s awkward.”

“In this game,” Alleyn said, “one learns to be wary of assumption.”

“I suppose I’m making one now. Very reluctantly.”

“The boy?”

“Yes.”

“Well, of course, he’s the prime suspect. One can turn on all the clichés: ‘lust turned to hatred,’ ‘humiliation,’ ‘breaking point’—the lot. He was supposedly in his room at the crucial time but could have slipped out, and he had his key to her room. He had motive and opportunity and he was in an extremely unstable condition.”

“Do the rest of them think—?”

“Some of them do. Hanley does, or behaves and drops hints as if he does. Maria, and Marco I fancy, have been telling everyone he’s the prime suspect. As I daresay the rest of the domestic staff believe, being aware, no doubt, of the changed relationship between the boy and the diva. And of course most of them witnessed the curtain speech and the fainting fit.”

“What about Lattienzo?”

‘Troy and I overheard the jocund maestro in the shrubbery or near it, and in far from merry pin, threatening an unseen person with an evidently damaging exposure if he or she continued to spread malicious gossip. He spoke in Italian and the chopper was approaching so I missed whole chunks of his discourse.”

“Who was he talking to?”

“Somebody perfectly inaudible.”

“Maria?”

“I think so. When we emerged she was handy. On the front steps watching the chopper. Lattienzo was not far off.”

“I thought Lattienzo was not in his usual ebullient form when he came up here just now.”

“You were right,” said Alleyn and gave an account of the interview.

“The Italian element with a vengeance,” said the doctor thoughtfully.

“I must go along and fix things up in that room and then hie me to the library and Mr. Reece’s displeasure. Look in on Troy, like a good chap, would you, and tell her this studio’s free? Do you mind? She’s in our bedroom.”

“I’m delighted,” said the gallant doctor.

And so Alleyn returned to the Sommita’s death chamber and found Sergeants Franks and Barker in dubious consultation. A brace and a selection of bits was laid out on a sheet of newspaper on the floor.

“The boss said you’d put us wise, sir,” said Franks.