“I thought you’d say that,” murmured Antony.
“Tony, do you mean to say that you knew all this?”
“I guessed some of it. I didn’t quite know all of it, of course.”
“Good Lord!” said Bill again, and returned to the letter. In a moment he was looking up again. “What did you write to him? Was that last night? After I’d gone into Stanton?”
“Yes.”
“What did you say? That you’d discovered that Mark was Robert?”
“Yes. At least I said that this morning I should probably telegraph to Mr. Cartwright of Wimpole Street, and ask him to—”
Bill burst in eagerly on the top of the sentence. “Yes, now what was all that about? You were so damn Sherlocky yesterday all of a sudden. We’d been doing the thing together all the time, and you’d been telling me everything, and then suddenly you become very mysterious and private and talk enigmatically—is that the word?—about dentists and swimming and the Plough and Horses, and—well, what was it all about? You simply vanished out of sight; I didn’t know what on earth we were talking about.”
Antony laughed and apologized.
“Sorry, Bill. I felt like that suddenly. Just for the last half-hour; just to end up with. I’ll tell you everything now. Not that there’s anything to tell, really. It seems so easy when you know it—so obvious. About Mr. Cartwright of Wimpole Street. Of course he was just to identify the body.”
“But whatever made you think of a dentist for that?”
“Who could do it better? Could you have done it? How could you? You’d never gone bathing with Mark; you’d never seen him stripped. He didn’t swim. Could his doctor do it? Not unless he’d had some particular operation, and perhaps not then. But his dentist could—at any time, always—if he had been to his dentist fairly often. Hence Mr. Cartwright of Wimpole Street.”
Bill nodded thoughtfully and went back again to the letter.
“I see. And you told Cayley that you were telegraphing to Cartwright to identify the body?”
“Yes. And then of course it was all up for him. Once we knew that Robert was Mark we knew everything.”
“How did you know?”
Antony got up from the breakfast table and began to fill his pipe.
“I’m not sure that I can say, Bill. You know those problems in Algebra where you say, ‘Let x be the answer,’ and then you work it out and find what x is. Well, that’s one way; and another way, which they never give you any marks for at school, is to guess the answer. Pretend the answer is 4—well, will that satisfy the conditions of the problem? No. Then try 6; and if 6 doesn’t either, then what about 5?—and so on. Well, the Inspector and the Coroner and all that lot had guessed their answer, and it seemed to fit, but you and I knew it didn’t really fit; there were several conditions in the problem which it didn’t fit at all. So we knew that their answer was wrong, and we had to think of another—an answer which explained all the things which were puzzling us. Well, I happened to guess the right one. Got a match?”
Bill handed him a box, and he lit his pipe.
“Yes, but that doesn’t quite do, old boy. Something must have put you on to it suddenly. By the way, I’ll have my matches back, if you don’t mind.”
Antony laughed and took them out of his pocket.
“Sorry. … Well then, let’s see if I can go through my own mind again, and tell you how I guessed it. First of all, the clothes.”
“Yes?”
“To Cayley the clothes seemed an enormously important clue. I didn’t quite see why, but I did realize that to a man in Cayley’s position the smallest clue would have an entirely disproportionate value. For some reason, then, Cayley attached this exaggerated importance to the clothes which Mark was wearing on that Tuesday morning; all the clothes, the inside ones as well as the outside ones. I didn’t know why, but I did feel certain that, in that case, the absence of the collar was unintentional. In collecting the clothes he had overlooked the collar. Why?”
“It was the one in the linen-basket?”
“Yes. It seemed probable. Why had Cayley put it there? The obvious answer was that he hadn’t. Mark had put it there. I remembered what you told me about Mark being finicky, and having lots of clothes and so on, and I felt that he was just the sort of man who would never wear the same collar twice.” He paused, and then asked, “Is that right, do you think?”
“Absolutely,” said Bill with conviction.
“Well, I guessed it was. So then I began to see an x which would fit just this part of the problem—the clothes part. I saw Mark changing his clothes; I saw him instinctively dropping the collar in the linen-basket, just as he had always dropped every collar he had ever taken off, but leaving the rest of the clothes on a chair in the ordinary way; and I saw Cayley collecting all the clothes afterwards—all the visible clothes—and not realizing that the collar wasn’t there.”
“Go on,” said Bill eagerly.
“Well, I felt pretty sure about that, and I wanted an explanation of it. Why had Mark changed down there instead of in his bedroom? The only answer was that the fact of his changing had to be kept secret. When did he change? The only possible time was between lunch (when he would be seen by the servants) and the moment of Robert’s arrival. And when did Cayley collect the clothes in a bundle? Again, the only answer was ‘Before Robert’s arrival.’ So another x was wanted—to fit those three conditions.”
“And the answer was that a murder was intended, even before Robert arrived?”
“Yes. Well now, it couldn’t be intended on the strength of that letter, unless there was very much more behind the letter than we knew. Nor was it possible a murder could be intended without any
