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.