“But there was only one dead body—Arlena’s. Then, could it be—a live body—someone pretending to be dead? Could it be Arlena herself, inspired by Patrick to play some kind of a joke. I shook my head—no, too risky. A live body—whose? Was there any woman who would help Redfern? Of course—his wife. But she was a white-skinned delicate creature. Ah yes, but suntan can be applied out of bottles—bottles—I had one of my jig-saw pieces. Yes, and afterwards, of course, a bath—to wash that telltale stain off before she went out to play tennis. And the scissors? Why, to cut up that duplicate cardboard hat—an unwieldy thing that must be got out of the way, and in the haste the scissors were left behind—the one thing that the pair of murderers forgot.

“But where was Arlena all the time? That again was perfectly clear. Either Rosamund Darnley or Arlena Marshall had been in the Pixy’s Cave, the scent they both used told me that. It was certainly not Rosamund Darnley. Then it was Arlena, hiding till the coast should clear.

“When Emily Brewster went off in the boat, Patrick had the beach to himself and full opportunity to commit the crime. Arlena Marshall was killed after a quarter to twelve, but the medical evidence was only concerned with the earliest possible time the crime could have been committed. That Arlena was dead at a quarter to twelve was what was told to the doctor, not what he told the police.

“Two more points had to be settled. Linda Marshall’s evidence gave Christine Redfern an alibi. Yes, but that evidence depended on Linda Marshall’s wristwatch. All that was needed was to prove that Christine had had two opportunities of tampering with the watch. I found those easily enough. She had been alone in Linda’s room that morning—and there was an indirect proof. Linda was heard to say that she was ‘afraid she was going to be late,’ but when she got down it was only twenty-five past ten by the lounge clock. The second opportunity was easy—she could alter the watch back again as soon as Linda turned her back and went down to bathe.

“Then there was the question of the ladder. Christine had always declared she had no head for heights. Another carefully prepared lie.

“I had my mosaic now—each piece beautifully fitted into its place. But, unfortunately, I had no definite proof. It was all in my mind.