When Poirot touched it, the tile fell clean out, and something else fell with it: a key with a number on it: 238. “Sacre tonnerre,” Poirot whispered. “So the thorough search was not so thorough after all.”

Poirot replaced the key where he had found it, then set about inspecting the rest of the room, inch by inch. He discovered nothing else of interest, so he proceeded to Room 317 and then to Room 121, which was where I found him when I returned from my errands with exciting news of my own.

Poirot being Poirot, he insisted on telling me his news first, about his finding of the key. All I can say is, in Belgium it is evidently not considered unseemly to gloat. He was quite puffed up with pride. “Do you see what this means, mon ami? The open window was not opened by Richard Negus, it was opened after his death! Having locked the door of Room 238 from the inside, the murderer needed to escape. He did so using the tree outside Mr. Negus’s window, after he had hidden the key behind a tile in the fireplace that had come loose. He perhaps loosened it himself.”

“Why not conceal it in his clothing, take it with him and leave the room in the customary way?” I asked.

“That is a question I have been asking myself—one that, for now, I am unable to answer,” Poirot said. “I have satisfied myself that there is no hidden key in this room, 121. Nor is there a key anywhere in Room 317. The killer must have taken two keys with him when he left the Bloxham Hotel, so why not the third? Why is the treatment of Richard Negus different?”

“I haven’t the faintest idea,” I said. “Listen, I’ve been talking to John Goode, the clerk—”

“The most dependable clerk,” Poirot amended with a twinkle in his eye.

“Yes, well . . . dependable or not, he’s certainly come up trumps for us on the information front. You were right: the three victims are connected. I’ve seen their addresses. Harriet Sippel and Ida Gransbury both lived in a place called Great Holling, in the Culver Valley.”

“Bon. And Richard Negus?”

“No, he lives in Devon—place called Beaworthy. But he’s connected too. He booked all three hotel rooms—Ida’s, Harriet’s and his own—and he paid for them ahead of time.”

“Did he indeed? This I find very interesting . . .” Poirot murmured, stroking his mustache.

“Bit puzzling, if you ask me,” I said. “The main puzzle being: why, if they were coming from the same village on the same day, did Harriet Sippel and Ida Gransbury not travel together? Why did they not arrive together? I went over it several times with John Goode and he is adamant: Harriet arrived two hours before Ida on Wednesday—two full hours.”

“And Richard Negus?”