“Catchpool, I am talking not about morally wrong but about factually impossible. Is this how you force me to explain before I am ready, by exasperating me? Bien, I will draw one detail to your attention in the hope that it will lead you to others. According to Jennie Hobbs, how did the keys to rooms 121 and 317 of the Bloxham Hotel end up in Nancy Ducane’s blue coat?”

“Samuel Kidd planted them there. To frame Nancy.”

“He slipped them into her pocket on the street?”

“It’s easy enough to do, I imagine.”

“Yes, but how did Mr. Kidd get hold of the two keys? Jennie was supposed to find both, along with Richard Negus’s key, in Room 238 when she went there to kill Richard Negus. She was supposed to pass all three keys to Samuel Kidd after she had left and locked Room 238. Yet according to her, she did not go to Richard Negus’s room or to the Bloxham Hotel at all on the night of the murders. Mr. Negus locked his door from the inside and killed himself, having hidden his key behind a loose tile in the fireplace. So how did Samuel Kidd get his hands on the other two keys?”

I waited a few moments in case the answer came to me. It didn’t. “I don’t know.”

“Perhaps when Jennie Hobbs did not arrive, Samuel Kidd and Richard Negus improvised: the former killed the latter, then took Harriet Sippel’s and Ida Gransbury’s keys from Mr. Negus’s hotel room. In which case, why not also take Mr. Negus’s key? Why hide it behind the loose tile in the fireplace? The only reasonable explanation is that Richard Negus wanted his suicide to look like murder. Mon ami, this could have been achieved just as easily by having Samuel Kidd remove the key from the room. There would have been then no need for the open window to give the impression of the murderer escaping from the room in that way.”

I saw the strength of his argument. “Since Richard Negus locked his door from the inside, how did Samuel Kidd get into room 238 in order to remove the keys to rooms 121 and 317?”

“Précisément.”

“What if he climbed in through the open window, having first climbed a tree?”