“You?” I said, somewhat perturbed. Words of protest formed in my head, but I knew they would never reach Poirot’s ears. Famous detective or not, his ideas about the case had so far been, frankly, ridiculous, but if he was offering his company, I wouldn’t turn it down. He was very sure of himself and I was not—that was what it boiled down to. I already felt bolstered by the interest he was taking.

“Oui,” he said. “Three murders have been committed that share an extremely unusual feature: the monogrammed cufflink in the mouth. Most assuredly I will go to the Bloxham Hotel.”

“Aren’t you supposed to be avoiding stimulation and resting your brain?” I asked.

“Oui. Précisément.” Poirot glared at me. “It is not restful for me to sit in this chair all day and think of you omitting to mention to anybody my meeting with Mademoiselle Jennie, a detail of the utmost importance! It is not restful for me to consider that Jennie runs around London giving her murderer every opportunity to kill her and put his fourth cufflink in her mouth.”

Poirot leaned forward in his chair. “Please tell me that this at least has struck you: that cufflinks come in pairs? You have three in the mouths of the dead at the Bloxham Hotel. Where is the fourth, if not in the pocket of the killer, waiting to go into the mouth of Mademoiselle Jennie after her murder?”

I’m afraid I laughed. “Poirot, that’s just plain silly. Yes, cufflinks normally come in pairs but really, it’s quite simple: he wanted to kill three people, so he only used three cufflinks. You can’t use the notion of some dreamed-up fourth cufflink to prove anything—certainly not to link the hotel murders to this Jennie woman.”

Poirot’s face had taken on a stubborn cast. “When you are a killer who decides to use cufflinks in this way, mon ami, you invite the thought of the pairs. It is the killer who has put before us the notion of the fourth cufflink and the fourth victim, not Hercule Poirot!”

“But . . . then how do we know he doesn’t have six victims in mind, or eight? Who is to say that the pocket of this killer doesn’t contain five more cufflinks with the monogram PIJ?”

To my amazement, Poirot nodded and said, “You make a good point.”

“No, Poirot, it’s not a good point,” I said despondently. “I conjured it up out of nowhere. You might enjoy my flights of fancy, but I can promise you my bosses at Scotland Yard won’t.”

“Your bosses, they do not like you to consider what is possible? No, of course they do not,” Poirot answered himself. “And they are the people in charge of catching this murderer. They, and you. Bon. This is why Hercule Poirot must go tomorrow to the Bloxham Hotel.”

3. At the Bloxham Hotel