I HOPED POIROT MIGHT warm up a few degrees once Lazzari had left us alone, but there was no change to his stern demeanor, and I realized that he was probably always like this “at work,” as it were—which seemed a bit rich since it was my work and not his, and he was doing nothing to lift my spirits.

I had a master key, and we visited the three rooms one by one. As we waited for the lift’s elaborate gold doors to open, Poirot said, “We can agree on one thing, I hope: Monsieur Lazzari’s word cannot be relied upon with regard to those working in the hotel. He speaks of them as if they are above suspicion, which they cannot be if they were here yesterday when the murders were committed. The loyalty of Monsieur Lazzari is commendable, but he is a fool if he believes that all the staff of the Bloxham Hotel are des anges.”

Something had been bothering me, so I made a clean breast of it: “I hope you don’t also think I’m a fool. What I said before about plenty of other guests also arriving on Wednesday . . . That was a harebrained thing to say. Any guests that arrived on Wednesday and didn’t get murdered on Thursday are irrelevant, aren’t they? I mean, it’s only a noteworthy coincidence that three or any number of apparently unconnected guests arrive on the same day if they also get murdered on the same evening.”

“Oui.” Poirot smiled at me with genuine warmth as we stepped into the lift. “You have restored my faith in your mental acuity, my friend. And you hit the head of the nail when you say ‘apparently unconnected.’ The three murder victims will turn out to be connected. I will swear to it now. They were not selected at random from among the hotel’s guests. The three were killed for one reason—a reason connected with the initials PIJ. It is for the same reason that they all came to the hotel on the same day.”

“It’s almost as if they received an invitation to present themselves for slaughter,” I said in a cavalier fashion. “Invitation reads: ‘Please arrive the day before, so that Thursday can be devoted entirely to your getting murdered.’ ”

It was perhaps undignified to joke about it, but joking is what I do when I feel despondent, I’m afraid. Sometimes I succeed in tricking myself into imagining that I feel all right about things. It didn’t work on this occasion.

“Devoted entirely . . .” Poirot muttered. “Yes, that is an idea, mon ami. You were not being serious, I understand. Nevertheless, you make a point that is very interesting.”

I did not think I had. It was an asinine joke and nothing more. Poirot seemed intent on congratulating me for my most absurd notions.