I recently read Agatha Christie’s novel One, Two, Buckle My Shoe. It is the nineteenth novel to feature Hercule Poirot and was written during a very turbulent time. Published in November of 1940, it would have been written mostly during World War 2, or entirely if Christie had started it after the publication of Sad Cypress in early 1940.

It has some vivid, if not always pleasant characters, and among other things deals with the kind of revolutionary socialists who are the counterpart to the German ones who started the second world war. Her portrayals of human beings are at times almost painfully realistic and well done. I’m inclined to agree with the reviewer Maurice Richardson, who in his review in 1940 wrote:

The Queen of Crime’s scheming ingenuity has been so much praised that one is sometimes inclined to overlook the lightness of her touch. If Mrs Christie were to write about the murder of a telephone directory by a time-table the story would still be compellingly readable.

Agatha Christie’s style is so simple it might be easy to miss the subtlety of her observation of human nature in its varied forms.

All of that said, there does seem to be a pretty big plot hole in the story, which I find quite surprising because there are usually no plot holes in Agatha Christie’s work, not even small ones. (spoilers follow.)

I can’t see any way that Alistair Blunt could have arranged for a dentist appointment shortly before Mr. Amberiotis’ appointment which was right after Miss Sainsbury Seale’s appointment. And that’s assuming we were to grant the coincidence of the two men having the same dentist as Mabelle Sainsbury Seale, which seems difficult on its face since she was of a different social class than them. Oh, and also the same dentist as “Mrs. Chapman.” (Mabelle and “Mrs. Chapman” had to have the same dentist because the switching of dental records was an important plot point. [See the second update below for more.])

The coincidences are not insurmountable; coincidences do happen and when they merely shape the result rather than make it possible, it’s not disappointing.

But what I can’t for the life of me figure out is how Alistair Blunt (or “Mrs. Chapman”) ever found out about this coincidence. People—especially foreigners who are only visiting—don’t visit the dentist often enough that one would just call around to all of the dentists asking if they had an appointment for the victim. Even if this coincidence was known, how would Alistair Blunt then get an appointment for shortly before Mr. Amberiotis? Requesting it would be far too suspicious. Not to mention that setting up having been patients would take months, at least.

And there’s no way that the entire thing could be coincidence on the day of the murders, since the murders and switching of the dental records were planned ahead of time, as was the fake telegram getting the secretary out of the way.

I can’t help but wonder if there’s something I’m missing, because this is very unlike Agatha Christie.

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UPDATE: A reader brought up the timing of Amberiotis’ making an appointment with the dentist. This, I think, was in advance of the day of his murder. I’m going to quote the section in full since it’s short.

At the Savoy Hotel Mr. Amberiotis was picking his teeth with a toothpick and grinning to himself.

Everything was going very nicely.

He had had his usual luck. Fancy those few kind words of his to that idiotic hen of a woman being so richly repaid. Oh! well—cast your bread upon the waters. He had always been a kindhearted man. And generous! In the future he would be able to be even more generous. Benevolent visions floated before his eyes. Little Dimitri… And the good Constantopolus struggling with his little restaurant… What pleasant surprises for them…

The toothpick probed ungaurdedly and Mr. Amberiotis winced. Rosy visions of the future faded and gave way to apprehensions of the immediate future. He explored tenderly with his tongue. He took out his notebook. Twelve o’clock. 58, Queen Charlotte Street.

He tried to recapture his former exultant mood. But in vain. The horizon had shrunk to six bare words.

“58, Queen Charlotte Street. Twelve o’clock.”

While the text is slightly ambiguous, I think the most natural interpretation of these words would be that Mr. Amberiotis already had an appointment with the dentist, which was why upon feeling the pain, he merely looked at his notebook and there was no mention of making a telephone call.

On the other hand, this text also makes it sound like Mr. Amberiotis had just had his conversation with the real Miss Sainsbury Seale but that had to have happened at least a week before, since that was the length of time that “Miss Chapman” pretended to be Miss Sainsbury Seale.

That said, if the goal is to figure out an interpretation of these words that resolves all plot issues, this section must describe Mr. Amberiotis merely considering the anticipated fruit of having been kind to Miss Sainsbury Seale over a week ago, and then suddenly, by poking the sore place in his mouth, recollecting the appointment he made a while ago with the dentist.

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UPDATE: In checking up on something, I came across the fact that Mabelle Sainsbury Seale did, by coincidence, have the same dentist as Alistair Blunt and that’s how they met in London. Approximately three months before the murders, Mabelle was coming out of the dentist’s office as Alistair was going into it and she recognized him and said that she used to be a great friend of his wife’s. So that part was a coincidence which shaped how the murder later took place. Moreover, this coincidence was revealed less than halfway into the book. With the dentist of Miss Sainsbury Seale known three months before the murder, “Sylvia Chapman” had time to become a patient of the same dentist. So there’s no plot hole on how Sylvia and Mabelle had the same dentist in order to make the switch of the records possible.

One solution for how Mr. Amberiotis had the same dentist as Blunt and Sainsbury Seale would be what the ITV version of the story starring David Suchet did, which was to have Mabelle recommend her dentist to Mr. Amberiotis. I don’t remember this being in the novel, but neither was there anything which contradicted it.

This still does not explain how they found out about Mr. Amberiotis’ appointment in order for Alistair to get an appointment on the same day. The fake Mabelle’s appointment does not require an explanation since the dentist, himself, said that it was made the day before as an emergency appointment. But how on earth did they know for which day Mr. Amberiotis had an appointment?