One, Two, Buckle My Shoe

As Hercule Poirot leaves the dentist's office, a woman arrives.  He returns to her the buckle that has fallen off her shoe.  Later he learns from Inspector Japp that his dentist has died from a single gunshot wound.  Between his appointment and the dentist's death, there were only three appointments:  Alistair Blunt, a banker; Mabelle Seale the woman who lost her shoe buckle; and a Greek secret agent named Amberiotis.

Amberiotis later dies of an anathesia overdose, thought to be the result of his dentist's visit.  Some believe that the dentist, Dr. Morley, killed himself over the guilt from the overdose he gave his patient.  But Poirot remains unconvinced.  He investigates the dentist's partner, but he lacks a motive.  Dr. Morley's secretary has been called away by a fake telegram.  The secretary's boyfriend might be motivated by the fact that Dr. Morley tried to discourage her from seeing him.  Also present at the dental surgery was Howard Raikes, a hardnosed American left wing activist, who was opposed to Blunt but who liked Blunt's niece, Jane.  Poirot talks to another patient of the day, Mr. Barnes, who suspects that Blunt was the target of the murder.

In the meantime, Mabelle Seale goes missing and her body is found in the apartment of Mrs. Chapman, who is also missing.  Poirot examines the body and notices the buckled shoes.  He dispels the theory that Mrs. Chapman killed Mabelle and fled.  Once the dental records are uncovered, it appears the body is that of Mrs. Chapman, not Mabelle.  Mr. Barnes may be right when two attempts are made on Blunt's life.  The smoking gun is found in the hands of Frank Carter who has taken a job as a gardener at Blunt's house.

Dr. Morley's maid says she saw Frank Carter on the stairs of the dentist's apartment.  He is also found with a smoking gun.  Poirot gets him to admit that not one but two people were scene entering dr. Morley's office and that when he entered. Morley was already dead.  The real Mabelle had known Blunt and his first wife, Gerda.  Blunt attended his dental appointment, shot Morley and left.  He pretended to leave the building as the fake Mabelle was showing up for her appointmentl.l  He gave the fatal overdose to Amberiotis, a new patient who had never met Morley.  As soon as Amberiotis left, Blunt moved the dead dentist's body back into the chair to make it a appear like a murder/suicide.  Frank Carter saw both Blunt and Amberiotis leave only to be shocked by the dead body of the dentist.