"What's wrong with my proposition?" Poirot rose. "Forgive me for being personal - I do not like your face, M. Ratchett," he said. And with that he left the restaurant car."

This quotation occurs in Part One, Chapter Three when Ratchett offers Poirot a large sum of money in exchange for his protection. Poirot’s blunt refusal hints at his knack for reading people and emphasizes the strength of his morals. Although he cannot identify a specific reason to distrust Ratchett, he knows just from looking at him that he is a dangerous man. This ability will ultimately serve him as he observes the other passengers on the train to determine the killer. The fact that Ratchett’s money does not persuade Poirot also establishes him as an impartial and upstanding figure, a position which makes him an ideal candidate to solve the crime.

"See you, my dear doctor, me, I am not one to rely upon the expert procedure. It is the psychology I seek, not the fingerprint or the cigarette ash. But in this case I would welcome a little scientific assistance. This compartment is full of clues, but can I be sure that those clues are really what they seem to be?" 

In Part One, Chapter Seven, Poirot and Dr. Constantine go into Ratchett’s compartment to examine the body and find numerous clues that may hint at details of the crime. Part of what makes Poirot such a successful detective, however, is the fact that he questions everything and does not rely on the first clues he finds to solve the case. He does not immediately conclude that the killer is a woman purely because of the handkerchief on the floor of Ratchett’s compartment, nor does he immediately accept the time on the broken stopwatch as the definitive moment of the crime as Dr. Constantine suggests.

"Did I not tell you that I was, like you, a very puzzled man? But at least we can face our problem. We can arrange such facts as we have with order and method."

This quotation, which comes from Part Two, Chapter Thirteen, emphasizes Poirot’s level-headed nature and practical approach to problem solving. Unlike M. Bouc and Dr. Constantine who feel helplessly confused after hearing the passengers’ testimonies, Poirot approaches the plethora of information that lays before them in a very organized manner. This approach allows him to envision how the different pieces of evidence might fit together, even when he is in the early stages of his investigation.