The three men think, but neither M. Bouc nor Dr. Constantine think very productively and are distracted by private, unrelated thoughts. Poirot awakens from his reverie muttering “And if so—why, if so, that would explain everything.” When his eyes opened, “they were green like a cat’s.
M. Bouc and Dr. Constantine reach a dead end almost immediately, but it’s implied that Poirot’s thoughts bring him the solution to the case. Again, Christie focuses on Poirot’s eyes in a moment of epiphany, and the comparison to a cat suggests an almost predatory insight into the identity of the culprit.
Poirot begins to explain the results of his contemplation. He targets a few suggestive details beginning with the grease spot on Countess Andrenyi’s passport. He connects this to the handkerchief monogrammed with an “H.” Ignoring the letter for a moment, the elegance and expense of the handkerchief point to two women in particular: Princess Dragomiroff and Countess Andrenyi. He notes the convenience of the grease spot near the first letter of her name, “Elena,” and reasons that the grease spot was deliberately placed.
Poirot begins to combine small details that may have been overlooked by the reader, but that combined point to a powerful conclusion. It was always too easy for the handkerchief to lead to someone like Mrs. Hubbard, whose name obviously begins with “H.”
And in fact, Poirot deduces that the grease spot was placed to obscure an “H” after the handkerchief was found. He concludes that Countess Andrenyi’s true first name is Helena. As evidence, he cites the wet label on the Countess’s luggage.
When searching the Countess’s luggage, Poirot had made small talk, ostensibly to hide the embarrassment of searching a noblewoman’s luggage. But it seems this also had the effect of hiding the revelation of the altered luggage tag and pretending that the Count and Countess were not suspects. Poirot, again, is in the business of managing suspects’ knowledge and emotion, just as he had in a different way with Ms. Debenham.
Poirot brings up a major constraint on any planned attempt to murder Ratchett: the blizzard. He reasons that the culprit planned to depict the murder as an outside job committed by someone who had boarded and left the train at the next station; the existence of the extra conductor’s uniform supports this, and Poirot says that if not for the snow, the uniform would be found in the “toilet.” But since the train was stalled, the culprit or culprits would be shown to be still on the train, complicating the plan.
Poirot had previously thought the murder to be premeditated, but here he demonstrates just how meticulously planned the murder was. It’s only the interruption of a force of nature that makes the murder a dilemma for the investigators. If not for the snow, it would seem obvious that the murder was committed by a stranger who boarded the train, and the investigation would lead away from any of the current passengers.
Continuing with his theory, Poirot brings up the threatening letters Ratchett received. He notes they sounded as if they were “lifted bodily out of an indifferently written American crime novel.” Those letters, Poirot says, were intended for the police rather than Ratchett. The only genuine letter was the half-burnt one that mentioned Daisy Armstrong.
Christie gets in a sly dig at her competitors by attributing the clunky writing of the letters to pulp American crime novels. Now Poirot realizes the reason for that is that they were intended to convince police, who already had compelling evidence in the form of the conductor’s uniform, that the murderer wasn’t a registered passenger on the train. In a heavily-constructed crime scene, the one authentic clue is one Poirot had to work to decipher.
Returning to the handkerchief, Poirot claims that it was inadvertently dropped by someone whose name began with “H.” Dr. Constantine concludes that this means that the Countess dropped the handkerchief and tried to obscure her name. Poirot disagrees, thinking that the handkerchief may have been planted to shift suspicion to someone connected to the Armstrong family, namely, Countess Andrenyi. The doctor responds that an innocent person wouldn’t hide their identity in this way, but Poirot thinks otherwise, saying, “I know human nature.”
As the thinking on the murder approaches a dizzying level of complexity, Poirot considers not just what a guilty person might do if suspected, but what an innocent person would do. As suspicion falls on her, Countess Helena Andrenyi would panic and alter her passport and luggage. But she would only do this if she were connected to the Armstrong case and likely to have been involved in the murder of someone who destroyed the family.
Poirot recalls further that Linda Arden, Sonia’s mother, was a stage name, and that her actual surname was Goldenberg. Linda also had another daughter, one much younger than Sonia. He concludes from this that Countess Elena Andrenyi is actually Helena Goldenberg, Sonia Armstrong’s younger sister. As a result, Princess Dragomiroff, who knew the Armstrong family well, must have known Helena was on the train and lied that she had married an Englishman and moved to England.
In the same way, as Poirot observed previously, that each passenger on the train provides an alibi for another, such that it’s difficult to determine the truth, when one passenger is shown to be lying it implicates others. Princess Dragomiroff’s account of Sonia Armstrong’s sister had always been vague, and now Poirot knows that’s because she was trying to deflect from that sister’s presence on the train.