The passengers gather in the restaurant car. They sit around the tables. Greta Van Ohlsson continues to weep. Poirot makes an announcement that there are two potential solutions to the crime. He says that he will present both to them. After that, M. Bouc and Dr. Constantine can decide which one is accurate.
Poirot sets out he fist possible solution:
The evidence provided by Mr. Hardman demonstrates that no one came in or left the Stamboul-Calais coach. The enemy that Ratchett described to Hardman came on the coach at Vincovci through a door that was left open by McQueen and Arbuthnot. The enemy was wearing a Wagon Lit uniform, and this person ventured into Ratchett’s compartment and killed him. The watch Ratchett was wearing was found to be stopped at 1:15 as a result of the fact that Ratchett neglected to set it back when at Tzaribrod. The crime was carried out at 12:15 a.m. The voice that was heard at 12:47 was caused by a third person who was in the compartment.
Poirot then sets out the second potential solution:
During the first day on the train, M. Bouc made a strange comment to Poirot. He said, “the company assembled was interesting because it was so varied—representing…all classes and nationalities.” Poirot recognized that this sort of assembly would be a possibility only in America, and this caused him to begin the guessing scheme.
Poirot was tipped off by McQueen’s second interview. When Poirot informed him that a note bearing the name of Armstrong had been discovered, he says “But surely—” and fails to complete the sentence. Poirot believed he had begun to say, “But surely that was burnt.” It was this that made Poirot think that McQueen was in some way involved in the crime.
The fact that Masterman insisted that Ratchett always drank a sleeping draught caused suspicion. If Ratchett thought that someone wanted to murder him, he wouldn’t have taken the drought.
The evidence presented by Hardman that no person came in or left the coach helped confirm that the murderer was within the Stamboul-Calais coach. The discussion that Poirot hears between Colonel Arbuthnot and Miss Debenham shows that they were on intimate terms and not strangers who had just met on a train. Arbuthnot addressed her as “Mary.” When an Englishman addresses a woman by her first name, this means that he must know her extremely well.
The story told by Mrs. Hubbard that she asked Greta Ohlsson to find out whether the communicating door was bolted was clearly a lie, as she was able to see it herself. The bolt is situated one foot above the door handle.
The cry heard by Poirot at 12:47 was clearly not Ratchett. This is because Ratchett was drugged and it seems that he didn’t struggle. Also, Ratchett was unable to speak French.
Poirot thinks that the scene that took place at 12:47 was meticulously planned and carried out. Ratchett was killed at around two in the morning.
The great difficulty involved in convicting any one individual in the crime and the number of people on the train that have a connection of some kind to the Armstrong family caused Poirot to reach one solution—they were all involved in the crime. The Armstrong family created a sort of “jury” of twelve people that conspired to stab the man twelve times. While Ratchett was able to escape justice in the United States, the Armstrong family was able to carry out another form of it.
Understanding that the Wagon Lit conductor must have been aware of the plot, Poirot realizes that there are thirteen people with a connection to the crime. Only one person on the train is innocent. It is Princess Andrenyi. Her husband was her substitute. Poirot lists the passengers. When he reaches Mrs. Hubbard, he reveals her real identity: Linda Arden, a famous actress and Sonia Armstrong’s mother.
Mrs. Hubbard says to Poirot: “I always fancied myself in comedy parts.” Mrs. Hubbard tells Poirot about the entire plot. It was felt that the death sentence that Cassetti had escaped needed to be carried out in order to stop him from hurting other children. Mrs. Hubbard requests for Poirot to only convict her and leave the others alone.
Poirot asks M. Bouc and Dr. Constantine for their opinions. M. Bouc says a solution could be to contact the police as soon as the train gets to the station. The Doctor says that he could have “one or two fantastic suggestions.”