The passengers crowd into the restaurant car and sit around the tables. Greta Van Ohlsson is still weeping. Poirot announces that there are two possible solutions to the crime, he will present both and then Dr. Constantine and M. Bouc will decide which one is correct.
Poirot reveals the first solution:
Mr. Hardman's evidence shows that no one passed in or out of the Stamboul- Calais coach. The enemy described to Hardman by Ratchett joined the coach at Vincovci through the door left open by Arbuthnot and McQueen. Wearing a Wagon Lit Uniform, the enemy went into Ratchett's compartment and murdered him. Ratchett's watch was found stopped at 1:15 because Ratchett forgot to set it back at Tzaribrod. The murder was committed at 12:15 a.m. The voice heard at 12:47 was a third person in the compartment.
Poirot expounds the second possible solution:
The first day on the train, M. Bouc said something curious to Poirot; "the company assembled was interesting because it was so varied—representing...all classes and nationalities. Poirot realized that only such an assembly would be possible in America, which led him to the guessing scheme.
McQueen's second interview tipped off Poirot. When Poirot told him that a note with the name Armstrong had been found he starts, "But surely—" and did not complete his sentence. Poirot felt he had started to say, "But surely that was burnt." This convinced Poirot that McQueen was somehow involved with the murder.