Alone again, M. Bouc expresses certainty to Poirot that the Countess is guilty, but Poirot reminds him that there was another option for the owner of the handkerchief. Indeed, Princess Dragomiroff enters the dining-car to claim ownership of it.
With each twist of the case, M. Bouc has seized on the new evidence to claim that the solution to the case is beyond doubt. But Poirot has discovered as much as he has by being patient and suspending conclusions. He’s proved correct, again, when the Princess claims the handkerchief.
M. Bouc is shocked, objecting that her first name is Natalia, to which the Princess responds that the letter “N” appears as an “H” in the Russian alphabet. Poirot notes that the Princess didn’t say that the handkerchief was hers, but the Princess only says, “You did not ask me.” She has no idea how her handkerchief ended up in Ratchett’s room, but Poirot suspects that she’s lying.
The case turns on an international misunderstanding, one Poirot no doubt had grasped earlier. To anyone unversed in the differences between the Roman and Cyrillic alphabets, the Princess would not have been considered an owner of the handkerchief, despite its finery and her wealth.
Princess Dragomiroff admits that she lied to protect the Countess, who she knew was Sonia Armstrong’s sister. Poirot tries to admonish her by appealing to her sense of justice, but she replies, “In this case I consider that justice—strict justice—has been done.”
The Princess draws a distinction between superficial and “strict” justice, which she believes herself to be on the correct side of. Her notion of justice is that the wicked are punished, as Ratchett has been, and the innocent and suffering are protected, as she attempted with Helena. In a case concerned with the legitimacy of vigilante justice, the Princess seems to support it.
The Princess departs, and Poirot confers with the doctor to determine whether it’s physically possible that she inflicted the wounds on Ratchett. Dr. Constantine concedes that it’s possible the “feebler ones” were inflicted by the Princess. Frustrated, M. Bouc laments the lies that the passengers have told them, but Poirot is unfazed by them. The detective notes that "If you confront anyone who has lied with the truth, he will usually admit it—often out of sheer surprise.”
The Princess has told the most brazen lies to the investigators, but Poirot, even as he criticizes the suspects for their dishonesty, finds in them an investigative tool. Indeed, Poirot’s approach has been to guess at the truth and surprise his suspects with it, on the off-chance that they will instinctively confirm it.