Poirot approaches Count and Countess Andrenyi and tells the Countess he knows her real identity—Helena Goldenberg, sister of Mrs. Armstrong. The Count, her stogy husband, immediately denies Poirot's accusation, but Helena confesses. She tells Poirot that she tried to conceal her identity because she has the greatest motive of any of the passengers to murder Ratchett because she was intimately involved with the Armstrong family. Ratchett killed her niece, her sister, and broke her brother-in-laws heart. Helena claims she never laid a hand against Ratchett, she never left her compartment. The handkerchief found in Ratchett's compartment is not hers, despite the "H." Poirot asks the Countess about the Armstrong case, specifically the death of Suzanne, Daisy's nursery maid. Helena can't remember Suzanne's last name, knows that she was French. Suzanne committed suicide because she thought she was under suspicion in the case. Poirot asks Helena about Daisy's nurse. Helena tells Poirot she was a trained hospital nurse by the name of Stengleberg. Helena herself had a dragon, a governess and secretary to Sonia, named Miss Freebody. This governess was "English—or rather Scotch, a big red-haired woman." Besides Princess Dragomiroff, Helena does not recognize anyone on the train.
After hearing the Countess Andrenyi speak, M. Bouc is certain of her guilt. Poirot isn't so sure; he thinks the Count may be telling the truth—his wife, Countess Andrenyi, might be innocent. Princess Dragomiroff enters the car and walks straight to Poirot, "I believe, Monsieur...that you have a handkerchief of mine." Poirot triumphantly hands the Princess her handkerchief, his assumptions were right. The Princess explains that the "H" on the handkerchief is the Russian character "N." The Princess has no idea how the cloth got in the murdered man's room and insists she is telling the truth, despite the fact that she concealed Countess Andrenyi's identity. The doctor assures Poirot that the Princess could not have murdered Ratchett, "never, never, could anyone with so frail a physique inflict them." Poirot remembers a remark the Princess made during her interview. The Princess said there was more strength in her arm than in her will and then looked down at her arms. M. Bouc is astonished at the amount of lies he and Poirot have been told by the passengers. Poirot cheerfully retorts, "there are still more to discover."
Colonel Arbuthnot is summoned for a second interview. As soon as he sits down, Poirot asks him about the pipe cleaners found in Ratchett's cabin. Arbuthnot says he did not drop them in Ratchett's compartment; he never even spoke to the man. Poirot asks if he might have murdered him, but not spoken to him. Arbuthnot insists he did not. Poirot again asks the meaning of Mary's words at the Koya station, "Not now. When it's all over. When it's behind us," but Arbuthnot refuses to tell him.
In Chapters 4–6, Poirot simply tightens the noose on the Armstrong family. He knows the solution to the murder case and is now simply confirming his suspicions. Chapters 4–6 begin the final decent to denouement in Chapter 9. At this point, the reader still isn't quite sure how much Poirot knows. It is later revealed that he pretty much had the whole case put together by this point, but, to keep the reader's interest, it is important to make this secret. In doing so, Christie intermixes discovery and detection to propel the novel and gradually unravel the mystery. The "unraveling" of Chapter 4, revealing the true identity of Countess Andrenyi, isn't too surprising. The audience knows that something is suspicious about the Countess. Although the only real suspicious finding against the Count and Countess Andrenyi is a wet luggage label and a grease spot on the Countess' passport, both are quite out of character for the prim and proper Count and beautiful and poised Countess. Neither the Count nor the Countess seems the type to spill things on their luggage or eat hamburgers atop their passports. The wet label not the grease spot are not elaborated on, but things stick in the readers mind because they are out of character and, of course, because of the title of Chapter 4—"The Grease Spot on the Hungarian Passport." There is a balanced mix of detection and discovery in this chapter. Poirot discovers the identity of the Countess. With this new information, he asks her more questions about the Armstrongs and goes once again into detection mode.
Chapter 5 has a surprising discovery—the Handkerchief with the letter "H" on it is Princess Dragomiroff's. This is clearly a discovery, since the princess marches in and demands her handkerchief. It is unclear whether Poirot knows that that handkerchief is the princess's at this point, although he shoots a "glance of triumph" at the doctor and M. Bouc when she reveals the news. After this news, Poirot again goes into detective mode—he asks the Princess why she did not tell him this earlier. Poirot did not ask her if she owned the handkerchief earlier because he didn't think about the Russian initial "N." It seems Poirot knew she was involved in the crime, but did not know she owned the handkerchief. This is a new finding, a discovery, but not a surprise.
In Chapter 6, there are fewer discoveries. Poirot seems to know all of the answers to the questions he asks Colonel Arbuthnot. Poirot even tells Arbuthnot, "I think there is some information that I think you might be able to give us." Poirot knows that the conversation between Debenham and Arbuthnot was about Ratchett, but still wants to ask Arbuthnot and Debenham about it. If for no other reason, Poirot wants to show off to M. Bouc and Dr. Constantine. The more answers he gets right, the better he looks. This is not to say, of course, this is the only reason that Poirot continues the investigation: like all good detectives he must fully, thoroughly prove his case. Poirot must also be right—he must keep in detective mode until he is perfectly clear his theories are correct.