To supplement the suspect list, Poirot makes a list of unresolved questions. He notes that they haven’t assigned ownership of the handkerchief. The scarlet kimono is still an open question, as every female passenger has denied ownership of it. The precise time of the murder is also in question.
Poirot’s list of questions illustrates the difficulty of a case in which no witness can be believed unconditionally and each piece of physical evidence, except the half-burnt note that mentioned Daisy Armstrong, could have been faked.
M. Bouc narrows it down to Mrs. Hubbard, Mary Debenham (whose middle name is Hermione), and Hildegarde Schmidt. To this, Poirot responds, “Ah! And of those three?” Dr. Constantine notes that it is expensive and so he thinks it belongs to the American Mrs. Hubbard, as Americans “do not care what they pay.”
Dr. Constantine, like M. Bouc, reasons on the basis of stereotypes. His notion that Americans “do not care what they pay” doesn’t apply to this American, Mrs. Hubbard, as she’s made clear that her tastes are practical rather than expensive. In this case, Poirot’s response, “Ah! And of those three?” is condescending, indicating that he’s willing to let M. Bouc and Dr. Constantine explain their thinking, but that he himself thinks the owner is someone other than those three.
Then there’s the matter of the pipe-cleaner. Dr. Constantine cites Poirot saying, “two clues is too much carelessness.” He reasons that the handkerchief may be genuine, but the pipe-cleaner is a faked clue. As evidence, he points to Colonel Arbuthnot’s impassive reaction when asked about the pipe-cleaner.
Here, the three men face the difficulty of determining which clues are planted, if any, and which are genuine. Constantine is willing to accept one clue may have been left by mistake but speculates that the pipe-cleaner was planted to implicate Colonel Arbuthnot. This points to an already observed feature of the crime scene. A meticulous criminal could ensure that the crime scene offers no clues or many clues. Ratchett’s murder is the second scenario, but the effect it has to frustrate an investigation is similar.
Poirot leads them through several other questions. The scarlet kimono is unique in that none of them can even propose a solution to who wore it and why.
The scarlet kimono stands apart as a clue that seems overwhelmingly significant but doesn’t lead to any further information or speculation.
Dr. Constantine then raises the issue of multiple murderers acting independently. He cites as evidence Ratchett’s wounds, as some are deep and other are superficial, and some suggest a left-handed murderer and others a right-handed one. Poirot reveals that he had invited each witness to write their name precisely to determine whether they are right- or left-handed. Only Princess Dragomiroff didn’t participate.
Poirot reveals that the recording of name and address that seemed an act of basic policework was actually a way to find information without the suspect knowing it was important. This is another instance of Poirot trying to investigate by compelling automatic behavior.
At one point, M. Bouc “struggles in mental agony.” They try out several plausible and implausible theories, after which Poirot asks them to sit back and think, having all the facts arranged before them. He notes, “one or more of those passengers killed Ratchett. Which of them?”
The possibility of multiple murderers, acting either independently or together, makes the mystery extraordinarily complex. Some mysteries offer the reader a fair chance to solve the murder given the facts of the case; in other words, they don’t introduce extraneous or unknowable factors to explain the murder. Here, Christie seems to be inviting the reader to participate in the exercise.