How It All Goes Down
Part I: The Facts
The great Belgian detective Hercule Poirot has just finished a case in Syria and is en route to London. On a train called the Taurus, he finds himself riding with an odd pair: Mary Debenham and Colonel Arbuthnot, both British. They seem not to know each other, but they kind of act like they do. Then Poirot catches them whispering on the train platform and acting suspicious. Miss Debenham gets especially antsy when it looks like the train will be delayed. Weird.
When the train arrives in Stamboul (modern-day Istanbul), Poirot leaves Miss Debenham and the Colonel, who are traveling on the connecting train, the Simplon Orient Express. Poirot has decided to play tourist in Stamboul. When he arrives at the hotel, though, he learns from a telegram that he actually has to get to London as soon as he can. He books passage on the connecting train, the Orient Express, for that evening. It looks like we'll be seeing more of Miss Debenham and the Colonel.
In the hotel dining room, Poirot runs into Monsieur Bouc (sidekick alert), who is an old friend and also a big shot at the train company. While the two men are dining together at the hotel before catching their train, they see a man named Ratchett, who's with his secretary, a young man named MacQueen. They are both American. Poirot immediately senses something is up with Ratchett. He gets an eerie feeling that the man is pure "evil" (1.2.56).
Everyone boards the train, which is weirdly full for the time of year. Poirot gets punted into a second-class car with MacQueen, with the promise that he'll be promoted to first class when they stop in Belgrade.
In the dining car, M. Bouc and Poirot observe all of the passengers. We've got a trio of men sitting together at a table (American, Italian, and British), a loud American lady who always talks about her daughter, a yellow-haired Swedish woman with a sheep-like face, a count and countess, an ugly old woman who is a Russian princess (and has a German maid), Mary and the Colonel, and, of course, Ratchett and MacQueen.
On his way out of the dining car, Ratchett tells Poirot that he's been receiving death threats. He asks if Poirot will take on his case. Poirot refuses, because he doesn't like Ratchett's "face" (1.3.85). Ouch.
Poirot is moved to a first class cabin, and he gets into bed. That night, a bunch of really strange things happen. First, Poirot hears Mr. Ratchett speak to the conductor in the next room over. Then he hears the American lady quarrel with the conductor down the hall. Eventually he hears something bump against his door. He pokes his head out and sees a woman in a red kimono walking down the hallway. Then he falls asleep. (Busy night.)
When Poirot wakes up, the train has stopped moving. It turns out that it's caught in a snowdrift. Everyone is complaining when Poirot gets to the dining car. Poirot chitchats a bit with the other passengers, including with Mary Debenham, who is now curiously calm. Poirot is then summoned to a compartment with M. Bouc.
Once in the compartment, M. Bouc tells Poirot that there has been a murder. Someone is dead! It's Ratchett, and he was stabbed twelve times. M. Bouc and the little Greek doctor, Dr. Constantine, think the culprit might be a woman.
Poirot goes with Dr. Constantine to inspect the body, and we get some evidence. The window is open, but the murderer did not leave the car that way. The murderer was both right-handed and left-handed. Some wounds were left later than others, after Ratchett had already died. Poirot and Dr. Constantine also find two clues: a piece of cambric with an "H" on it (from a lady's handkerchief) and a pipe cleaner (presumably belonging to a man). The evidence is just a little bit too perfect, so Poirot starts to get suspicious.
Oh, and Poirot finds something else important: there are two matches in the ashtray (of two different kinds) and a scrap of paper. Poirot uses a fancy scientific setup and burns the paper to reveal the writing. It mentions a young girl named Daisy Armstrong, who had been kidnapped and murdered in the United States. Her murderer got off free. Was Ratchett Daisy Armstrong's kidnapper? If so, was he killed for revenge?
We also learn more about the Armstrong kidnapping case. Apparently, the ordeal affected a lot of different people. The girl's parents are both dead (her mother died in childbirth, and her father shot himself). Daisy's mother was the daughter of famous tragic actress Linda Arden. Also, a maid threw herself out of a window when she was falsely accused of involvement in the plot. It's a pretty messed up story.
Part II: The Evidence
Poirot sets up a makeshift courtroom in the dining car and begins to collect the testimonies of each person on the train. In the chapters that follow, we get a rundown of the timeline and whereabouts of the Wagon Lit conductor, the American lady, the Swedish woman, the Russian Princess, the Count and Countess, Mr. Hardman, the Italian, Miss Debenham, and the German lady's maid.
No matter how much evidence Poirot accumulates, everyone on board has an airtight alibi. Their testimonies and evidence consistently point to the small, dark, womanish man theory.
After the interviews, Mrs. Hubbard finds a dagger in her sponge-bag (a kind of case for toiletry items). Now we've got the murder weapon. Poirot then searches the luggage of all the passengers and finds the Wagon Lit conductor's uniform in the Swedish woman's suitcase. He finds the scarlet kimono in his own. He considers this an act of "defiance" (2.15.28). In other words, it's on!
Part III: Poirot Sits Back and Thinks
Now we get Poirot's analysis of the events. First, he gives us a summary of all the evidence to date. There isn't a whole lot to go on. Then, he gives us a list of questions he needs to answer. Poirot, M. Bouc, and Dr. Constantine sit around and mull it over.
Finally, Poirot thinks he has it. First, though, he has to test his hypothesis. He returns to the Countess and finds out that she's really the daughter of Linda Arden and the sister of Daisy Armstrong's mother. Poirot then finds out that the handkerchief he found a piece of belongs to Princess Dragomiroff. That leads us to Mary Debenham, who, it turns out, was the governess for the Armstrong family.
The plot unravels: everyone on the train was connected to the Armstrong family. The annoying American woman, Mrs. Hubbard, is Linda Arden herself, the famous actress and mother of Daisy Armstrong's mother. At the end, Poirot proposes two possible solutions. In the first one, an outsider got on the train when it was stopped and killed Ratchett. The other, though, is the truth: the passengers were all in on it together in order to get justice for little Daisy Armstrong.
M. Bouc and Dr. Constantine choose to present the first, false solution to the police when the train starts moving again. This shows that they think Ratchett was not so much murdered as he was brought to justice.