4.50 from Paddington

Mrs. McGillicuddy witnessed a woman being strangled on a parallel train track. When police found no body, Miss Marple deduced the killer must have thrown the victim from the train onto nearby grounds. Since Rutherford Hall sat adjacent to the train line, she concluded the body would be found on that estate and sent Lucy Eyelesbarrow there as a housekeeper to investigate.

Early in the story, the train passes rapidly while the crime occurs, suggesting the killer had a method for disposing of the body mid-journey.

The arsenic was deliberately placed in Lucy's curry to kill members of the Crackenthorpe family. Dr. Quimper, who was secretly the killer, used the poisoning to eliminate rivals for inheritance. The attempt on Lucy's life suggests she had become a threat to his plans, possibly because she was getting too close to discovering the truth.

Lucy's role as an observant housekeeper made her a danger to someone hiding crimes within the household.

Dr. Quimper murdered Alfred and Harold to increase Emma Crackenthorpe's share of the family inheritance. Since the estate capital was held in trust to be divided among Luther Crackenthorpe's surviving children, removing two beneficiaries would leave more money for Emma, whom Quimper wanted to marry for financial gain.

The inheritance structure was explained early, showing that fewer surviving children meant larger shares for those remaining.

Dr. Quimper killed his wife because she refused to grant him a divorce. He wanted to marry Emma Crackenthorpe for her inheritance, but his wife would not release him. Rather than remain trapped in an unwanted marriage, he murdered her and disposed of the body at Rutherford Hall, making it appear as though she was a missing dancer named Anna Stravinska.

The dead woman was initially identified as a French dancer, a cover that allowed Quimper to hide his crime behind a false identity.

Miss Marple staged a feigned choking incident during afternoon tea, pretending a fish bone was stuck in her throat. When Dr. Quimper rushed to help her, Mrs. McGillicuddy, who had witnessed the original train murder, immediately recognized him as the man she saw strangling the woman. This dramatic reveal confirmed Quimper as the killer seen on the train.

Miss Marple's habit of watching people carefully was established early, and she used this observation skill to set a deliberate trap.

Miss Marple recruited Lucy Eyelesbarrow to go to Rutherford Hall as a freelance housekeeper to investigate the train murder. Lucy was chosen for her intelligence and resourcefulness, allowing her to observe the Crackenthorpe family dynamics and uncover clues that a normal servant might miss.

Miss Marple's reputation for solving crimes was well-known, and she personally selected Lucy for her investigative abilities.

Lady Stoddart-West was the Martine whom Edmund Crackenthorpe planned to marry before he died in World War II. After Edmund's death, she married another man and chose not to reconnect with the Crackenthorpe family due to the painful memories. She only came forward when she heard the dead woman might be identified as Martine, wanting to set the record straight before the mistaken identity was officially recorded.

The two letters, one from Edmund stating his intention to marry Martine, and one supposedly from Martine, created the confusion that prompted her actual reveal.

Harold received tablets from Dr. Quimper back in London, which contained aconitine, a deadly poison. Quimper had sent the poisoned medication to Harold, killing him outside of Rutherford Hall and expanding his murder scheme beyond the estate. This demonstrated Quimper's willingness to kill anyone who stood in his way, regardless of location.

The pattern of family deaths had already begun with Alfred, showing someone was systematically eliminating beneficiaries.

After killing his wife, Dr. Quimper disposed of her body by throwing it from the train onto Rutherford Hall grounds, then hid it in a barn on the estate. This location kept the body hidden for years while he pursued his plan to marry into the Crackenthorpe family. The barn provided seclusion away from the main house where the body would not be immediately discovered.

The train traveled past Rutherford Hall, making it a logical place to discard a body while the killer continued on the moving train.

Dr. Quimper targeted Emma because marrying her would give him access to her share of the Rutherford Hall estate. The estate capital was locked in trust, to be divided among Luther Crackenthorpe's surviving children upon his death. By eliminating Alfred and Harold, Quimper ensured Emma would inherit more, making her a more financially attractive marriage prospect.

Emma was described as the unmarried daughter who would receive an inheritance share, making her a target for someone seeking wealth.

Emma Crackenthorpe told police about two letters: an old one from Edmund stating he intended to marry a woman named Martine, and a newer letter apparently from Martine seeking contact with the family. Since Martine had been unheard from for years, police suspected the newly found body might be Martine trying to reconnect, though the letter turned out to be a scam or red herring.

The letters created a false lead that distracted investigators from the true identity of the dead woman.

Mrs. McGillicuddy witnessed a man strangling a woman on a parallel train track. Though she only saw the killer for a moment as the trains passed, she memorized his face. Later, during Miss Marple's staged choking incident, Mrs. McGillicuddy recognized Dr. Quimper as the same man she saw on the train. This direct identification tied Quimper to the original murder and confirmed his guilt.

The brief nature of the sighting made precise identification difficult but not impossible, a detail Miss Marple exploited.