Stephen comforts Pilar after she learns that she was left out of the will. They find Christmas decorations and play with balloons in the hall. When they release them outside, one pops. Pilar suddenly recalls picking up a pink balloon fragment in her grandfather’s room the night of the murder. Poirot overhears this and looks grave. He remarks, “It is indeed regrettable that the English are so fond of open windows” (231).

Tressilian tells Poirot that one of the two large stone cannonballs flanking the front door is missing. The old butler frets that his senses have become untrustworthy since Harry’s return. Pilar emerges from Alfred’s study, her pride apparently hurt that the family is giving her money. Poirot warns her to be on guard, predicting that she “will never be in greater danger than [she is] today” (235). Sugden arrives with a telegram from South Africa that states, “Ebenezer Farr’s only son died two years ago” (236).

Pilar tells the family that she refuses their money and that she intends to leave the house immediately. After she runs from the room, a crash is heard upstairs. Poirot and Sugden find Pilar in her room, where a booby trap—the missing cannonball balanced on her door—has just missed her. Poirot confronts Pilar about her alibi, revealing she was hiding in the recess near Simeon’s room with the two statues. Pilar admits that she lied and says that she saw a woman standing at her grandfather’s door shortly before he was killed. However, she is unable to identify the figure at the door.

Poirot gathers the family. Sugden confronts Stephen with the telegram, and he admits that his real name is Stephen Grant. He knew Ebenezer and his late son, so he recognized the address of Gorston Hall on Pilar’s suitcase. He says that he pretended to be Farr’s son to get close to Pilar, whom he met on the train and instantly fell for. Pilar then confesses that she is not Pilar Estravados; the real Pilar was killed in Spain, and she assumed her identity. She deliberately threw Pilar’s passport into the garden so that she could smudge the photograph with dirt and make it harder to tell that it doesn’t belong to her. Sugden accuses her of stealing the diamonds and murdering Simeon.

Poirot refutes Sugden’s accusation against Pilar, stating that the murder was committed by a family member. He lays out possible motives and opportunities for the family members, even constructing scenarios in which Lydia could have committed the murder or in which Alfred and Harry conspired together. He concludes by repeating that the solution lies in “the character of Simeon Lee himself” (250).

Poirot notes the seemingly nonsensical clues, such as the piece of rubber and the wooden peg. He emphasizes the importance of blood and family resemblances. Poirot points out that Tressilian’s confusion upon meeting Stephen was because Stephen and Harry are strikingly similar, both resembling a young Simeon. At this, Sugden realizes he made the same mistake. Poirot reveals that Stephen is Simeon’s illegitimate son, and Stephen admits that he came to England “for one reason only—to see the man who was [his] father” (256). Sugden accuses Pilar of lying to protect Stephen, claiming he was the person at the door. Before Pilar can answer, Hilda confesses that she was the woman Pilar saw.

Hilda explains that she went to confront Simeon about the emotional harm that he caused David, found his door locked, and then heard furniture crashing and a horrible scream. She insists that no one came out of the room.

Poirot reveals that the killer was another of Simeon’s illegitimate sons: Superintendent Sugden. Sugden killed his father during his first visit to Gorston Hall on the evening of December 24 and staged the scene. He used animal blood mixed with sodium citrate to make the crime scene look fresh when it was later discovered. What Hilda heard was Sugden, from outside the house, pulling a cord that toppled the furniture and activated a toy “Dying Pig” balloon to create the scream to fake the time of death. Pilar’s discovery of the balloon fragment put her in danger, and Sugden set the booby trap on her door. Poirot explains his own final clue: He bought a false moustache and placed it on a portrait of young Simeon, revealing a perfect likeness to Sugden. Confronted with the truth, Sugden declares, “God rot his soul in hell! I’m glad I did it!” (263).

Pilar, whose real name is Conchita Lopez, plans to marry Stephen and move to South Africa. As the household prepares to disperse, she speaks with Lydia about the future. Conchita asks if, in time, she and Stephen can return to Gorston Hall for “a real English Christmas” (268). Lydia assures her that they will be welcome.

Harry says goodbye to Alfred, apologizing for his behavior and past grievances. He intends to move to Hawaii. The brothers part on amicable terms.

Alfred tells David that he and Lydia have decided to sell the house, and he offers David some of their mother’s belongings. David declines, explaining, “I feel it’s better to break with the past altogether” (269).

George and Magdalene say their goodbyes. George worries about the possibility of a scandal, even suggesting that Sugden could lie about his motive to lessen the damage. Magdalene suggests that they celebrate Christmas abroad next year.

After all their guests leave, Alfred and Lydia are alone. Lydia reveals that George was snooping in Alfred’s desk during the murder, confirming her earlier suspicions about his money problems. With the case over and the house to be sold, they discuss their plans and look ahead to rebuilding a quieter life together.

Colonel Johnson expresses his shock to Poirot that the most capable officer of his police force was the killer. The detective observes, “Even policemen have private lives!” (272).