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oirot is visited by a distraught girl, Norma Restarick, who fears she may have killed someone but runs away, telling him that he's too old rather than explaining further. By coincidence, Poirot's friend Ariadne Oliver lives in the same apartment block as Norma and her two roommates and recently went to their party, where Norma was distressed when she was offered ice cream. Norma's ex-nanny, Miss Lavinia Seagram, an alcoholic, also lived in the block but was recently found dead, with the verdict being suicide. Ariadne is unconvinced and searches the nanny's apartment, finding a clue which she puts in her handbag. Soon afterward she is attacked and the bag and its contents are stolen. Poirot visits the Restarick family home in the country, owned by Norma's great-uncle, Sir Roderick, an elderly and half-blind man who is dependent upon Sonia, his young personal assistant (who may well be a gold-digger). Andrew Restarick, Norma's father, explains to Poirot that he spent much of Norma's childhood working abroad, leaving her with her unstable mother and Nanny Seagram. Norma admits to Poirot that she blames herself for her mother's suicide, which took place when the little girl was on an outing with the nanny and wanted to stop for an ice cream. She now believes that if she had got home earlier she would have saved her mother, hence her revulsion at being offered ice cream. Poirot and Ariadne visit Miss Battersby, Norma's former school teacher, where they discover something very suspicious about Norma's friends and family. Also convinced that Miss Seagram's death was not suicide, Poirot enlists Norma's help in setting a trap to catch whoever killed her old nanny and is now trying to frame her.

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