The story involves a series of murders taking place in a wealthy neighborhood of New York. The first murder, of a Mr. Joseph Cochrane Robin who is found pierced by an arrow, is accompanied by a note signed "The Bishop" with an extract from the nursery rhyme Who Killed Cock Robin. This crime takes place at the home of an elderly physicist with a beautiful young ward and a private archery range. District Attorney Markham finds the circumstances so unusual that he asks his friend Philo Vance to advise upon the psychological aspects of the crime. Further murders connected with the family and neighbours of the physicist are accompanied with similar extracts from Mother Goose, such as the case of Johnny Sprigg, "who was shot through the middle of his wig, wig, wig." Midway through the book, an elderly woman confesses to the crimes, but this possibility is discounted by the police for physical reasons and by Philo Vance for psychological ones. The kidnapping and confinement of a little Miss Moffatt is luckily discovered by Vance and the police before the child suffocates in the closet in which she has been locked. Vance finally realizes the significance of one character's pointed reference to The Pretenders, a play written by Henrik Ibsen. Bishop Arnesson, of Oslo, was a prominent character in Ibsen's play. Vance arranges a spectacular finale in which the criminal is poisoned by a glass of liqueur which that person prepared for another suspect.