At the Greene Mansion, District Attorney John F. X. Markham investigates the shooting of heiress Julia Greene, allegedly by a burglar. Mrs. Tobias Greene, a widow, lies paralyzed in her bed, calling her daughter Ada her only comfort among her four living children, Ada, Chester, Rex and Sibella. After Chester is shot dead and Ada is shot in the arm, the district attorney asks detective Philo Vance to circumvent Sergeant Heath's investigation and solve the murders. Sibella loves the family physician, Dr. Carl Von Blon, whom Rex suspects wants the Greene fortune. Heath is anxious to arrest Carl, but Vance takes his time. Sibella openly admits to Vance that all the siblings hate each other. They have been forced by a codicil in their father's will to stay in the house until 1942 or be disinherited. Sibella accuses Ada of the murders, explaining that, as an adopted child, Ada is the only one who may leave the house at her will and still inherit. Philo then meets the German cook, Mrs. Manheim, who has been with the family for thirteen years and whose husband knew Tobias. Philo discovers a pair of muddy galoshes in the hall closet. The next day, Ada visits Philo and tells him Rex knows a secret about the murders. She says she found a floor plan of the bedrooms marked with X's across those of Chester, Ada and Rex. Philo telephones Rex, and Ada tells him to retrieve the plan from their "private mailbox," but while they are on the telephone, Rex is shot dead. When he returns to the house, Philo finds the galoshes missing. Later, he learns that the house library has been closed since Tobias' death and will be donated to the police department after fifteen years. Suspicious, Philo enters and discovers the galoshes and evidence that someone has been reading about criminology, poisons and hysterical paralysis and sleepwalking. Sibella tells Vance that Ada is trying to frame Mrs. Greene as the killer. While Philo sleeps in the library, Ada is nearly poisoned by tea that had been sent up on Mrs. Greene's orders. She is saved by Dr. Malone, who was hired by Heath when he became suspicious of Carl. Mrs. Greene is murdered by drug injection before Malone can confirm that she truly was paralyzed. Philo then discovers that the crimes fit those in a German history book in the library and learns the whole family speaks German. Remembering that Rex spoke no word of alarm over the telephone when he was killed, Philo discovers a device attached to Rex and Ada's "private mailbox." Ada had rigged her gun to fire when their secret safe was opened. Before Vance can arrest Ada, she shoots herself and nearly dies in the arms of Mrs. Manheim, her real mother. She recovers, however, and fully confesses to all the murders. Sibella and Carl then marry.