Plot summary
Nero Wolfe is approached by corporate attorney Rudolf Hansen and his clients Oliver Buff, Vernon Assa and Patrick O'Garro, the chief executives of Manhattan advertising agency Lippert Buff Assa (LBA). The group want Wolfe to save them from embarrassment and ruin following the murder of Louis Dahlmann, an up-and-coming advertising executive with the firm. Dahlmann's wallet was also stolen, and inside were the final answers for a series of cryptic poetic riddles run as part of a promotional competition for Pour Amour, a brand of perfume designed by one of LBA's clients. The first prize of the competition is $500,000, and in a meeting with the final five contestants the night before his death Dahlmann had revealed that he kept the answers in his wallet, both of which lead the police to suspect one of the contestants. The executives, however, do not want Wolfe to investigate the murder but to find out who stole the wallet before the contest deadline—midnight of the nineteenth of April, exactly one week later—in order to ensure the integrity of proceedings and restore their reputation. Despite tension between the advertising agency and Talbott Heery, owner of the company that produces Pour Amour, Wolfe agrees to their terms.
Wolfe dispatches Archie Goodwin to secure a copy of the final riddles and their answers for Wolfe's reference, and proceeds to interview each of the contestants: Gertrude Frazee, the leader of an anti-cosmetics women's group who has been using her members to find the answers for the riddles to try and embarrass the cosmetics industry; Carol Wheelock, a housewife who wants the prize money to secure a better life for her family; Harold Rollins, a condescending academic who entered the competition as part of an intellectual exercise; Susan Tescher, a magazine editor who wants to do a profile on Wolfe himself; and Philip Younger, a retiree seeking to recover a fortune he lost during the Great Depression. Although skeptical that Wolfe is only investigating the theft and not the murder, Inspector Cramer shares what the police have learned about the case so far. Other than the financial motive, none of the contestants appears to have had any serious reason or opportunity to either murder Dahlmann or steal the answers, and much to Archie's concern Wolfe's investigation appears to lose energy and focus.
As the deadline nears, the LBA executives begin to panic and lash out, resulting in a contradictory sequence where Wolfe is fired and then rehired within a span of minutes. When all seems lost, however, an anonymous source sends copies of the answers to each of the contestants, thus voiding the contest and saving LBA. Although Archie, the LBA executives and the police suspect Wolfe of doing so, he insists that he was not responsible, and begins to suspect one of the advertising executives of at least stealing the wallet, if not murdering Dahlmann. After the letters are sent, Vernon Assa approaches Wolfe and attempts to unilaterally dismiss him from the case, but Wolfe refuses. His suspicions aroused, Wolfe summons the major players to his office and claims he will reveal the identity of the thief, and in doing so provide the police with vital information to help them identify the murderer. Before he can do so, however, Vernon Assa is poisoned with cyanide surreptitiously slipped into his drink and dies on the floor of Wolfe's office. Dahlmann's wallet is found in his pocket, suggesting that he was the thief and murderer.
Infuriated at the murder of someone who was enjoying his hospitality and skeptical of Assa's guilt, Wolfe determines to identify the true culprit. He, along with Archie and Saul Panzer, travels to the offices of LBA and inspects a display of products from their clients, discovering a bottle of cyanide that he suspects was used to murder Assa; this confirms in Wolfe's mind the guilt of one of the executives. Confronting Buff, O'Garro and Hansen, Wolfe lays out the facts of the case and accuses Buff of murdering both Dahlmann and Assa. Buff is the only man who had clear means and opportunity, and Wolfe speculates that he was driven to murder Dahlmann out of jealousy and fear over Dahlmann's skills eclipsing and threatening his position. Assa discovered the wallet that Buff stole from Dahlmann to cover his tracks, and Buff murdered him to silence him. When Buff tries to throw suspicion on O'Garro, O'Garro reveals that Wolfe is correct. Buff is convicted of murder, but the remaining LBA executives challenge Wolfe's fee, arguing that as the thief and murderer Buff presumably exposed himself when he sent out the letters containing the final answers. In response, Wolfe reveals in confidence that he will be adding onto his bill the price of a used typewriter that has been disposed of in the East River, implying that he was in fact responsible for sending out the letters and saving them from humiliation after all.
