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Gentleman detective Philo Vance begins an investigation when he receives an anonymous letter stating that society man Lynn Llewellyn will be in danger when he appears at the casino owned by his uncle, Kinkaid.  Vance visits the Llewellyn estate, which is run by Mrs.  Priscilla Kinkaid-Llewellyn, the matriarch of the household, and stumbles into one of the family's many quarrels.  At the end of the bitter quarrel, which involves Mrs. Llewellyn's son Lynn and his wife Virginia, Virginia announces that she has decided to leave the house and go to Chicago.  During the tiff, Vance and Doris, Mrs. Llewellyn's secretary, are introduced to each other and Doris immediately takes a liking to Vance.

Vance takes Doris to his home, where he and District Attorney Markham show her the mysterious letter.  Doris immediately recognizes the return address as being that of the Llewellyn's townhouse in Closter and notices that the letter was typed on her typewriter.  Vance assigns Sergeant Heath to help stake out the casino that night, but their presence does not prevent Lynn from suddenly collapsing at the card table.  At the same time, Doris informs Vance that Virginia has died at the Llewellyn house.  Markham begins his investigation of the murder by questioning Mrs. Llewellyn, who recalls having quarreled with Virginia before she was poisoned, and Amelia, Mrs. Llewellyn's daughter, who admits that she too had a spat with Virginia.

Meanwhile, Doris finds Mrs.  Llewellyn's recently altered will, in which she disinherited Kinkaid, making it apparent that Lynn and Amelia would be the only ones who would benefit from Mrs.  Llewellyn's death.  Other clues begin to surface, including Kinkaid's unusual collection of books on chemistry and poisons, and a loaded gun found in Virginia's bedroom.

Soon after Lynn's recovery, Mrs. Llewellyn is found dead of an apparent suicide with a note, bearing her signature, in which she confesses to Virginia's murder.  Not convinced that the mystery has been solved, Vance pursues his theory that Mrs.  Llewellyn may have been poisoned by heavy water, which leads him to Kinkaid's secret laboratory, where he and Doris are being held at gunpoint by Kinkaid.  Vance and Doris escape, but Vance does not believe that Kinkaid is the murderer, thinking instead that he is merely one of many decoys set up by the real killer to lead the investigation astray.

The real killer turns out to be Lynn, who has lured Vance and Doris to the Closter townhouse to kill them.  But before Lynn completes his "perfect crime," Vance reads from a letter he wrote earlier in which he detailed his theory about the killings.  In it, Vance names Lynn as the murderer, calling him a rich, egomaniacal weakling, who, being tired of his wife, poisoned her and threw the blame on his uncle, whom he despised.  After hearing Vance's summary of the murder plot, Lynn tells his captors that he has arranged to pin Vance and Doris' forthcoming murder on Kinkaid.  However, when Lynn shoots Vance, Heath and others emerge from behind a door where they have been recording Lynn's confession and arrest him.

After thanking Becky, Mrs. Llewellyn's maid, for loading Lynn's gun with blanks, Vance resumes his romance with Doris.