Oliver is an involuntarily retired professor with a yen for Beethoven, Jazz and puzzles of all kinds. Diane Priest is a WPC (Woman Police Constable) whose suspicions about a superior officer get her booted from the force. They team up on a journey that Oliver thinks will lead to love, since Diane's statement "Diane, not Priest" is an anagram for "predestination." She thinks he's a loony, but is intrigued by his promise to tell her "the very funny thing I know about sex."
Though Oliver is bound for the Orkneys to find Aristotle, Diane declares she is only going as far as Shrewsbury. But after some successful undercover work there, Diane decides to travel a little further with Oliver. He takes her to the deserted mining town where he grew up. Then she takes over the wheel.
Diane decides to make her connection to Oliver temporarily permanent and the couple exchanges "vows" on sacred ground. They begin their "honeymoon" at an inn with a proprietress who is delighted to play along. Next day at Hadrian's Wall, their union is blessed with the surprise appearance of a son. They plot their next move when Oliver discovers that Aristotle is giving them clues to the mystery in the crosswords.
At the palatial digs of the groovy Baron Kite, Oliver and Diane discover the link between the murder victims and the Farquhar Group. The hospitable baron follows up with an aerial assault. Only divine intervention gets them on the Orkney boat. Meanwhile, Michael discovers that his hacker friend is still in jail, but has left behind a girl as talented as he is.
Oliver and Diane find Aristotle's home but are too late to meet Aristotle. But then who is doing the current crosswords? Michael manages to get a long incriminating fax to his mother that wraps up the case, and the persistent Mr. Baxter has a final surprise.