Two episodes feature Professor Augustus S.F.X. Van Dusen, "the Thinking Machine," a character created by Jacques Futrelle. Futrelle, an American who lived in Scituate, Massachusetts, is perhaps best known for having perished with the Titanic in 1912 after nobly giving up his place in a lifeboat to his wife. Van Dusen (Douglas Wilmer), an insufferably superior hyper-genius, uses the power of pure logic to solve problems and make fools out of the mere mortals he outright calls, "stupid people."
"Cell 13" is based on the very first Van Dusen story and features one of biggest "stars" to appear on the series: Michael Gough, one of the actors who lent their class to Hammer Films' horror movies, and who played Alfred in the 1980s Batman films. Here he is the governor of Grangemoor Prison, a "modern" facility claimed to be inescapable. Van Dusen volunteers to be locked into the prison's most secure cell, promising that he'll be free in a week, despite the blank incredulity of the complacent governor and the hostility of the prison guards.
Van Dusen appears again in the episode, "The Superfluous Finger." A surgeon is visited by a woman who demands that he amputate part of her healthy forefinger. When he refuses, she deliberately injures herself so badly that he has no choice but to perform the operation. The surgeon asks Van Dusen to find out what's going on, but the plot thickens when the mystery lady is found murdered—or is she? It's not hard to guess the outcome of this story, which uses a trick more recently seen in the movie The Prestige (2006). Douglas Wilmer played Sherlock Holmes in a 1960s television series and the movie The Adventure of Sherlock Holmes' Smarter Brother (1975).
"The Secret of the Magnifique" is based on a story by E. Phillips Oppenheim. Oppenheim styled himself "The Prince of Storytellers" and was featured on the cover of Time magazine in 1927. He was a very successful early genre fiction author credited with inventing the modern "spy" style of mystery-thriller and laying the foundations for characters like James Bond. His novels and stories were adapted into dozens of movies, of which the best known, The Great Impersonation (1920), was filmed three times. "The Secret of the Magnifique" presents Oppenheim's character J.T. Laxworthy (Bernard Hepton), a reformed criminal who uses his expertise to skirt the law for beneficial motives. Two convicts who have completed their prison sentences and been released with a bundle of clothes and a few shillings are met by a cabbie and taken to a plush apartment, where they're made an offer they can't refuse. If they help Laxworthy in an elaborate scheme, he won't tell the police about the crimes they committed that weren't found out during their previous trials. Six months later, they're all at a classy resort hotel in France. Laxworthy won't tell his associates exactly what they're after, but a French Admiral, his mistress and a American multi-millionaire pacifist are involved somehow. Bernard Hepton appears in the extremely popular BBC series I, Claudius (1976). Also featured is Christopher Neame, a deep-voiced young actor who at the time was being groomed by Hammer Films as a possible successor to horror stars Christopher Lee and Peter Cushing, a vision he failed to realize. (Several actors in The Rivals of Sherlock Holmes appeared in Hammer Films productions.)