To my mind, the highest form of mystery novel is the “locked room” murder or “impossible crime.” While Agatha Christie is the mistress of misdirection with an unequaled gift for plotting, John Dickson Carr remains the master of those howdunits involving what is sometimes facetiously referred to as a “hermetically sealed chamber.” For example, in Carr’s masterpiece, “The Three Coffins,” two murders are committed by seemingly supernatural means. In one, a man is shot at point-blank range while standing in a courtyard covered with freshly fallen snow. His are the only tracks in the snow. Moreover, there are eyewitnesses who can swear that they saw no one near the victim at the time of the shot and that it wasn’t suicide. How was he killed?

If you like such puzzles, especially when they are spiced with a little screwball-comedy dialogue and a touch of the occult, don’t miss “The Memory of Blood,” Christopher Fowler’s eighth novel about London’s Peculiar Crimes Unit. This police team tackles only cases involving sensitive issues that are also a “high risk to public morale.” Like Ed McBain’s 87th Precinct novels, the PCU books feature a half-dozen characters but focus particularly on its senior detectives, in this instance, Arthur Bryant and John May. Now getting on toward retirement, the two friends complement each other, May being more sociable than his partner, knowledgeable about technology and susceptible to any pretty woman who comes along.

Bryant, by contrast, is the Sherlock Holmes of the PCU. Bookish, crotchety, anti-establishment, possessing an eidetic memory and a flair for lateral thinking, he gathers “much of his information from a loose network of psychics, healers, New Age fringe-dwellers, police time-wasters and anarchists.” The PCU offices, appropriately enough then, are located in a building that was once a spiritualist temple, a place where Aleister Crowley — here misspelled Alistair Crowley — summoned spirits and where an automaton Madame Blavatsky tells fortunes. The unit’s specialized personnel spend a lot of time there, most of them having no personal lives to speak of. They are all underpaid, rather a thorn in the side of their political overseers, but extremely loyal to each other.

When the book opens, Dan Banbury, the unit’s crime-scene manager, is reading “Forensic Analysis in the Home — Volume 4: Drains.” Bryant, we learn, has been working on his memoirs, concentrating on “a selection of our more eccentric cases,” including “the Leicester Square Vampire, that business with the Belles of Westminster, the Deptford Demon, the Shepherd’s Bush blowtorch murders and the hunt for the Odeon Strangler.” Meanwhile, the unit’s doltish acting head, Raymond Land, is completely unaware that his wife is carrying on an affair with her flamenco instructor. As these details already suggest, this is a briskly playful novel, although aspects of it are quite dark, even tragic.

In its fourth chapter, “The Memory of Blood” finally kicks into high gear. A rapacious real-estate developer named Robert Julius Kramer is throwing a party for the cast and backers of a play called “The Two Murderers.” Now in his mid-40s, Kramer possesses a trophy wife, a baby son and what he hopes will be a future money-maker, the New Strand Theatre. Fowler has great fun in depicting various theatrical types and hangers-on drinking and gossiping, but quickly zeroes in on the recently hired assistant stage manager Gail Strong, the playgirl daughter of a government minister.