“The Paris Enigma” (Harper/HarperCollins, $24.95) is a whodunit that provokes thought as well as entertainment, on subjects from waterproof shoeshine cream to ancient Greek physics.

It fires multiple, intense bursts of crime stories at the reader, some only a page or so long. And it climaxes with serial murders that tie into the building of the Eiffel Tower and the Paris World’s Fair of 1889.

It’s the first book to appear in English by Pablo De Santis, the first winner of the new Casa de America Prize for best American novel.

“The Paris Enigma” is based on the exploits of a cartoonishly improbable club called The 12 Detectives. It’s an almost priestly brotherhood – “the most elite detectives in the world,” the book calls them. Membership consists of a private sleuth from each of a dozen countries.

The detective from Buenos Aires and co-founder of the club, Renato Craig, publishes an ad inviting young people to a course on solving crime – he’s looking for an assistant. Club members’ assistants are called acolytes.

Among those who reply to Craig’s ad is the narrator of the novel, Sigmundo Salvatrio. His father, a shoemaker, had regularly given him jigsaw puzzles of increasing complexity for his birthday. They may have helped cause the young man’s addiction to detective stories. Sigmundo eagerly joins the course, becomes Craig’s acolyte and is sent to Paris for a meeting of the club, to represent his ailing master.

The French member of the club, Louis Darbon, has a rival for the Paris post: an expatriate from Poland, Viktor Arzaky. Darbon is killed, apparently murdered, by a fall from a platform of the Eiffel Tower.

Arzaky asks Sigmundo to work for him. Sigmundo accepts, and remains with Arzaky until the detective dies at the hands of the one violent acolyte – the late Darbon’s.

Where does ancient physics come in? The Greeks believed there were just four elements in nature: earth, air, fire and water. The scholarly detectives associate this lore with the serial murders in Paris. Did Darbon die from his long fall from the tower through the air, or from hitting the earth at the end of it?

The shoeshine cream? Sigmundo’s father, the shoemaker, gave him some of his concoction that was also said to be effective against wounds. Traces of the cream are found on the corpse of an actress who was apparently Arzaky’s lover. But it failed to prevent her death during her stage performance, which included a naked dive into a pool of icy water.

That makes three of the four Greek elements: air, earth, water.

The story is a lot more complicated than that.