Most movies pose a problem at the beginning that is solved by the final scene. That’s why many films seem like mathematical equations.

“The White Ribbon,” winner of last year’s top prize at the Cannes Film Festival, goes in a different direction. This utterly unnerving film offers a number of problems, but instead of answering them all, it allows us to draw sinister conclusions.

What is “The White Ribbon”? A cerebral horror movie, a film about 20th-century history that takes place entirely in a small village over the course of a couple of years, a mystery with multiple possibilities.

Set in a German village just before World War I, the film introduces us to a range of characters and a series of bizarre acts of cruelty. It begins with the town’s doctor being injured when his horse trips over a wire that has been deliberately stretched across a lane.

Other odd mysteries happen: child abuse, accidental death, arson, suicide. And even in ordinary domestic scenes, a sense of cruelty and repression is the dominant mood — including around the children. Especially around the children.

The only exception is the tender courtship of the 31-year-old schoolteacher (Christian Friedel) and a shy lass (Leonie Benesch) from a nearby town. The teacher narrates the film from the vantage of old age, and says he is telling us the story to “clarify things that happened later in our country.”

That suggestion prompts us to imagine that the children will probably be soldiers in Hitler’s Third Reich when they grow up. But the film doesn’t spell this out, and the vague sense of evil percolating beneath the surface of every incident does not need to be limited to what happened in Germany in the first half of the last century.

Along with those blandly disturbing children, we also come to know the adults, who are a cross-section of society: the baron whose harvest employs one and all, the pastor who rules his children with an iron fist, the doctor whose conversation with his servant/mistress might be the harshest scene between two people since Ingmar Bergman’s last film, and other farmers, laborers and sundry folk.

This world is conjured up by Austrian writer-director Michael Haneke, a major European filmmaker whose films include “Cache” and “The Music Teacher.” Haneke is a master of detail, an impeccable technician who orchestrates every aspect of the movie — sound, lighting, performance — into an extraordinary finished product.

It’s all the more perverse that with the technical skills of a Spielberg, he consistently leaves out the pieces that would give his audience closure. What is the cause of the strange events of “The White Ribbon”? I don’t know. Repeat viewings might gather clues and stitch it all together.

But that would be beside the point. Haneke is describing a general mood of horror and shared responsibility. It takes a village to foster evil, he might be saying, not just a single warped culprit.