Sometimes it’s enough to drown out the painful memories that she doesn’t ever talk about of her life before joining the force.

“Murder by Numbers” begins with Cassie (Sandra Bullock) being introduced to her new partner Sam (Ben Chaplin). When this former vice officer asks why other cops call her “hyena,” she explains it’s because the females of that species “have a mock penis.”

It’s kind of a shock when Cassie attempts to seduce Sam on the evening of their first assignment.

“What are you doing?” he asks.

She replies, “It’s called sex. It’s fun. You should try it.”

Apparently, the advance is not because she really likes him, but it’s more to give her the upper hand in their relationship.

While Cassie spends her off-time watching “Matlock,” the engaging police procedural “Murder by Numbers” is fashioned more like a “Columbo” episode. It focuses on a flawed, sometimes exasperating lead character. The killers are revealed to the audience from the get-go, and a cat-and-mouse game of forensics is initiated to determine who is smarter: the cops or the criminals.

There are times when the movie plays like a version of Alfred

Hitchcock’s “Rope” if the Jimmy Stewart role were replaced with the team from TV’s “C.S.I.” Though somewhat contrived, the setup is certainly intriguing.

At the local high school, the “cool kid” Richard (Ryan Gosling) and the introspective genius Justin (Michael Pitt) have spent a little too much time studying the book “Techniques in Crime Scene Investigation.” They decide to commit a murder primarily to see if they can get away with it, but also because the idle rich boys have nothing better to do.

By choosing a random victim, establishing alibis and planting misleading evidence, they hope to taunt the police with their superior tactics. And they’re aided by the fact that nobody at school even knows they hang out together.

Not surprisingly, Cassie doesn’t quite fall for it.

Director Barbet Schroeder (“Reversal of Fortune”) and screenwriter Tony Gayton create an accessible, plot-driven tale that comes across like a mainstream production of an indie script. Ultimately, “Murder by Numbers” hinges less on its laboring-to-be-clever story than on the performances of its three central characters.

Bullock is given a role with a little darkness in its soul so often the actress gets by on her sunny charisma. While she doesn’t quite burrow into the part with the certitude of some of her Oscar-winning peers (the actress has difficulty selling the enigmatic flashbacks that justify her psychological quirks), Bullock is always watchable.

It’s really the skill of the two young villains that elevates the picture. The college-age actors who play these disturbed high-schoolers are thoroughly convincing. Pitt (“Bully”) captures the cadence of a remote intellectual with a refreshing amount of subtlety. With his Spandau Ballet hairstyle and puffy face, his Justin bears a striking resemblance to the imprisoned “murderer” Damien Echols in the “Paradise Lost” documentaries. Similarly, he constantly has viewers questioning the scope of his quilt.

Gosling (who established his rep as the Jewish skinhead in last year’s “The Believer”) plays the affluent Richard with the assured precision of a kid who’s spent his entire life being able to get away with anything. Whatever his own charm can’t conquer, then his dad’s lawyers can. A scene where he is brought to the police station to be interrogated provides a fine example of the actor’s ability to balance ruthlessness with immaturity.

If the movie had as much conviction as its central actors, then

“Murder by Numbers” could have been a real achievement. While the story builds slowly and seems to be inching toward a devastating payoff, it flounders in the final scenes. From the first shot of a condemned building on the edge of a cliff, the film’s climax is preordained to involve the hero hanging on for dear life to a breakaway balcony high above the rocky beach below.

Cassie’s internal revelation during the epilogue is just as conventional and is staged in a way that reaps the least amount of emotional impact. Despite the good work that proceeds it, the filmmakers eventually back themselves into a narrative corner one that really is by the numbers.