7. Kill John Doe, He Doesn't Win. He's Dead - Se7en
The Dilemma: Detective Mills (Brad Pitt) has just discovered that John Doe (Kevin Spacey), the movie's serial killer, has just murdered his pregnant wife. Mills wants to murder Doe, but doing so will simply complete the cycle of 7 Deadly Sins that Doe has been perpetrating throughout the film. This will allow Doe to "win" in effect.
The Solution: Mills shoots Doe through the head anyway, essentially "losing" by the film's logic.
How It Should Have Been Solved: This film ends the right way, though makes a big deal about how Mills has failed, because taking Doe to prison would have been an easy way to prevent the sin cycle from completing itself. Taking a nihilistic view of things - appropriate given the nihilism of the film - Doe is dead, he's not a winner of anything. That's not to say Mills has won either - his pregnant wife is dead - but hey, burning a round through the douchebag's head must take the edge off a little. Jail just wasn't an option with a crime so heinous.