Help the exhausted student complete her triumphant text message by choosing the correct preposition.

I managed to pass the dreaded quantum mechanics final _____ dint of sheer luck and an unhealthy amount of espresso!

The correct answer is by.

The fixed idiomatic expression is "by dint of," which means "by means of" or "as a result of." It is a formal, C2-level phrase often used to emphasize the effort, force, or method used to achieve something.