Classroom exercises always have nice, tidy solutions. So students implicitly assume that all problems have nice, tidy solutions. If the solution isn’t working out simply, you must have made a mistake.
Outside the classroom, applications seldom have simple solutions. So after a while you get jaded and quit trying to find a simple solution. But sometimes real problems do have simple solutions, or at least simpler solutions than seemed possible.
The Extreme Programming folks have a saying “Try the simplest thing that could possibly work.” If that doesn’t work, then try the next simplest thing that could possibly work. That line of thinking has paid off a few times lately.
I’ve had a couple math problems that I first assumed had to be approximated numerically that were more easily computed exactly. And I’ve had a couple programs where I was able to debug a section of code by simply deleting it. Things don’t always work out that well, but it’s fun when they do.