In college, when I was taking a devices and circuits class, I found myself stuck on a problem on the first problem set of the semester. I asked an upperclassman for help and we determined that the problem could be solved by setting up a system of something like 12 equations, and grinding through the process of solving it. His solution was correct of course, but I wondered if this approach might be more complex than it needed to be given that it was for one of a number of problems in the first problem set of the course, and given that the theme of the first few classes was more conceptual than about doing calculations .
When I later saw the solution to the problem it turned out that by making some simplifying assumptions, the 12 equations reduced to 2, and the solution was quite simple and quick. The lesson that the problem was mean to teach was not how to solve linear equations, but about how to understand when how to use a simple model to understand a complex circuit. The direct, labor intensive approach ignored what the problem was meant to teach.
I don't recall much about the specifics of the problem, but one thing I learned from that experience is that while working harder will often (though not always!) give you a correct solution, it's always good to think about more than one approach before diving in and solving a problem.
Sometimes just working harder is the right thing to do. But if you need to get past a deadline, before diving in to solving a problem it's good to think about whether you're doing more work than the situation merits, and that, perhaps, you are overlooking a simpler, quicker, solution.
