If you're tackling a project or question that doesn't have an easy answer, sometimes the best thing you can do is... wait.
You could spend hours pouring all of your mental energy out.
Or you could just come back to it tomorrow. Nine times out of ten I find that the answer was easier and more obvious than I thought. Or I'll have a random insight pop into my head at another time of the day.
This is not an authorization of procrastination. If you have work to do, do it. But if you don't have an answer and you have time... mull it over.