I've observed this personally! After finding a solution to a problem and repeating it numerous times, I'll often randomly change one parameter of the solution (I'm talking about things like opening jars, not building complex systems, but it could apply there as well) to see if it works better. This often happens randomly because I ask my self "what if I did this?" as I'm performing the action.
The result is that almost invariably, I found a new way of doing something that's better than before. It often takes multiple tries, but it's something that takes little energy because it can be done throughout the day and the stakes are small.
Applied to a larger scale, random adjustments to larger systems can be exactly what's needed.
Before I was using my teeth, then one day I randomly tried using my hands. It surprisingly worked much better and I'm shocked more people don't do it this way.
Kidding =]. I actually don't have a better way of opening jars, it was more an example to show the triviality of the type of problems this kind of trial and error can work for. Maybe a better example is figuring out a repeatable way to get a stubborn door to shut. Things like that.
EDIT: Actually, you probably already know this, but if you turn a jar upside down and hit it on a counter top, it can knock the lid loose enough to twist off. I didn't mention it because I didn't figure that one out on my own, but if you're looking for jar-opening tips, that's a good one.
The result is that almost invariably, I found a new way of doing something that's better than before. It often takes multiple tries, but it's something that takes little energy because it can be done throughout the day and the stakes are small.
Applied to a larger scale, random adjustments to larger systems can be exactly what's needed.