The first type of interesting problem is the one everyone talks about: novel problems. New stuff, stuff that hasn’t been tackled before — either by the person doing it or the world as a whole.
These are interesting for obvious reasons: it’s fun to experiment — to try new things and push both individual and collective knowlege further.
The second type of interesting problems is less intuitive. These are problems that have been solved before — specifically problems that a given individual is tackling again. These old problems are a way to refine a craft. Know how to solve something already? Make an incremental improvement to it. Try a new design pattern. Push to take that known solution to the next level.
Everyone wants to feel like a badass, and known problems are a way to do something in a truly excellent way.
Next time a solved problem comes up try making little tweaks and take pride in doing it extremely well.