As a self-studier, I have no due dates and no time pressure. This is partly a good thing since I do have a life outside of my pursuit of mathematics. However, the lack of pressure is also a bad thing, as I often do not progress as quickly as I would like.
I am very often faced with a dilemma: how much time should I spend on a given problem? I am sure there is something to be said for seeing a problem through to the end and pushing and struggling until one solves it. However, there are times that I ask for a solution or a hint here, and upon seeing it feel certain that I would not have seen what I would have needed to in order to solve that problem, simply due to lack of experience.
So what I want to know is:
How much time is too much time to put into a single problem? At what point should one move on, so as not to get bogged down on one problem too much? How does one balance 'giving up' (or let's call it "moving on/prioritizing one's time") with spending so much time on single problems as to impede progress?
EDIT: This seems to be a somewhat popular question, and honestly I'm surprised it hasn't received any answers yet. This matter seems to be highly nontrivial, and especially so for those doing research and trying to prove things that may not even be true! I'm sure mathematicians have developed some sort of strategy for these situations. I'd love to hear some. Anyone?