Finding the worst solved problem and the next unsolved problem in the same area seems like a good starting position for making a self-improvement plan. You know the boundaries of your skills and the area next beyond that.
My worst problem ever, solved: Having a good relationship. It requires social skills, knowledge of yourself, knowledge of other people, it changes with circumstances, and it also needs some luck.
Next problem, unsolved: Building a community. When I have some idea I consider good, even when I find some people who express enthusiasm, I can't bring them to work together. Either I am wrong at convincing those people to cooperate, or the ratio of "usable" people is naturally low and I am wrong at bringing my idea to enough people so that even the "usable" subset is large enough. Or both.
Other great problem, solved: Making enough money to buy my own home. The solution involved a great help from other people. I made most of money myself, but other people lended me the rest (my country was early post-communist at that time, the mortgages were not as widely available as they are today), and especially they helped me to find a good and affordable apartment (I absolutely would not have time to do so, nor the skills).
Next problem, in progress: Making enough money to become independent on work for some time, and then using that time wisely for my projects.
Other big problem, solved: Learning enough about Java programming and design patterns so I can write a nontrivial computer game (including menu, intro screen, saving game progress, etc.) reliably without bugs. Especially to understand the thread model and how it relates to events.
Next problem, in progress: Completing the game. ;-)
EDIT: No one was doing what the post suggests, so I accepted an idea from one of the comments, and embedded my response in a comment, not the post itself
I'd like to ask this question to you, and I'll respond it myself as well.
What Is The Worst Problem You've Ever Encountered and Solved? And the One You Didn't, Yet!
Some prior considerations:
1) I mean "problem" in a very general sense, it could be a math problem, an existential problem, a social problem, an akrasia problem, a disease problem etc...
2) I'd like people to give informative/didactic responses. Try not only to state the facts, but also to help someone who'd encounter similar situations to be able to deal with them.
3) When talking about the one you didn't, give enough specifics that someone would actually be able to help you.
The general idea is to teach people how to Win by example, taking in consideration all the shortcomings of biases etc...
Well, that is all. One solved, one not yet solved. State your own issues and help others here. Someone else's rationality is always welcome.