Of course, it may be that believing that problems don't have solutions is what helps cause the bad days.
How likely are you to find the solution to a problem if you really believe that the problem is insoluble? I'll submit that you won't find the solution you need, because you aren't even going to bother to look for it. What's the point of hunting Snarks and Boojums? May as well sit here in the dark and be miserable.
If, on the other hand, you start out assuming that the problem can be solved, you have a chance of solving it. The solution may not be obvious, it may not be simple, it may not even exist. And still, even if the solution doesn't exist, you may find that your understanding of the problem changes, because you've spent time looking for the solution. The old problem may have been intractable, but the new problem may not.
My father was going to, absent a miracle that didn't occur, die from metastatic colon cancer. He couldn't solve that problem, but he could make a choice about how he was going to spend his last days. He might have taken an experimental course of chemotherapy with an extremely low chance of success and a big chance of side effects that would make the end of his life miserable -- or he could skip the chemotherapy and spend his time being as healthy as he could during the time that he had left.
He chose to skip the chemo. I might not make the same choice, but it wasn't my choice to make, it was his. And he was happy with that choice, which was important.
We make choices all the time. We choose to go here and do this, or stay at home and do that, or eat this thing today whether it's good for us or not, or maybe choose not to eat it now, but reserve the right to do so in the future. The choices that we make may help create our problems (or not); they can also help create the solutions to the problems.
I will make no bones about this: I have been lucky. I had a good family when I was growing up, I got a good education, I have been fortunate in my employment, I have good friends and good family now. Not everyone is this lucky.
But -- to some extent -- we make our own luck. There's a Heinlein quote that I'm particularly fond of from Have Space Suit -- Will Travel:
"Seems to me I fumbled everything I tried. But I had help and an awful lot of luck." ...
"'Luck' is a question-begging word," he answered. "You spoke of the 'amazing luck' that you were listening when my daughter called for help. That wasn't luck."
"Huh? I mean, 'Sir'?"
"Why were you on that frequency? Because you were wearing a space suit. Why were you wearing it? Because you were determined to space. When a space ship called, you answered. If that is luck, then it is luck every time a batter hits a ball. Kip, 'good luck' follows careful preparation; 'bad luck' comes from sloppiness. You convinced a court older than Man himself that you and your kind were worth saving. Was that mere chance?"
"Uh... fact is, I got mad and almost ruined things. I was tired of being shoved around."
"The best things in history are accomplished by people who 'get tired of being shoved around'."
I'm lucky. I've got a good job -- almost 24 years now at what was supposed to be a temporary job! -- because I learned how to program computers primarily outside of my course work; met a professor at Northwestern / Kellogg whose class I took because I realized that he would be teaching all of the same sort of stuff I'd get out of the "Mergers and Acquisitions" course, except I wouldn't have to use all of the bidding points I had for classes to get into it; he turned out to be a reconverted high-energy physicist who had a lot in common with the reconverted chemist going for his MBA; and when -- after some persistence on my part -- he offered me a temporary job writing Fortran code, I did the job so well that he decided that keeping me around was a good idea.
Now, some of that was pure "luck" and some of it was skill and some of it was simply being in the right place at the right time. But if you're not prepared to grab onto opportunity when it comes your way, you won't be able to. And that's bad luck, isn't it?
The problem that I had set out to solve -- I was graduating with my MBA and had no job! -- was to find something that would tide me over until I found a permanent job. And I was convinced that a solution existed. In the worst case, I could find a job flipping burgers and keep looking until my money ran out. And the money could be stretched pretty thin if it need be. As it turned out, it didn't get that bad -- Carl offered me the temporary job on the day of my graduation. This was, admittedly, cutting it close. :) And it turned out that the solution to one problem was the solution to the other, which doesn't always happen, but was a nice bit of serendipity.
Money does help. It can't buy happiness, but it can help you find a solution, depending on what the problem is that you're trying to solve.
Money can make situations worse too, as can "throwing money at a problem". The trick is figuring out when and how to apply the money to the situation to get a good result. (I eagerly await Congress figuring out this trick. I'm not holding my breath.)
I have found problems that can't be solved in the way that I'd like to solve them. This doesn't mean that a solution doesn't exist. I may even get to like the alternate solution. It's all a matter of perspective.
The glass is neither half full, nor half empty. It does, however, contain water.
If you're thirsty, drink it.