Can any prove or disprove the statement “Every problem has a solution”? I guess we need to define “problem” so let’s say “Any state of affairs that one finds dissatsifying”. And a solution should be something that satisfies this unhappy state of affairs without greating an equal or greater problem.
Death is a final solution. 
All of our problems become extinguished then.
I suppose that is one answer - although it brings up a myriad of other questions - like: is there nothing after death? Or, wouldn’t suicide (or other forms of death) create problems for others close to you (i.e. are we defining a solution as something that doesn’t create equal or greater problems for one’s self or for all sentient beings)?
It might be better to look for an answer to this question on a more abstract/general level. Maybe we should ask if there’s anything inherent in the defition of “problem” that entails the necessity of an associated solution.
I take it this doesn’t have a solution? Okay, so not every mathematical problem hasa solution. Can we come up with similar proofs for other kinds of problems?
Maybe we have to split the universe of problems into categories. Does every physical problem have a solution? Does every psychological problem have a solution? Every political problem? Every philosophical problem? etc.
Physical Problem: the onset of cancer
Psychological Problem: women getting upset when the toilet seat is left up (the problem is that they get upset, not that the seat is left up)
100 years in the future: they find a cure for cancer.
100 years in the future: women take drugs to curtail their PMS
Unsolvable problem: finding an actual unsolvable problem (except this one)
Its like saying “There are no absolutes except this one”
All you have to say is “100 years later: they solve the problem”
Just wait a bit. All problems will end. If it doesn’t happen within the next 5 millennia, just wait longer.
I think that there’s a solution for every problem. It’s just a matter of accepting that not every solution will be satisfactory.
Dissatisfaction is a problem in and of itself. How do you solve that one?
Now that’s what I’m talking about. You see how the proof is in the pudding - or rather, the definition of the problem itself?
You realize the fact that polarity is a by product of perception, you accept that you can’t see around it and you don’t assume that it’s a part of reality outside what you perceive.
I don’t know if you just mean situational problems… but I know mathematically (and logically) there are problems that have no solution and this has been proved. (Godel)
Right now I"m wearing a shirt with Godel on it that says…“Godel your problems, realize that they aren’t even complete”.
Haha. I bet you see a lot of people with that “I’m focusing and reading your shirt” look… followed by the “What the hell does that mean?” look.
I’ve got another one w/ J.L. Austin that says…
“Perlocutionary acts?? Don’t ask me!!”
compromise
A multitude of ways. Dissatisfaction diminishes when you find that which satifies you
When I first saw this post, I thought “self reference” (c.f. Smears mentioning Gödel).
So, what about the problem of creating a solutionless problem? 
With your failure to come up with such a thing you automatically create one.