All problems have solutions.
That’s what makes them problems.
The solution might involve trade-offs or expenses that you don’t want to incur. You might choose not to solve the problem. But there is a solution. Perhaps you haven’t found it yet. Perhaps you need to do more research or make some tradeoffs in what you’re hoping for.
If there is no solution, then it’s not a problem.
It’s a regrettable situation. It’s a boundary condition. It’s something you’ll need to live with.
Which might be no fun, but there’s no sense in worrying about it or spending time or money on it, because it’s not a problem.
“I want to go to the wedding, but it’s a thousand miles away.” That’s a problem. You can solve it with a plane ticket and some cancelled plans.
“I want to go to the wedding, but I’m not willing to cancel my meeting.” That’s not a problem. That’s an unavoidable conflict. If you need to violate a law of physics to get out of a situation, it’s not a problem. But you’ve already given up turning into a problem, so it doesn’t pay to pretend it’s solvable.
Once we can walk away from unsolvable situations that pretend to be problems, we can focus our energy on the real problems in front of us.