How to deal with math problems if there is no solution book and no helpful teachers? Since a short time ago, I refuse to try solving math questions of which there is no solution available, unless I'm working on an own/open problem in my thesis. In subjects however, I refuse, because it is frustrating to get stuck for days and knowing that a solution exists. So knowing that I miss some important way of thinking.

Now you might think Why? If you can't solve it, just look at the course material and if that doesn't help then ask the teacher. Yes I tried that. By both mouth and mail. Unfortunately a lot of them don't like to get disturbed by students, because they are actually not real teachers, but very busy researchers who hardly have time for anything else. I also tried google, mathstack and asking students, but without a solution book it seems like it is always possible that nothing helps and you thus stay where you are: stuck. 

Having said this, is there a way to learn without solution books but with the guarantee that you can always get access to the solution for the problem you work on? Maybe I do something wrong with the ways already tried?
frustrating to get stuck for days and knowing that a solution exists.
  So knowing that I miss some important way of thinking.


So your solution to missing some important way of thinking is ... to not think at all? 

If you try hard to solve a problem, you are learning. You learn what doesn't work and why. That's a valuable lesson, and it's how you get better. In fact, I'd venture to say if it takes you 4 days to solve a problem, then even if you don't end up solving it, you probably learned more than the person who solved it in 1 hour. 

In mathematics, knowing the exact solution of some made-up problem usually isn't the key. After all, the exercise question tells you the conclusion of the solution. You already know the result from the onset. You just have to prove it, and it is the things you learn from proving it that are important, and that's my point: even if you don't manage to prove it, you still did worked with the details and learned similar concepts to the person who did manage to prove it. You just learned it slighty differently, e.g. somebody who proved it learned "okay, this technique works in this case", while you learned "okay, this technique doesn't work in this case". Both are equally valuable.