* There is no known solution or path to the solution
* There might be none
* There might be one
* There might be multiple
* These might be approximations
* The solution will be so complex, it will not be sustainable
All these are possible ways of having no solution and lots of real world applications fall into the area of having lots of solutions, but sometimes it's just not sustainable. Theoretical research of course is different.
I usually just try to solve it with my current knowledge, as practical as i can (implementing it). Even if i cant solve it that way, i will have learned something and i can try again another time or using another approach. Looking for similar topics and approaches helps. Mind-Map thinking can help broadening the field and see adjacent topics which help finding a solution. Very often the knowledge from other fields help me solve something i could not without the broader knowledge.
* You might be bought-in, eg emotionally, to a situation that prevents solution
For example, you used something in the project you made, and that part needs to be ditched; or maybe you're not working in that team; or you consider yourself the best person to do something when really someone else is and your pride is getting in the way ... et cetera.
* There is no known solution or path to the solution
All these are possible ways of having no solution and lots of real world applications fall into the area of having lots of solutions, but sometimes it's just not sustainable. Theoretical research of course is different.I usually just try to solve it with my current knowledge, as practical as i can (implementing it). Even if i cant solve it that way, i will have learned something and i can try again another time or using another approach. Looking for similar topics and approaches helps. Mind-Map thinking can help broadening the field and see adjacent topics which help finding a solution. Very often the knowledge from other fields help me solve something i could not without the broader knowledge.