Swami Gulagulaananda said:
"Every problem comes with a solution - The problem then is to find the solution to the problem with the solution, the solution of which is the solution of the original problem"
A lot of people say that every problem has a solution. This is definitely not true in mathematics, where certain equations don't have any solutions. However, if you are talking about life in general, then, again, I don't know if I would still agree with this statement. There may be solutions, but then again, if the solution is not feasible, then it is of no use.
How would you solve the population problem? Kill 50% of the population - That will definitely solve the problem, but it is not right. Therefore, simply getting something that can remove the problem is not a solution. Some solutions may not be morally incorrect like the previous one, but may not be feasible because of other issues, like say, economic, or others.
Some times, solving problems will be extremely difficult - Like, how would you get a billion people in India to adhere to rules? Just asking them won't do. Again, by enforcing the law strictly, it is still possible, but not very easy because people who are to enforce the law themselves must be clean and should adhere to the law themselves in the first place. Otherwise, it will be like the case of Keeg from Artistick, trying to solve corruption using his Corruption Detector. Therefore, all problems cannot be solved. Although some that can be solved are not solved because of other reasons that will be discussed in another post.