I suppose they can assign a problem that was once a problem in the past and was later solved. However, for some problems, it seems the problem creator omitted enough information so as to leave the problem solvable. How do they know which information to omit?
I suppose one way to create problems is to start out with a "solved" system and then work backwards to eliminate just enough information to make the system solvable. Is this an algorithm for creating solvable problems? Are there any other algorithms for problem creation?