Well, the moment you talk about 'possible solutions', you've already accepted the original claim. A problem described in vague terms has many possible solutions. Some of them will actually solve the exact problem, some of them won't. Deciding which is which is not trivial.
Ho do you go about it? Do you build and deliver all possible solutions, and then the customer gets to chose one? Do you prototype many possible solutions, agree with the customer which prototype is most promising, and turn that into the final deliverable, hoping you had captured the relevant details?
Or do you start working on a basic solution, let the customer use that and provide detailed feedback on what it's doing well or not, rinse and repeat until the customer says 'good enough, thanks'?
Ho do you go about it? Do you build and deliver all possible solutions, and then the customer gets to chose one? Do you prototype many possible solutions, agree with the customer which prototype is most promising, and turn that into the final deliverable, hoping you had captured the relevant details?
Or do you start working on a basic solution, let the customer use that and provide detailed feedback on what it's doing well or not, rinse and repeat until the customer says 'good enough, thanks'?