Oh, I hate this. I get your point but as a potential new hire of your company I'm also interviewing you. This means that if you state a problem in a very ambiguous way (like you did in your first message) that's already a red flag for me. Sure, I don't expect 100% accuracy in your problem statement, but I don't expect either lazynnes for the sake of "let's see if the interviewer asks good questions before implementing anything".
Expect professionalism from both parts.