I agree that the problem should be engaging for students. I think the problem also needs to invite exploration, hopefully with several possible approaches for solution. Exploring and trying different ideas invites discussion, as does comparing different ways to arrive at the solution. What should we try? Does this work? Is each valid? How are they alike? How are they different? When I hear a student say something like, "I'm not sure about that. You are going to have to prove that to me," then I think I have been successful.