It did get closer. For that type of query you can ask it check its work and can usually triangulate on correct answer within a single prompt, eventually.
I would be cautious of a Clever Hans effect there. If you repeat the question until you get the right answer you're providing the AI with significant extra information.
No, in a single prompt, you can instruct it to check its work and keep going until it’s right (or at least have it tell you which of the N answers were right or wrong). Essentially chain of thought reasoning.