Two Agents, One Prompt, and Your Weight

We investigate a quantitative variant of the classic Two Doors logic puzzle, in which the answer space is no longer binary, for example when the goal is to recover a numerical fact (such as one's true weight) rather than choose between two doors. The puzzle retains the original structure: one agent always tells the truth, the other always lies. Our central contribution is to identify a class of self-referential prompts that successfully extract the correct quantitative answer under minimal assumptions. We also explore how well does \texttt{ChatGPT} does in reasoning for this problem which is just a little bit out of distribution.