The discussion revolves around a classic logic puzzle involving two doors, each guarded by a truth-teller and a liar. The objective is to determine which door leads to the correct room using a single question. Several solutions are proposed, including asking one guard what the other would say about which door is correct. This method ensures that both guards will indicate the wrong door, allowing the man to choose the opposite door. Another suggested question is to ask a guard what they would answer if asked directly which door is correct, which would also yield the correct door regardless of which guard is asked. The conversation touches on the nuances of the puzzle and the implications of asking about door colors, but ultimately focuses on the effectiveness of the proposed questions to solve the dilemma. The puzzle is noted to have appeared in the movie "Labyrinth," highlighting its popularity in logic problem discussions.