In a school, chemistry, English, French, geography, mathematics, and physics are taught by the following teachers: Barna, Kovács, Horváth, and Nagy. Each teacher is specialized in three subjects, and each subject is taught by two teachers. The English and French are taught by the same teachers. Nagy teaches two of the subjects that Kovács also teaches. Mathematics is taught by Nagy and Horváth. If Horváth also teaches chemistry and Kovács does not teach physics, then who teaches geography?
We know that Nagy and Kovács teach two subjects together. It cannot be physics, because Kovács does not teach it, it cannot be mathematics, because we already know both teachers of it, and it cannot be chemistry either, because one of its teachers is Horváth. Since according to the condition, English and French are taught by the same teachers, these two subjects can only be the common subjects of Nagy and Kovács. Barna does not teach mathematics, English, and French, so he teaches the other three subjects: physics, chemistry, and geography. We do not know one subject each for Horváth and Kovács, and we have not yet known one teacher each for physics and geography. Kovács does not teach physics, so he can only teach geography. Therefore, the two teachers of geography are Barna and Kovács.