The interviewer gave the OP a simple question that could be answered within a short time to gauge how well they understood OO design, and OP specifically implemented it in a way to frustrate them. So again, whose the idiot?

If OP wanted to crush the question, they could quickly answer it by saying this is how you could implement using classes and inheritance, now let me explain why OO is a poor solution for this specific problem, and what kind of problem sets OO design is most useful in.