But if the cardinality of the sets are equal, as is the case in each step of the solution, the set containing the max-weight ball is necessarily heavier. Can you explain further?
when it is further specified that all remaining balls are of equal weight then your solution cannot be optimal since comparing two thirds yields the required information about the remaining third.
First, it is trivial to communicate the problem and any moderately competent person will find a solution within a short time frame. Second, it tests how precisely someone takes a problem definition. (In my experience, the kind of person who glances over such details will also tend to make trivial programming mistakes like off-by-ones.) Third, by varying a well-known question slightly you can easily filter out those who have simply learned the "correct" solution from the internet rather than thinking it through.