Why is one an idiot savant for being able to see how to proceed with the question? Or in other words, what fault do you find with my solution that yeilded taking two weights on the scale to solve the problem?
The answer desired was the least number of weightings needed. And that is ZERO. Sorry, your answer may be pedagogically interesting as some abstracted example of non-real world engineering, but in the real world someone would figure out how to answer correctly with NO weighting.