. Find an adversary argument that proves 3 weighings are necessary in worst case), and therefore the algorithm you found in (b) is best possible. (Hint: study the adversary argument for the min-max problem discussed in class to gain some insight into this problem. Further hint: put some marks on the 4 bars and design an adversary strategy that, on each weighing, removes the fewest possible marks, then show that if the balance scale is only used 2 times, not enough marks will be removed.)