7. A stack of fake coins There are n stacks of n identical-looking coins. All of the coins in one of these stacks are counterfeit, while all the coins in the other stacks are genuine. Every genuine coin weighs 10 grams; every fake weighs 11 grams. You have an analytical scale that can determine the exact weight of any number of coins. a. Devise a brute-force algorithm to identify the stack with the fake coins and determine its worst-case efficiency class. b. What is the minimum number of weighings needed to identify the stack with the fake coins?