14. Having determined that the Twelve Coins Problem requires us to weigh three combinations of coins to identify the false coin: How many weighings would be needed to determine a false coin amongst 15 coins? What about 20 coins? Can you develop an algorithm to prove your conclusions?

Hint: Consider the underlying minimum number of weighings needed for 2,3,4, and 5 coins to develop a knowledge base of facts for a bottom up solution to this problem.++ (Reference AIP&TS Ch. 4)