You are a coin collector who recently acquired a set of rare antique coins. The set contains 14 coins - 12 are authentic but 2 are counterfeit. The real coins each weigh 1 oz, while the fakes each weigh 1.1 oz.
You have an accurate digital scale, but it can only measure the weight of up to 3 coins at a time. What is the minimum number of weighings needed to guarantee you can identify both counterfeit coins?