４つの山

You have 4 stacks of 7 gold coins each. Each stack contains either all counterfeit coins or all real coins, with at least one stack containing counterfeit coins. Multiple stacks may contain all counterfeit coins, and you need to identify all such stacks. A real coin weighs exactly 10.00 grams. A counterfeit coin weighs exactly 10.01 grams. You have access to a digital scale that measures weight to the nearest 0.01 grams. For each weighing, you may select any number of coins from any of the stacks and place them on the scale simultaneously. The scale will give you the total weight of the selected coins in grams. Important note: Different combinations of counterfeit stacks may result in the same total weight when following a specific weighing strategy. Your solution must be able to distinguish between all possible combinations of counterfeit stacks. What is the minimum number of weighings needed to determine which stacks contain all counterfeit coins?

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