There are 50 coins. Half of them are genuine and the other half are counterfeit. Genuine coins weigh 10 grams, while counterfeit coins differ from the genuine coins by 1 gram (some of them weigh 9 grams, and some of them weigh 11 grams). You have a balance scale with two pans. In each weighing the scale shows the difference of the weights placed in each pan. You will randomly choose a coin. What is the minimum number of weighings necessary to guarantee to determine whether it is genuine or not?
*You can't use the chosen coin in the weighing processes.
*You must place at least one coin to each pan.
*The scale displays only the difference of the weights as a non-negative number. It doesn't give any information that which side is heavier.
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