Okay, I'm working under the assumption that all of the coins in group 2 are real, and the fake coin is somewhere in group 1. Either way, the number of times you use the scale is the same.
Weigh the first three coins from group 1 against any three coins from group 2. If they weigh the same, the fake coin is one of the other three coins in group 1. That's how you figure out which group of three the fake coin is in. Forget about the control coins from group 2 -- weigh any coin from your group of three against any other coin, and that'll tell you which one is the fake. If the two you compare weigh the same, the third coin is the fake. We don't know if the fake coin is heavier or lighter, so we can't tell which one is the fake if it's one of those two. But that doesn't matter! The answer is three. You only need to use the scale three times!
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Weigh the first three coins from group 1 against any three coins from group 2. If they weigh the same, the fake coin is one of the other three coins in group 1. That's how you figure out which group of three the fake coin is in. Forget about the control coins from group 2 -- weigh any coin from your group of three against any other coin, and that'll tell you which one is the fake. If the two you compare weigh the same, the third coin is the fake. We don't know if the fake coin is heavier or lighter, so we can't tell which one is the fake if it's one of those two. But that doesn't matter! The answer is three. You only need to use the scale three times!