Ok split into 3 groups.
#1 Weight 4 vs 4. If they are the same weight you know the coin isn't in one of those.So you do 3 of the coins from the original weighing as your "controls" and weigh 3 of the remaining coins. If those are the same you know the coin you didn't weigh is the counterfit, weigh it against any one of the original coins to see if it is heavier or lighter. If the 3 vs 3 results in an imbalance (if it is heavier or lighter, you now know which direction the coin goes). Of the group that is off you weigh 1 vs 1. If they balance # 3 is the counterfeit. If they don't balance which ever one is off in the proper direction is the counterfit.
#2 if in your 4 vs 4 you have an imbalance. You know that the 4 coins that were set asside does not contain a fake. From here I am stumped because you don't know which side of the original weighing has a fake. So I need an extra weighing in order to figure it out.
#1 Weight 4 vs 4. If they are the same weight you know the coin isn't in one of those.So you do 3 of the coins from the original weighing as your "controls" and weigh 3 of the remaining coins. If those are the same you know the coin you didn't weigh is the counterfit, weigh it against any one of the original coins to see if it is heavier or lighter. If the 3 vs 3 results in an imbalance (if it is heavier or lighter, you now know which direction the coin goes). Of the group that is off you weigh 1 vs 1. If they balance # 3 is the counterfeit. If they don't balance which ever one is off in the proper direction is the counterfit.
#2 if in your 4 vs 4 you have an imbalance. You know that the 4 coins that were set asside does not contain a fake. From here I am stumped because you don't know which side of the original weighing has a fake. So I need an extra weighing in order to figure it out.