Part A:
What if 11 or 12 are lighter coins? All you checked for were the anomalies. That's only one part of the question.
Part B:
In i) 7,8 can't possibly be the anomaly, since they would have caused an imbalance in the initial weighing. If you've already determined that the anomaly is in 9,10,11,12 then weighing 1,9,10 against 2,11,12 will never result in a balance.
In ii) 9,10 are the anomaly *only if* the anomaly is a heavy coin rather than a lighter coin. You haven't determined this. 11 or 12 could easily be the lighter coin.
This was your undoing in the previous step. You made assumptions about whether the coin was heavy or light, and you cannot do that, because I will always be able to find a scenario where the coin you choose isn't the anomaly.
What if 11 or 12 are lighter coins? All you checked for were the anomalies. That's only one part of the question.
Part B:
In i) 7,8 can't possibly be the anomaly, since they would have caused an imbalance in the initial weighing. If you've already determined that the anomaly is in 9,10,11,12 then weighing 1,9,10 against 2,11,12 will never result in a balance.
In ii) 9,10 are the anomaly *only if* the anomaly is a heavy coin rather than a lighter coin. You haven't determined this. 11 or 12 could easily be the lighter coin.
This was your undoing in the previous step. You made assumptions about whether the coin was heavy or light, and you cannot do that, because I will always be able to find a scenario where the coin you choose isn't the anomaly.
