Here is my problem as follows. There are 2 counterfeit coins among 5 coins that look identical. Both counterfeit coins have the same weight and the other three real coins have the same weight. The five coins do not all weigh the same, but it is unknown whether the weight of each counterfeit coin is more or less than the weight of each real coin. Find the minimal number of weighings needed to find at least one real coin, and describe how to do so. (The balance scale reports the weight of the objects in the left pan, minus the weight of the objects in the right pan.)
In my solution approach, I tried to prove that it is possible by two moves. But I couldn't find any approach to show that one weighing won't be enough to identify and weight a real coin.
Can anyone help me show that one weighing isn't enough to identify a real one and weigh it?
You have to start with either one coin each in L and R pan,
or two coins each in L and R pan.
It is not difficult to see
that in neither case can you be certain to identify real/counterfeit