The fake coin

You have nine coins of which you know that one is false although you don't know which one since it is impossible to distinguish it. They tell you that the counterfeit currency is slightly heavier than the rest and you have a balance to check it.

Are you able to find the fake coin with only two weights in the balance?

Solution

1.- First we place three coins on one side of the balance and another three on the other side. If the balance is in equilibrium it means that all currencies weigh the same and therefore the false one will be one of the three currencies that did not intervene in the weighing. In this case we continue in step 2. If the balance is not in equilibrium we know that the lowest plate contains the counterfeit coin. In this case we continue in step 3.

2.- Of the three coins that had not been weighed, we put one on each plate of the balance and left another one out. If the balance is in equilibrium, the false currency is the one that is not in the balance, otherwise, the false currency is the one in the lowest plate of the balance.

3.- We take the three coins from the lowest plate of the balance since among them will be the false one. We put a coin in each dish and leave another one out. If the balance is in equilibrium, the false currency is the one that is not in the balance, otherwise, the false currency is the one in the lowest plate of the balance.