2. (10 points) It is known that one of four coins is counterfeit and differs in weight from the genuine ones. It is required to determine which coin is counterfeit using a balance scale without weights. Which of the following statements are true?

a) The counterfeit coin can be determined in 2 weighings.

b) The counterfeit coin can be determined in 3 weighings.

c) The counterfeit coin can be determined in 4 weighings.

d) None of the listed answers are correct.
Answer: a)

Solution: Let's choose two of the available coins and weigh them (one on each pan of the balance). This way, we can determine which pair contains the counterfeit coin (if the balance is even, the counterfeit coin is among the remaining two coins; otherwise, it is among the chosen ones).

Now, take one coin from the pair where both coins are genuine, and one coin from the pair where there is a counterfeit, and weigh them, remembering which pan of the balance the genuine coin was placed on. If the balance is even, meaning we weighed two genuine coins, then the counterfeit coin is the remaining coin in the pair that had one genuine and one counterfeit. If the balance shows a difference, then the counterfeit coin is the second coin on the balance.