23) Anna, Barbara, Chiara, and Donatella challenged each other in a swimming race to the buoy. Upon arrival, there were no ties. On the return,

Anna says: "Chiara arrived before Barbara";

Barbara says: "Chiara arrived before Anna";

Chiara says: "I arrived second".

Knowing that only one of them is telling the truth,

(A) one can only determine who won

(B) one can only determine who came in second

(C) one can only determine who came in third

(D) one can only determine who came in last

(E) it is impossible to determine the ranking position of any of them.
23) The answer is (C)

Chiara could not have arrived first because at least one of Anna and Barbara is lying. Chiara could not have arrived second because in this case, she should have arrived before at least one of Anna and Barbara, so both she and one of these two would be telling the truth, contradicting the assumptions. Therefore, Chiara is lying, but then she cannot have arrived last because either Anna or Barbara is telling the truth. Therefore, Chiara arrived third.

Note that if Anna and Barbara arrived with one before Chiara and the other after, the assumptions are still satisfied. Therefore, it cannot be determined who arrived first, who arrived second, or who arrived last.