10) In a bag there are some marbles. Maria says: "In the bag there are three marbles in total and they are black." Luca says: "In the bag there are two black marbles and two red marbles." Giorgio says: "In the bag there are only black marbles." Knowing that only one of the three is lying, how many marbles are in the bag?

(A) one, (B) two, (C) three, (D) four, (E) it is not possible to determine the number based on the information given in the problem.
10. The answer is $(\mathbf{C})$.

If Maria had lied, then the statement made by Luca would also be false, which is not possible since only one of the three is lying. The same conclusion is reached by assuming that Giorgio is the liar. The only possibility is that the liar is Luca: in this case, Maria's statement and Giorgio's statement are compatible, and from these it is deduced that there are 3 balls in the bag and they are all black.