23) Four friends, Anna, Bea, Caio, and Dino, are playing poker with 20 cards from the same deck: the four kings, the four queens, the four jacks, the four aces, and the four tens. Five cards are dealt to each. Anna says: "I have a four of a kind!" (four cards of the same value). Bea says: "I have all five hearts." Caio says: "I have five red cards." Finally, Dino says: "I have three cards of the same value and the other two also have the same value." We know that one and only one of these statements is false; who is lying?
(A) Anna,
(B) Bea,
(C) Caio,
(D) Dino,
(E) it is not possible to determine.
23. The answer is $(\mathbf{B})$.

Anna and Bea's statements are in contradiction with each other. Indeed, if Anna has a poker, she must have at least one heart, and therefore Bea cannot have all five hearts. Therefore, one of Anna and Bea is lying. If Anna were lying, the statements of Bea, Caio, and Dino would all have to be true. On the other hand, Dino claims to have three cards of the same value, so in particular, he has a red card, but Bea has all the hearts, and consequently, Caio, who has five red cards, must have all the diamonds. Therefore, Dino's statement is in conflict with those of Bea and Caio. We deduce that Bea, Caio, and Dino are not all telling the truth, so Anna is telling the truth and Bea is lying. We conclude by observing that the statements of Anna, Caio, and Dino are compatible with each other. For example: Anna could have a poker of aces and the king of spades; Caio could have the king of hearts, the king of diamonds, the queen of hearts, the queen of diamonds, and the jack of hearts; Dino could have the jack of diamonds, the jack of spades, and the jack of clubs, the ten of hearts, and the ten of diamonds, and Bea the remaining five cards.

[Problem proposed by D. Lombardo.]