13. For each chess player, a score is calculated every month, derived from their results and made public, indicating their level of skill at that time. Gerardo is about to start a chess tournament with 64 participants, which proceeds by direct elimination (first the 32nd round, then the 16th, then the 8th, etc.): the winner of a match advances to the next round, the loser is eliminated (in case of a draw, the match is repeated). The previous edition of the tournament was very stingy with surprises: in every match, the player with the higher score always won. Before the draw for the bracket (which is done randomly among all participants), Gerardo informs himself about the other players present (who all have different scores) and concludes that, if everything were to go as in the previous edition, he could at most reach the semifinal. It follows that, among the participants in the tournament, Gerardo's score...

(A) can be in any position after the $32^{nd}$

(B) can be in any position from the $32^{nd}$ to the $48^{th}$ (inclusive)

(C) can be in any position before the $50^{th}$

(D) can be in any position before the $49^{th}$

(E) can be in any position from the $34^{th}$ to the $49^{th}$ (inclusive)
(13) The correct answer is $(E)$.

Gerardo reaches the semi-final if all 15 other participants in his quarter of the draw have lower scores than his; to hope to reach the semi-final with a favorable draw, his score must be at most the $49^{\text{th}}$. Furthermore, he is certain not to reach the final, which means he cannot find 31 participants with a lower score than his: in other words, his score is at least the $34^{\text{th}}$.

Problem proposed by Matteo Rossi.