$36 \cdot 69$ Some students participate in three competitions, with the champion getting 5 points, the runner-up getting 3 points, and the third place getting 1 point, with no ties. Therefore, for a student to ensure their score is definitely higher than other students, the minimum score they need to achieve is
(A) 9.
(B) 10.
(C) 11.
(D) 13.
(E) 15.
(7th American Junior High School Mathematics Examination, 1991)
[Solution] The total score for the three events is $(5+3+1) \cdot 3=27$.
The highest three possible scores for each player are $15 ; 13, 11$, and once a player scores 13 points (two first places and one second place), no other player can reach this score.

Scores less than 13 points are not feasible, for example, if a player scores 11 points (one first place and two second places), other players can still score 13 points.

Therefore, the answer is $(D)$.