[Solution] If the son is the worst player, the daughter must be his twin sister, then the best player must be the brother, which is consistent with the given conditions, because the brother and the son can be the same age.
Assuming any other player is the worst, it will inevitably lead to a contradiction:
If the woman is the worst player, her brother must be her twin brother, her daughter must be the best player, but the woman and her daughter cannot be the same age.

If the brother is the worst player, the woman must be his twin sister, then the best player is the son, but the woman and her son cannot be the same age, so the woman's twin brother cannot be the same age as the son.

If the daughter is the worst player, the son must be the daughter's twin brother, then the best player is the woman, but the woman and her daughter cannot be the same age.
Therefore, the answer is $(B)$.
$15 \cdot 27$ A woman, her brother, her son, and her daughter (all relationships are by blood) are all chess players. The twin of the worst player (who is also one of the four players) and the best player are of opposite sex. The worst player and the best player are of the same age. The worst player is
(A) the woman.
(B) her son.
(C) her brother.
(D) her daughter.
(E) there is no unique solution consistent with the given information.
(26th American High School Mathematics Examination, 1975)