Problem: A woman, her brother, her son and her daughter (all relations by birth) are chess players. The worst player's twin (who is one of the four players) and the best player are of opposite sex. The worst player and the best player are the same age. Who is the worst player?
Answer Choices:
A. the woman
B. her brother
C. her son
D. her daughter
E. No solution is consistent with the given information.
Solution:
If the son is the worst player, the daughter must be his twin. The best player must then be the brother. This is consistent with the given information, since the brother and the son could be the same age. The assumption that any of the other players is worst leads to a contradiction:
If the woman is the worst player, her brother must be her twin and 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. The best player is then the son. But the woman and her son cannot be the same age, and hence the woman's twin, her brother, cannot be the same age as the son.
If the daughter is the worst player, the son must be the daughter's twin. The best player must then be the woman. But the woman and her daughter cannot be the same age.