1975 AMC 12 第 25 题

Question

一名女子、她的兄弟、她的儿子和她的女儿都是国际象棋棋手（所有亲属关系均为血缘关系）。水平最差者的双胞胎手足也是这四人之一，且与水平最佳者性别相反。水平最差者与水平最佳者年龄相同。谁的水平最差？

A woman, her brother, her son and her daughter are chess players (all relations by birth). 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?

这名女子

the woman

她的儿子

her son

她的兄弟

her brother

她的女儿

her daughter

不存在符合所给信息的答案。

No solution is consistent with the given information.

答案：B

知识点：逻辑推理分类讨论年龄问题

难度评级：1740

小提示：

列出这四人中同一辈分、可能构成双胞胎的所有配对

List the only possible same-generation twin pairs among the four people

大提示：

若儿子水平最差，他的双胞胎手足是女儿，而水平最佳者可以是女子的兄弟

If the son is worst, his twin is the daughter and the best can be the brother

解答：

若儿子水平最差，则女儿可以是他的双胞胎手足，女子的兄弟可以是水平最佳者；儿子与这位兄弟可能同岁，因此所有条件都能满足。若女子水平最差，则她的兄弟是其双胞胎，女儿必须水平最佳，但母女不可能同岁。若兄弟水平最差，则女子是其双胞胎，儿子必须水平最佳，年龄条件仍不可能满足。若女儿水平最差，则儿子是其双胞胎，女子必须水平最佳，同样不可能同岁。因此只有儿子符合条件。

因此，正确答案是 B。

If the son is worst, the daughter can be his twin and the brother can be best; the son and brother may have the same age, so all conditions can hold. If the woman is worst, the brother is her twin and the daughter must be best, but mother and daughter cannot be the same age. If the brother is worst, the woman is his twin and the son must be best, again impossible in age. If the daughter is worst, her twin is the son and the woman must be best, also impossible in age. Thus only the son works.

Therefore, the correct answer is B.

1975 AMC 12 第 25 题

答案：B

难度评级：1740

小提示：

大提示：

解答：

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