1975 AMC 12 第 25 题
先试着解答 1975 AMC 12 第 25 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1975 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
25.
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.
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.
其他年份的第 25 题
1950 AMC 12 · 1951 AMC 12 · 1952 AMC 12 · 1953 AMC 12 · 1954 AMC 12 · 1955 AMC 12 · 1956 AMC 12 · 1957 AMC 12 · 1958 AMC 12 · 1959 AMC 12 · 1960 AMC 12 · 1961 AMC 12 · 1962 AMC 12 · 1963 AMC 12 · 1964 AMC 12 · 1965 AMC 12 · 1966 AMC 12 · 1967 AMC 12 · 1968 AMC 12 · 1969 AMC 12 · 1970 AMC 12 · 1971 AMC 12 · 1972 AMC 12 · 1973 AMC 12 · 1974 AMC 12 · 1976 AMC 12 · 1977 AMC 12 · 1978 AMC 12 · 1979 AMC 12 · 1980 AMC 12 · 1981 AMC 12 · 1982 AMC 12 · 1983 AMC 12 · 1984 AMC 12 · 1985 AMC 12 · 1986 AMC 12 · 1987 AMC 12 · 1988 AMC 12 · 1989 AMC 12 · 1990 AMC 12 · 1991 AMC 12 · 1992 AMC 12 · 1993 AMC 12 · 1994 AMC 12 · 1995 AMC 12 · 1996 AMC 12 · 1997 AMC 12 · 1998 AMC 12 · 1999 AMC 12 · 2000 AMC 12 · 2001 AMC 12 · 2002 AMC 12A · 2002 AMC 12B · 2003 AMC 12A · 2003 AMC 12B · 2004 AMC 12A · 2004 AMC 12B · 2005 AMC 12A · 2005 AMC 12B · 2006 AMC 12A · 2006 AMC 12B · 2007 AMC 12A · 2007 AMC 12B · 2008 AMC 12A · 2008 AMC 12B · 2009 AMC 12A · 2009 AMC 12B · 2010 AMC 12A · 2010 AMC 12B · 2011 AMC 12A · 2011 AMC 12B · 2012 AMC 12A · 2012 AMC 12B · 2013 AMC 12A · 2013 AMC 12B · 2014 AMC 12A · 2014 AMC 12B · 2015 AMC 12A · 2015 AMC 12B · 2016 AMC 12A · 2016 AMC 12B · 2017 AMC 12A · 2017 AMC 12B · 2018 AMC 12A · 2018 AMC 12B · 2019 AMC 12A · 2019 AMC 12B · 2020 AMC 12A · 2020 AMC 12B · 2021 AMC 12A Spring · 2021 AMC 12B Spring · 2021 AMC 12A Fall · 2021 AMC 12B Fall · 2022 AMC 12A · 2022 AMC 12B · 2023 AMC 12A · 2023 AMC 12B · 2024 AMC 12A · 2024 AMC 12B · 2025 AMC 12A · 2025 AMC 12B