1985 AMC 8 第 20 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
20.
某一年，一月正好有四个星期二和四个星期六。那一年的一月 日是星期几？
In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January fall that year?
星期一
Monday
星期二
Tuesday
星期三
Wednesday
星期五
Friday
星期六
Saturday
小提示：
一月有 天，也就是 个完整星期加 天
January has days, which is full weeks plus extra days
大提示：
出现五次的三个星期几，就是一月 日、 日和 日所对应的星期几；星期二和星期六不能在其中
The three weekdays that occur five times are the days of January and Tuesday and Saturday must not be among them
解答：
因为 ，一月 日、 日和 日所对应的三个星期几各出现五次，其余星期几各出现四次。
要让星期二和星期六都只出现四次，它们都不能是一月 日、 日或 日。唯一可行的开始日是星期三：这样星期三、星期四、星期五出现五次，而星期二和星期六各出现四次。
所以正确答案是 C。
Since the weekdays falling on January and each occur five times that month, and every other weekday occurs four times.
For Tuesday and Saturday to occur only four times, neither may be January or The only starting day that works is Wednesday: then Wednesday, Thursday, and Friday occur five times, while Tuesday and Saturday each occur four times.
Thus, the correct answer is C .
其他年份的第 20 题
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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