Question

假设某年 $N$ 的七月有五个星期一。下列哪一天在该年 $N$ 的八月一定出现五次？（注意：这两个月都有 $31$ 天。）

Suppose July of year $N$ has five Mondays. Which of the following must occur five times in August of year $N?$ (Note: Both months have $31$ days.)

星期一

Monday

星期二

Tuesday

星期三

Wednesday

星期四

Thursday

星期五

Friday

答案：D

知识点：日期与时间模运算分类讨论

难度评级：1370

小提示：

一个 $31$ 天的月份中， $1$ 日的星期以及接下来两天的星期会出现五次，所以七月 $1$ 、 $2$ 、 $3$ 日之一是星期一。

With $31$ days, the weekday of July $1$ is the one that repeats five times, so Monday is July $1,$ $2,$ or $3$

大提示：

八月 $1$ 日比七月 $1$ 日晚三天；检查三种情况，找出八月中共同出现五次的星期。

August $1$ falls three weekdays after July $1$ ; test the three cases and find the August weekday common to all

解答：

七月有 $31=4\cdot7+3$ 天，所以七月 $1$ 日的星期会出现五次；既然星期一出现五次，星期一必在七月 $1$ 、 $2$ 或 $3$ 日之一。八月中出现五次的是八月 $1$ 、 $2$ 、 $3$ 日的星期，而八月 $1$ 日比七月 $1$ 日晚三天。

检查三种情况，八月出现五次的星期分别是星期四、星期五、星期六；星期三、星期四、星期五；以及星期二、星期三、星期四。

每种情况都包含星期四，所以正确答案是 D。

Since July has $31=4\cdot7+3$ days, the weekday of July $1$ occurs five times, so Monday falls on July $1,$ $2,$ or $3.$ The days that occur five times in August are those of August $1,$ $2,$ $3,$ and August $1$ is three weekdays after July $1.$

Testing the three cases, the August weekdays occurring five times are Thursday through Saturday, Wednesday through Friday, and Tuesday through Thursday. Thursday appears in every case.

Thus, the correct answer is D.

2002 AMC 12B 第 8 题

答案：D

难度评级：1370

小提示：

大提示：

解答：

其他年份的第 8 题