Question

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 $1$ 日是星期几？

In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January $1$ fall that year?

星期一

Monday

星期二

Tuesday

星期三

Wednesday

星期五

Friday

星期六

Saturday

答案：C

知识点：日期与时间模运算

难度评级：1090

解答：

因为 $31 = 4 \cdot 7 + 3$ ，一月 $1$ 日、 $2$ 日和 $3$ 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 $1$ 日、 $2$ 日或 $3$ 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 $31 = 4 \cdot 7 + 3,$ the weekdays falling on January $1,$ $2,$ and $3$ 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 $1,$ $2,$ or $3.$ 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 .

1985 AMC 8 第 20 题

答案：C

难度评级：1090

解答：

其他年份的第 20 题