Question

根据闰年规则，年份能被 $400$ 整除就是闰年，例如 $2000$ 年；或者能被 $4$ 整除但不能被 $100$ 整除也是闰年，例如 $2012$ 年。Charles Dickens 诞辰 $200$ 周年的庆祝日是 $2012$ 年二月 $7$ 日，星期二。他出生那天是星期几？

A year is a leap year if and only if the year number is divisible by $400$ (such as $2000$ ) or is divisible by $4$ but not $100$ (such as $2012$ ). The $200$ th anniversary of the birth of novelist Charles Dickens was celebrated on February $7,$ $2012,$ a Tuesday. On what day of the week was Dickens born?

星期五

Friday

星期六

Saturday

星期日

Sunday

星期一

Monday

星期二

Tuesday

答案：A

知识点：日期与时间模运算

难度评级：1540

小提示：

按模 $7$ 计算星期几的偏移。

Count day shifts modulo $7$

大提示：

这 $200$ 年中要计入闰日，但 $1900$ 年不是闰年。

In $200$ years, include leap days but exclude $1900$

解答：

平年有 $365$ 天，向未来移动一年，星期几会向后移动一天，因为 $365 = 52 \cdot 7 + 1\text{。}$

闰年有额外的一天，所以星期几会向后移动两天。

在 $1812$ 年到 $2012$ 年之间，有五十个年份是 $4$ 的倍数，但要去掉 $1900$ 年，所以共有 $49$ 个闰年。

因此，往回推 $200$ 年需要往回移动 $200 + 49 = 249 = 35 \cdot 7 + 4$ 天，也就是星期几往回移动 $4$ 天。

星期二往前推四天是星期五，也就是 $1812$ 年二月 $7$ 日。

所以正确答案是 A。

On a typical year with $365$ days, moving one year into the future moves the day of the week forward one since $365 = 52 \cdot 7 + 1.$

On a leap year however, the day of the week gets moved forward twice since there is an extra day.

Fifty of the years between $2012$ and $1812$ are multiples of $4,$ but we have to discard $1900,$ which leaves us with $49$ leap years.

Therefore, moving back $200$ years means we have to go back $200 + 49 = 249 = 35 \cdot 7 + 4$ days, which means we move back $4$ days in the week.

This takes us back to Friday, which is the day that corresponds to February $7,$ $1812.$

Thus, A is the correct answer.

2012 AMC 10A 第 12 题

答案：A

难度评级：1540

小提示：

大提示：

解答：

其他年份的第 12 题