Question

Marvin 在闰年 $2008$ 年五月二十七日星期二过生日。他的生日下一次落在星期六是哪一年？

Marvin had a birthday on Tuesday, May 27 in the leap year $2008.$ In what year will his birthday next fall on a Saturday?

$2011$

$2012$

$2013$

$2015$

$2017$

普通年有所以同一日期在下一年会向后移一天。 $365 = 52 \cdot 7 + 1,$

对于闰年中位于二月二十九日之后的日期，星期会向后移两天。

因此 $2009$ 年这一天是星期三， $2010$ 年是星期四。

$2011$ 年是星期五；由于 $2012$ 年是闰年，这一天变为星期日。

接下来三年每年向后移一天。到 $2016$ 年又因闰年向后移两天，落在星期五。

最后， $2017$ 年这一天是星期六。

所以正确答案是 E。

Note that on a normal year, we have that $365 = 52 \cdot 7 + 1,$ which means that for a specific day, it moves to the day after the next year.

On a leap year, the day of the week moves forward two since there is an extra day.

Then in $2009,$ this day falls on a Wednesday. In $2010,$ it falls on a Thursday.

Similarly, in $2011,$ it falls on a Friday. In $2012,$ however, since it is a leap year, it falls on a Sunday.

Now, for the next three years, the day moves forward one. Then in $2016,$ it moves forward two, landing on a Friday.

Finally, in $2017,$ the day of the week is a Saturday.

Thus, E is the correct answer.