Question

某个有 $31$ 天的月份中，星期一和星期三的天数相同。这个月的第一天可能是七天中的多少种？

A month with $31$ days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month?

$2$

$3$

$4$

$5$

$6$

$31$ 天中，有三个星期几会多出现一次。

In $31$ days, three weekdays occur one extra time

星期一和星期三必须同时是多出的日子，或同时不是。

Monday and Wednesday must either both be extra days or both not be extra days

注意 $31$ 除以 $7$ 时余数为 $3$ 。

因此，如果这个月从星期六、星期日、星期二或星期三开始，星期一和星期三的天数就不相等。

所以这个月只能从星期一、星期四或星期五开始。

所以正确答案是 B。

Note that $31$ days leaves a remainder of $3$ when divided by $7.$

This means that if the month starts on a Saturday, Sunday, Tuesday, or Wednesday, there will be an uneven number of Mondays and Wednesdays.

Then the month can only start on a Monday, Thursday, or Friday.

Thus, B is the correct answer.