How many days in a year have a $3$ in the tens digit of the day of the month?
I want to count how many days in a year have a $3$ in the tens digit of the day of the month. That means the day of the month is either $30$ or $31$. There are $12$ months in a year, and each month has either $30$ or $31$ days, except for February, which has $28$ or $29$. So I can ignore February, since it never has a $3$ in the tens digit of the day of the month. For the other $11$ months, I need to check which ones have $30$ days and which ones have $31$ days. I can use the rhyme "Thirty days hath September, April, June, and November; All the rest have thirty-one, Save February, with twenty-eight we're done." So September, April, June, and November have $30$ days, and the other seven months have $31$ days. That means each of those four months has one day with a $3$ in the tens digit, namely the last day of the month. The other seven months have two days with a $3$ in the tens digit, namely the $30$th and $31$st day of the month. So the total number of days with a $3$ in the tens digit of the day of the month is $4 \times 1 + 7 \, \times \, 2 = 4 + 14 = 18$. 