Are you smarter than a fifth grader- Part 3

Three even dates are possible in a month only when there are five Tuesday's. This is because when we add 7 to any odd integer it becomes even and when we add 7 to any even integer it becomes odd. There are only two possibilities to make 5 Tuesday's a month i.e either when the month starts on Monday or the month starts on Tuesday.When the month starts on Monday,the Tuesday's are the 2nd,9th,16th,23rd and the 30th of that month. But when 1st is a Tuesday, The Tuesday's of that month fall on the 1st,8th,15th,22nd and the 29th. In the first case there are three even dates,but in the second case there are only two Hence the answer is 2nd,9th,16th,23rd and the 30th of that particular month. Therefore from the above line we get that the 21st as a Sunday.

Well, I took a good look on the calender in my room (June 2014) & found that the Monday's column was $2, 9, 16, 23, 30$ .

Also, this was the only column with three even numbers. So, I applied this column to Tuesday & I got the $21^{\text{st}}$ as Sunday.

$\Rightarrow$ Our answer is $\boxed{7}$ .

MAKE a no. from 1-7, then ratio it..1:1,2:2, 3:3, 4:4, 5:5, 6:6, 7:7, then 8:1, 9:2, 10:3 and so on..........until 21:7. so seven is the correct answer.