Question 14
There are $n$ pairs of students, with each pair consisting of a boy and a girl. At each turn, Ah Meng chooses $1$ boy and $1$ girl (not necessarily belonging to the same pair), and gives each of them a peanut. The same student may be chosen more than once. After several turns of choosing $1$ boy and $1$ girl, Ah Meng finds out that for each pair, either the boy has $21$ peanuts more than the girl, or the girl has $36$ peanuts more than the boy. Determine the minimum possible value of $n$.