Question 2
Given two odd positive integers $k$ and $n$. For each two positive integers $i, j$ satisfying $1 \le i \le k$ and $1 \le j \le n$ Martin wrote the fraction $i/j$ on the board. Determine the median of all these fractions, that is a real number $q$ such that if we order all the fractions on the board by their values from smallest to largest (fractions with the same value in any order), in the middle of this list will be a fraction with value $q$. (Martin Melicher)