Question 16
A2 (RUS). The numbers from $1$ to $n^2$ are randomly arranged in the cells of a $n\times n$ square ($n\ge2$). For any pair of numbers situated in the same row or in the same column, the ratio of the greater number to the smaller one is calculated.
Let us call the characteristic of the arrangement the smallest of these $n^2(n-1)$ fractions. What is the highest possible value of the characteristic?
Let us call the characteristic of the arrangement the smallest of these $n^2(n-1)$ fractions. What is the highest possible value of the characteristic?