Question 150
The natural numbers from $1$ to $n^2$ are distributed in the cells of an $n\times n$ square, where $n\ge2$. For every pair in the same row or column, divide the larger number by the smaller. The smallest of these $n^2(n-1)$ quotients is called the characteristic $C$ of the arrangement. Determine, with proof, the largest possible value of $C$.