Question 38
We consider an $n \times n$ ($n \in \mathbb{N}$, $n \ge 2$) square divided into $n^2$ unit squares. Determine all the values of $k \in \mathbb{N}$ for which we can write a real number in each of the unit squares such that the sum of the $n^2$ numbers is a positive number, while the sum of the numbers from the unit squares of any $k \times k$ square is a negative number.