Let $n_1,\ldots, n_k$ be not necessarily distinct natural numbers.
Let $A$ be a $k\times k$-matrix such that every row and every column of $A$ is a permutation of $n_1,\ldots, n_k$.
What is the range of the determinant of $A$ in terms of $n_1,\ldots, n_k$?
In particular, for which $n_1,\ldots, n_k$ is the determinant constant? For which is it zero?