A $\displaystyle n\times n$ matrix which entries from $\displaystyle {1,2,...,(2n-1)}$ is called "special" if for each $\displaystyle i$ the union of the $\displaystyle i$-th row and the $\displaystyle i$-th column contains $\displaystyle (2n-1)$ distinct entries. Prove that there exist no special matrix if $\displaystyle n=2007$. Prove that there exists an infinite number of special matrix.