Question 4
A $1991\times1992$ rectangle is divided into unit squares, indexed by $(m,n)$ with $1\le m\le1991$, $1\le n\le1992$ (row $m$, column $n$). Initially the squares $(m,n)$, $(m+1,n+1)$ and $(m+2,n+2)$ are colored, where $m\lt 1989$, $n\lt 1991$. Each subsequent move colors three uncolored squares lying in one row or one column. Can all the squares of the rectangle be colored in this way?