  In this paper we study the number $M_{m,n}$ of ways to place nonattacking
pawns on an $m\times n$ chessboard. We find an upper bound for $M_{m,n}$ and
analyse its asymptotic behavior. It turns out that
$\lim_{m,n\to\infty}(M_{m,n})^{1/mn}$ exists and is bounded from above by
$(1+\sqrt{5})/2$. Also, we consider a lower bound for $M_{m,n}$ by reducing
this problem to that of tiling an $(m+1)\times (n+1)$ board with square tiles
of size $1\times 1$ and $2\times 2$. Moreover, we use the transfer-matrix
method to implement an algorithm that allows us to get an explicit formula for
$M_{m,n}$ for given $m$.
