The Problem of Pawns

Abstract

Using a bijective proof, we show the number of ways to arrange a maximum number of nonattacking pawns on a $2m\times 2m$ chessboard is ${\left(\genfrac{}{}{0ex}{}{2m}{m}\right)}^2$, and more generally, the number of ways to arrange a maximum number of nonattacking pawns on a $2n\times 2m$ chessboard is ${\left(\genfrac{}{}{0ex}{}{m+n}{n}\right)}^2$.