The problem of pawns (Q2315442)

Summary: 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 \(\binom{2m}{m}^2\), and more generally, the number of ways to arrange a maximum number of nonattacking pawns on a \(2n \times 2m\) chessboard is \(\binom{m+n}{n}^2\).