I place some rooks on a chessboard (possibly more than one rook on some squares). Given:
* There is at least one rook on each rank.
* There is at least one file without a rook on it.
Prove: there are a file f and a rank r such that there is at least one rook at the intersection of f and r, and the number of rooks on f is bigger than the number of rooks on r.