IL-GILLIS 1998 Problem 3

A configuration of several checkers at the centers of squares on a rectangular sheet of grid paper is called boring if some four checkers occupy the vertices of a rectangle with sides parallel to those of the sheet. (a) Prove that any configuration of more than $3mn/4$ checkers on an $m\times n$ grid is boring. (b) Prove that any configuration of $26$ checkers on a $7\times 7$ grid is boring.