The "box problem" from introductory calculus seeks to maximize the volume of a tray formed by folding a strictly rectangular sheet from which identical squares have been cut from each corner. In posing such questions, one would like to choose integral side-lengths for the sheet so that the excised squares have rational or integral side-length. Building on the work of Philip Hotchkiss that earlier appeared in this Journal, we find the dimensions of the smallest sheet with distinct integral side-lengths such that the side-lengths of the excised squares are rational or integral.