IT-CESENATICO 1997 Problem 3

The positive quadrant of a coordinate plane is divided into unit squares by lattice lines. Is it possible to color the squares in black and white so that: (i) In every square of side $n$ ( $n \in N$ ) with a vertex at the origin and sides are parallel to the axes, there are more black than white squares; (ii) Every diagonal parallel to the line $y = x$ intersects only finitely many black squares?