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 (nāN) 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? latticesquare latticeColoringcombinatorial geometrycombinatorics