coloring the squares in bw of coordinate plane by lattice lines
Source: 1997 ITAMO p3
January 25, 2020
latticesquare latticeColoringcombinatorial geometrycombinatorics
Problem Statement
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 () 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 intersects only finitely many black squares?