Given a finite set of points in the plane, each with integer coordinates, is it always possible to color the points red or white so that for any straight line
![L](/media/m/f/c/1/fc1ae4eb78da7d1352cbf1f8217ab286.png)
parallel to one of the coordinate axes the difference (in absolute value) between the numbers of white and red points on
![L](/media/m/f/c/1/fc1ae4eb78da7d1352cbf1f8217ab286.png)
is not greater than
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
?
%V0
Given a finite set of points in the plane, each with integer coordinates, is it always possible to color the points red or white so that for any straight line $L$ parallel to one of the coordinate axes the difference (in absolute value) between the numbers of white and red points on $L$ is not greater than $1$?