1997 OIM Problems/Problem 3
Problem
Let be an integer and be the set of points of the plane whose coordinates are integers with
a. Three colors are available; each of the points of is colored with one of them. Show that no matter how this coloring has been done, there are always two points of of the same color such that the line containing them does not pass through any other point of .
b. Find a way to color the points of using 4 colors so that if a line contains exactly two points of , then those two points have different colors.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.