The chromatic number $\chi$ of an (infinite) plane is the smallest number of colors with which we can color the points on the plane in such a way that no two points of the same color are one unit apart. Prove that $4 \leq \chi \leq 7$.
Problem
Source: 2011 Philippine Math Olympiad National Stage Problem 5
Tags: combinatorics unsolved, combinatorics, Chromatic number