Problem

Source: Chinese Northern Mathematical Olympiad 2007

Tags: combinatorics proposed, combinatorics



For every point on the plane, one of $ n$ colors are colored to it such that: $ (1)$ Every color is used infinitely many times. $ (2)$ There exists one line such that all points on this lines are colored exactly by one of two colors. Find the least value of $ n$ such that there exist four concyclic points with pairwise distinct colors.