MathDB

Let

{n}

and

k

be positive integers. There are given

{n}

circles in the plane. Every two of them intersect at two distinct points, and all points of intersection they determine are pairwise distinct (i. e. no three circles have a common point). No three circles have a point in common. Each intersection point must be colored with one of

n

distinct colors so that each color is used at least once and exactly

k

distinct colors occur on each circle. Find all values of

n\geq 2

and

k

for which such a coloring is possible.
Proposed by Horst Sewerin, Germany

Problem Statement