Question 187
Given two positive integers $n$ and $k$. There are $n$ circles ($n \geq 2$) in the plane, so that each circle intersects every other one twice and all these intersection points are different in pairs.
Each intersection is colored with one of $n$ colors so that each color is used at least once and the same number of $k$ colors are represented on each of the circles.
Determine all values of $n$ and $k$ for which such coloring is possible.
Each intersection is colored with one of $n$ colors so that each color is used at least once and the same number of $k$ colors are represented on each of the circles.
Determine all values of $n$ and $k$ for which such coloring is possible.