Lucky and Jinx color segments of a polygon
Source: 2023 Macedonian Team Selection Test P6
May 21, 2023
combinatorics
Problem Statement
Lucky and Jinx were given a paper with points arranged as the vertices of a regular polygon.
They were then tasked to color all the segments connecting these points such that no triangle formed
with these points has all edges in the same color, nor in three different colors and no quadrilateral
(not necessarily convex) has all edges in the same color. After the coloring it was determined that
Jinx used at least two more colors than Lucky. How many colors did each of them use?Proposed by Ilija Jovcheski