MathDB

Problem 6

Part of 2023 Macedonian Team Selection Test

Problems(1)

Lucky and Jinx color segments of a polygon

Source: 2023 Macedonian Team Selection Test P6

5/21/2023
Lucky and Jinx were given a paper with 20232023 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
combinatorics