Problem

Source: Iran Team selection test 2024 - P6

Tags: combinatorics



Let A1A2...A99 be a regular 99gon and point A100 be its center. find the smallest possible natural number n , such that Parsa can color all segments AiAj ( 1i<j100 ) with one of n colors in such a way that no two homochromatic segments intersect each other or share a vertex. Proposed by Josef Tkadlec - Czech Republic