Problem

Source: Iran Team selection test 2024 - P6

Tags: combinatorics



Let $A_1A_2...A_{99}$ be a regular $99-$gon and point $A_{100}$ be its center. find the smallest possible natural number $n$ , such that Parsa can color all segments $A_iA_j$ ( $1 \le i < j \le 100$ ) 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