Problem

Source: India IMOTC 2024 Day 1 Problem 1

Tags: combinatorics, india, combinatorial geometry



A sleeping rabbit lies in the interior of a convex $2024$-gon. A hunter picks three vertices of the polygon and he lays a trap which covers the interior and the boundary of the triangular region determined by them. Determine the minimum number of times he needs to do this to guarantee that the rabbit will be trapped. Proposed by Anant Mudgal and Rohan Goyal