Question 94
Given is a convex 2024-gon $A_1A_2\dots A_{2024}$ and 1000 points inside it, so that no three points are collinear. Some pairs of the points are connected with segments so that the interior of the polygon is divided into triangles. Every point is assigned one number among $\{1, -1, 2, -2\}$, so that the sum of the numbers written in $A_i$ and $A_{i+1012}$ is zero for all $i = 1, 2, \dots, 1012$. Prove that there is a triangle such that the sum of the numbers in some two of its vertices is zero.
(Emil Kolev)
(Emil Kolev)