MathDB

IGO 2023 Intermidiate P5

Source: IGO 2023 Intermidiate P5

January 18, 2024

geometry

Problem Statement

There are

n

points in the plane such that at least

99\%

of quadrilaterals with vertices from these points are convex. Can we find a convex polygon in the plane having at least

90\%

of the points as vertices?
Proposed by Morteza Saghafian - Iran