MathDB

n - 3 points inside a triangle with vertices on convex hull of n points

Source: Ukraine TST 2014 p10

April 30, 2020

combinatorial geometrycombinatoricspointsConvex hull

Problem Statement

Find all positive integers

n \ge 4

for which there are

n

points in general position on the plane such that an arbitrary triangle with vertices belonging to the convex hull of these

n

points, containing exactly one of

n - 3

points inside remained.