MathDB

Convex quadrilaterals don't exist??

Source: Kyiv City MO 2023 Round 1, Problem 8.5

December 16, 2023

combinatoricscombinatorial geometrysquare grid

Problem Statement

You are given a square

n \times n

. The centers of some of some

m

of its

1\times 1

cells are marked. It turned out that there is no convex quadrilateral with vertices at these marked points. For each positive integer

n \geq 3

, find the largest value of

m

for which it is possible.
Proposed by Oleksiy Masalitin, Fedir Yudin