MathDB

lattice points in the plane

Source: 1rst National Women´s Contest of Mexican Mathematics Olympiad 2022 , problem 3 teams

July 23, 2023

lattice pointsMexico

Problem Statement

Consider a set

S

16

lattice points. The

16

points of

S

are divided into

8

pairs in such a way that
for every point

A

and any of the

7

pairs of points

(B,C)

where

A

is not included,

A

is at a distance of at most

\sqrt{5}

from either

B

C

Prove that any two points in the set

S

are at a distance of at most

3\sqrt5