MathDB

There is a rectangular sheet of paper on an infinite blackboard. Marvin secretly chooses a convex

2024

-gon

P

that lies fully on the piece of paper. Tigerin wants to find the vertices of

P

. In each step, Tigerin can draw a line

g

on the blackboard that is fully outside the piece of paper, then Marvin replies with the line

h

parallel to

g

that is the closest to

g

which passes through at least one vertex of

P

. Prove that there exists a positive integer

n

, independent of the choice of the polygon, such that Tigerin can always determine the vertices of

P

in at most

n

steps.

Problem Statement