This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND
OR
NO

Found problems: 1

2024 Middle European Mathematical Olympiad, 2
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.
question polygon guessing game combinatorics combinatorial geometry geometry number theory polygons