IMO Shortlist 2003 problem C3
Dodao/la:
arhiva2. travnja 2012. Let
![n \geq 5](/media/m/5/e/9/5e990d3574f9b0184a829af943b8630e.png)
be an integer. Find the maximal integer
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
such that there exists a polygon with
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
vertices (convex or not, but not self-intersecting!) having
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
internal
![90^{\circ}](/media/m/2/9/4/29404077a84f1539d9b7d5dcccb02023.png)
angles.
%V0
Let $n \geq 5$ be an integer. Find the maximal integer $k$ such that there exists a polygon with $n$ vertices (convex or not, but not self-intersecting!) having $k$ internal $90^{\circ}$ angles.
Izvor: Međunarodna matematička olimpijada, shortlist 2003