On each vertex of a regular n ≥ 3 sided polygon there is a real number so that the sum of these n numbers is zero. For any two vertices of the polygon with numbers x and y consider the line passing through these vertices dividing the polygon into two parts. Let the sum of numbers written on one of these parts be A and the sum of numbers written on the other part be B. If
|x − y| ≥ |A − B|
we say that this pair of vertices is good. For each fixed n find the minimal possible number of good vertex pairs.
Correct Solutions by,
- Toshihiro Shimizu Kawasaki, Japan
- Abdulkadir Tanrıverdi Eskişehir
- Ahmet Yüksel Aydın
- Murat Burç Soma, Manisa
- Magnus Jakobsson Lund, Sweden
- Roger Bengtsson Lund, Sweden
- Tamer Türkoğlu Bilkent University alumnus
- Mustafa Kaynak Gaziantep