2005 numbers on a circle with sum 7022
Source: Romanian Nationals RMO 2005 - grade 7, problem 4
March 31, 2005
Problem Statement
On a circle there are written 2005 non-negative integers with sum 7022. Prove that there exist two pairs formed with two consecutive numbers on the circle such that the sum of the elements in each pair is greater or equal with 8.
After an idea of Marin Chirciu