Problem 4
Source: Danube Mathematical Competition 2017, Romania
October 28, 2017
combinatoricsabstract algebraabsolute value
Problem Statement
Let us have an infinite grid of unit squares. We write in every unit square a real number, such that the absolute value of the sum of the numbers from any square is less or equal than . Prove that the absolute value of the sum of the numbers from any rectangular is less or equal than .