Problem

Source: Middle Europe Mathematical Olympiad 2009 TST Second Day Second problem

Tags: combinatorics unsolved, combinatorics



In each field of 2009*2009 table you can write either 1 or -1. Denote Ak multiple of all numbers in k-th row and Bj the multiple of all numbers in j-th column. Is it possible to write the numbers in such a way that $ \sum_{i=1}^{2009}{Ai}+ \sum_{i=1}^{2009}{Bi}=0$?