Turkish NMO First Round - 2012 Problem - 16 {Combinatorics}
Source:
July 1, 2012
Problem Statement
Every cell of 8×8 chessboard contains either 1 or −1. It is known that there are at least four rows such that the sum of numbers inside the cells of those rows is positive. At most how many columns are there such that the sum of numbers inside the cells of those columns is less than −3?<spanclass=′latex−bold′>(A)</span>6<spanclass=′latex−bold′>(B)</span>5<spanclass=′latex−bold′>(C)</span>4<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>2