MathDB
Pluses and minuses in a 30 x 30 table

Source: Baltic Way 2006

December 4, 2010
combinatorics proposedcombinatorics

Problem Statement

162162 pluses and 144144 minuses are placed in a 30×3030\times 30 table in such a way that each row and each column contains at most 1717 signs. (No cell contains more than one sign.) For every plus we count the number of minuses in its row and for every minus we count the number of pluses in its column. Find the maximum of the sum of these numbers.