Problem

Source: CRMO 2014 region 2 p6

Tags: combinatorics, number theory, grid



Suppose n is odd and each square of an n×n grid is arbitrarily filled with either by 1 or by 1. Let rj and ck denote the product of all numbers in j-th row and k-th column respectively, 1j,kn. Prove that nj=1rj+nk=1ck0