Each cell of a 1997x1997 square grid contains either +1 or -1, with no cell being vacant.

The product of all the numbers in the ith row, and the product of all the numbers in the ith column are respectively denoted by R_i and C_i.

               1997
Prove that  Σ_i=1(R_i + C_i) is always nonzero.

(In reply to a simple proof by Ady TZIDON)

I think you misread the problem, you have Ri and Ci as the sum of the row/column where in fact they are the products of the row/column.

Posted by Daniel on 2010-04-29 15:29:54