n x n Table With Numbers
Source: Spring 2006 Tournament of Towns Junior O-Level #2
April 15, 2015
Problem Statement
A table is filled with the numbers as follows: the first column is filled with ’s, the second column with ’s, and so on. Then, the numbers on the main diagonal (from top-left to bottom-right) are erased. Prove that the total sums of the numbers on both sides of the main diagonal differ in exactly two times.(3 points)