MathDB
n x n Table With Numbers

Source: Spring 2006 Tournament of Towns Junior O-Level #2

April 15, 2015

Problem Statement

A n×nn \times n table is filled with the numbers as follows: the first column is filled with 11’s, the second column with 22’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)