MathDB

Given a

n\times n

table with non-negative real entries such that the sums of entries in each column and row are equal, a player plays the following game: The step of the game consists of choosing

n

cells, no two of which share a column or a row, and subtracting the same number from each of the entries of the

n

cells, provided that the resulting table has all non-negative entries. Prove that the player can change all entries to zeros.

Problem Statement