Non-negative numbers in a table, row sum larger than column sum
Source: Bundeswettbewerb Mathematik 2020, Round 2 - Problem 4
November 17, 2020
combinatoricsinequalitiesnonnegativeSum
Problem Statement
In each cell of a table with rows and columns, where , we put a non-negative real number such that each column contains at least one positive number.Show that there is a cell with a positive number such that the sum of the numbers in its row is larger than the sum of the numbers in its column.