DE-BUNDESWETTBEWERB 2020 Problem 8
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.
Dataset text AI-MO AoPS. Quoted with source.
Official text: Bundeswettbewerb Mathematik 2020 official paper, page 1.
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