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real numbers from [0, 1] into (mn + 1) x (mn + 1) table

Source: Czech-Polish-Slovak Junior Match 2017, individual p5 CPSJ

February 20, 2020
combinatorics

Problem Statement

Each field of the table (mn+1)×(mn+1)(mn + 1) \times (mn + 1) contains a real number from the interval [0,1][0, 1]. The sum the numbers in each square section of the table with dimensions nxnn x n is equal to nn. Determine how big it can be sum of all numbers in the table.
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