Maximizing the Difference
In a board, we place a real number in every square. If the sum of the numbers in any row or column is , find the maximum value of .
The answer is 0.
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1 solution
Consider the sum of all elements in the table. Summing by rows, the sum is m . Summing by columns, the sum is n . Hence, m = n always, which means that the answer is 0 .