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table $(2k + 1) \times (2k + 1)$ is filled with real numbers not exceeding 1 in

Source: 2016 239 S8

October 11, 2020
combinatoricstable

Problem Statement

Given a natural number k>1k>1. Find the smallest number α\alpha satisfying the following condition. Suppose that the table (2k+1)×(2k+1)(2k + 1) \times (2k + 1) is filled with real numbers not exceeding 11 in absolute value, and the sums of the numbers in all lines are equal to zero. Then you can rearrange the numbers so that each number remains in its row and all the sums over the columns will be at most α\alpha.
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