KöMaL problem A, 2024

Combinatorics Difficulty 7.0 National Olympiad, round 2 Find the answer Hungary

We fill in an $n\times n$ table with real numbers such that the sum of the numbers in each row and each coloumn equals 1. For which values of $K$ is the following statement true: if the sum of the absolute values of the negative entries in the table is at most $K$ , then it's always possible to choose $n$ positive entries of the table such that each row and each coloumn contains exactly one of the chosen entries.

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