MathDB

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.
Proposed by Dávid Bencsik, Budapest

Problem Statement