IMO Shortlist 2004 problem C4


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2. travnja 2012.
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Consider a matrix of size n\times n whose entries are real numbers of absolute value not exceeding 1. The sum of all entries of the matrix is 0. Let n be an even positive integer. Determine the least number C such that every such matrix necessarily has a row or a column with the sum of its entries not exceeding C in absolute value.
Izvor: Međunarodna matematička olimpijada, shortlist 2004