MathDB

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.
Proposed by Marcin Kuczma, Poland

Problem Statement