Problem

Source: : 2019 Romania JBMO TST 2.4

Tags: combinatorics, table, square table



In every unit square of a$ n \times n$ table ($n \ge 11$) a real number is written, such that the sum of the numbers in any $10 \times 10$ square is positive and the sum of the numbers in any $11\times 11$ square is negative. Determine all possible values for $n$