Problem

Source: 2018 China North Mathematical Olympiad Grade 10 Test 1 P4

Tags: combinatorics, China, Find maximum



In each square of a $4$ by $4$ grid, you put either a $+1$ or a $-1$. If any 2 rows and 2 columns are deleted, the sum of the remaining 4 numbers is nonnegative. What is the minimum number of $+1$'s needed to be placed to be able to satisfy the conditions