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+1's and -1's in a 4x4 grid

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

July 26, 2018

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Problem Statement

In each square of a

4

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