2022 Polish Junior Math Olympiad Finals P5
Source: 2022 Polish Junior Math Olympiad Finals P5
May 21, 2023
combinatorics
Problem Statement
In the table shown in the figure, Zosia replaced eight numbers with their negatives. It turned out that each row and each column contained exactly two negative numbers. Prove that after this change, the sum of all sixteen numbers in the table is equal to .
https://wiki-images.artofproblemsolving.com//2/2e/17-3-5.png