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5.

Part of 2022 Polish Junior Math Olympiad Finals

Problems(1)

2022 Polish Junior Math Olympiad Finals P5

Source: 2022 Polish Junior Math Olympiad Finals P5

5/21/2023
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 00.
https://wiki-images.artofproblemsolving.com//2/2e/17-3-5.png
combinatorics