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Board and numbers

Source: Polish Junior Math Olympiad 2019 Finals

October 23, 2020
combinatorics

Problem Statement

In the every cell of the board 5×55\times5 there is one of the numbers: −1-1, 00, 11. It is true that in every 2×22 \times 2 square there are three numbers summing up to 00. Determine the maximal sum of all numbers in a board.
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