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cross with +1´s

Source: Mathematics Regional Olympiad of Mexico Southeast 2020 P4

October 23, 2021
combinatorics

Problem Statement

Consider a cross like in the figure but with size 20212021. Every square have a +1+1. Every minute we select a sub-cross of size 33 and multiply their squares by −1-1. It´s posible achieve that all the squares of the cross with size 20212021 have a −1-1?
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