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1000 red squares in 1999x1999 board (Chile NMO 1999 P3)

Source:

November 27, 2021
combinatoricsColoring

Problem Statement

It is possible to paint with the colors red and blue the squares of a grid board 1999×19991999\times 1999, so that in each of the 19991999 rows, in each of the 19991999 columns and each of the the 22 diagonals are exactly 10001000 squares painted red?
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