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A board painted

Source: Mathematics Regional Olympiad of Mexico Southeast 2021 P4

October 22, 2021
combinatoricsboardMexico

Problem Statement

Hernan wants to paint a 8×88\times 8 board such that every square is painted with blue or red. Also wants to every 3×33\times 3 subsquare have exactly aa blue squares and every 2×42\times 4 or 4×24\times 2 rectangle have exactly bb blue squares. Find all couples (a,b)(a,b) such that Hernan can do the required.
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