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2019 Cono Sur Mathematical Olympiad, P5

Source:

August 28, 2019
combinatoricstilescountingcono sur

Problem Statement

Let n≥3n\geq 3 a positive integer. In each cell of a n×nn\times n chessboard one must write 11 or 22 in such a way the sum of all written numbers in each 2×32\times 3 and 3×23\times 2 sub-chessboard is even. How many different ways can the chessboard be completed?
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