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paint the squares of a 6 x 6 board black or white

Source: 2019 Dürer Math Competition Finals Day2 E16 E+9 https://artofproblemsolving.com/community/c1621835_2019_

January 5, 2022
combinatoricsColoring

Problem Statement

How many ways are there to paint the squares of a 6×66 \times 6 board black or white such that within each 2×22\times 2 square on the board, the number of black squares is odd?
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