How many ways are there to paint the squares of a $6 \times 6$ board black or white such that within each $2\times 2$ square on the board, the number of black squares is odd?
Problem
Source: 2019 Dürer Math Competition Finals Day2 E16 E+9 https://artofproblemsolving.com/community/c1621835_2019_
Tags: combinatorics, Coloring