Is it possible to color each square on a $9\times 9$ board so that each $2\times 3$ or $3\times 2$ block contains exactly $2$ black squares? If so, what is/are the possible total number(s) of black squares?
Source: Singapore Senior Math Olympiad 2015 2nd Round p4 SMO
Tags: Coloring, combinatorics
Is it possible to color each square on a $9\times 9$ board so that each $2\times 3$ or $3\times 2$ block contains exactly $2$ black squares? If so, what is/are the possible total number(s) of black squares?