imc

Since there are five types of squares: $1\times 1,2\times 2,3\times 3,4\times 4,$ and $5\times 5.$ We must find how many of each square contain the black shaded square in the center. If we list them, we get that There is $1$ of all $1\times 1$ squares, containing the black square There are $4$ of all $2\times 2$ squares, containing the black square There are $9$ of all $3\times 3$ squares, containing the black square There are $4$ of all $4\times 4$ squares, containing the black square * There is $1$ of all $5\times 5$ squares, containing the black square Thus, the answer is $1+4+9+4+1=19\Rightarrow \boxed{19}$.