First, select at least 3 squares. Because in addition to the two blank cells in the lower left corner, there are 15 blank cells, that is, 1 blank areas are connected together. Suppose that the X cell needs coloring, it should be divided into at least (15-X)/3 to take an integer, and then+1.

Divide 2 blank areas (3 in the middle) for each drawn grid;

X= 1, at least 5 blank areas, and the maximum blank area is1-> 3, the assumption is not established;

X=2, at least 5 blank areas, and the maximum blank area is1-> 3, 3->4, the assumption is not established;

X=3, at least four blank areas, (1, 3), (3, 4) and (4, 2) are just colored, so at least three squares are colored.

Secondly, if it is replaced by a 6X6 rectangular frame, there are 1 regions and 16 blank grids in addition to the regions we divided above. The partition efficiency of (2, 1) and (5, 1) is the highest. Each 1 grid can be divided into two areas, and the rest.

So the total * * * needs at least 3+2+3=8 squares.

Hope to adopt ~ ~