Start with a $7 \times 7$ grid of houses where the center house is white and the other 48 houses are black. At each move, you select any $3 \times 3$ or $5 \times 5$ sub-grid and change the color of all its houses (from white to black and vice versa).
Is it possible to make all the cells of the $7 \times 7$ grid white with some sequence of moves? If not, why not?
My idea is to use coloring method to show is there possible to make the color of third row same with last and first row, but I got nowhere.