Question 86
Every cell of table $4 \times 4$ is colored white. It is permitted to place the cross (pictured below) on the table such that its center lies on the table (the whole figure does not need to lie on the table) and change the color of every cell which is covered to the opposite one (white and black). Find all $n$ such that after $n$ steps it is possible to get the table with every cell colored black.
