MathDB

Let

n

be a positive with

n\geq 3

. Consider a board of

n \times n

boxes. In each step taken the colors of the

5

boxes that make up the figure bellow change color (black boxes change to white and white boxes change to black) The figure can be rotated

90°, 180°

270°

. Firstly, all the boxes are white.Determine for what values of

n

it can be achieved, through a series of steps, that all the squares on the board are black.

Problem Statement