A board of size 2015×2015 is covered with sub-boards of size 2×2, each of which is painted like chessboard. Each sub-board covers exactly 4 squares of the board and each square of the board is covered with at least one square of a sub-board (the painted of the sub-boards can be of any shape). Prove that there is a way to cover the board in such a way that there are exactly 2015 black squares visible. What is the maximum number of visible black squares? combinatoricsgridColoring