This does not look like a mathematical chess problem. But this problem can be made to look like a mathematical chess problem. If we consider a 20×20 chessboard then two squares that are at a distance of √5 (distance between the centers of the squares) are squares that can be occupied by attacking knights. So the number of elements in B is the maximum number of non-attacking knights on the 20×20 chessboard. So what is the maximum number of non-attacking knights that can be placed on a 20×20 chessboard? Since a knight always move from a black square to a white square and vice versa it is clear that knights placed on all white color squares or all black color squares are non-attacking. So 200 non-attacking knights can be placed on the chessboard. Is this the maximum? We can pair all the squares in the chessboard as shown below for 4 squares: