We want to draw a number of straight lines such that for each square of a chessboard, at least one of the lines passes through an interior point of the square. What is the smallest number of lines needed for a
(a) 3×3;
(b) 4×4
chessboard? Use a picture to show that this many lines are enough, and prove that no smaller number would do. (M Vyalyi) combinatoricscombinatorial geometryChessboard