It doesn't have to go to infinity. Look at this solution for 9 dots/three lines: http://www.goodmorningcreativity.com/wp-content/uploads/2010/10/9-dot-puzzle-3

It doesn't have to go to infinity. Look at this solution for 9 dots/three lines: http://www.goodmorningcreativity.com/wp-content/uploads/2010/10/9-dot-puzzle-3-lines-solution.jpg http://www.goodmorningcreativity.com/wp-content/uploads/2010... That scales up to whatever sized square of dots you like, provided the "dots" are not points but are circles with a non-zero diameter.