Given an NxN grid, your mission is to select the maximum number of gridpoints such that no three are collinear. Obviously, it is impossible to select more than 2N points, because then at least 3 would lie on a horizontal gridline. So if you can find 2N, your solution automatically is optimal. For each N=2,3,4,5,..., 46, solutions with 2N points have been found. ** ** and **. *.* .** and *.*. ..** **.. .*.* are sample solutions for N=2, 3 and 4 respectively. However, it is unknown whether a 2N-point solution exists with N=47. More importantly, what happens when N-->infinity? It is known that a solution on an NxN grid with at least (1.5-epsilon)*N points always exists where epsilon-->0 for N large. Can the lower-bound constant 1.5 be increased? Can the upper-bound constant 2 be decreased? Are there an infinite set of 2N-point solutions? Problem originally posed by Dudeney 1917.