For any grid, x by x, figure out a formula for the greatest number of points that can be put on the inside of the grid such that no three points are colinear.

(In reply to So at least the first 32 are reachable... by Jer)

Maybe it's the algorithm Flammenkamp uses to find solutions, but it struck me that the 52x52 grid shown in the link Jer provided is 90° rotationally symetric.  I think some of the earlier solutions posted were similarly rotationally symetric (4x4).

It's also interesting to notice that in the 52x52 case, the corners are rather vacant, and occupied spaces seem to partially fill a circle.

Posted by Erik O. on 2005-05-20 14:44:29