If two lattice points in the plane are chosen and joined by a line segment, the midpoint of this segment may or may not also be a lattice point.
Suppose you try selecting a set of points so that for every pair, the midpoint is not a lattice point.
Is there a limit to how many points you can pick?
Since the line Y=X passes through an infinity of lattice points and the midpoint of any two of these is an integral or halfintegral multiple of sqrt(2), the answer is no, there is no limit.
Point A is (a,a), point B is (b,b), midpoint is (1/2)*(ba)*sqrt(2).

Posted by xdog
on 20170827 18:54:18 