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?

Seems very easy : IMHO

**4 is the upper limit.**There only 4 possible coordinates mod 2 :

point A (0,0),

point B (0,1),

point C (1,0),

point D(1,1)

====

Point E will be a match for one of the above ,say B - so the midpoint of EB** WILL HAVE INTEGER COORDINATES.**

*Edited on ***August 27, 2017, 10:52 pm**