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 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