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Avoiding lattice midpoints (Posted on 2017-08-27) Difficulty: 2 of 5
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?

No Solution Yet Submitted by Jer    
Rating: 5.0000 (1 votes)

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Solution Parity consideration s ..............spoilert | Comment 1 of 3
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
  Posted by Ady TZIDON on 2017-08-27 10:45:18

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