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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: spoiler | Comment 3 of 4 |
(In reply to spoiler by xdog)

huh?  Ady is right.  No sqrt(2) is involved.  The midpoint of (a,b) and (c,d) is ((a+c)/2,(b+d)/2).  It is a lattice point if and only if a and c are of the same parity, and b and d are also of the same parity.  And thus the set of points are limited to 4.
  Posted by Steve Herman on 2017-08-27 19:29:52

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