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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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spoiler | Comment 2 of 3 |
Since the line Y=X passes through an infinity of lattice points and the mid-point of any two of these is an integral or half-integral 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)*(b-a)*sqrt(2).

  Posted by xdog on 2017-08-27 18:54:18
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