The three vertices of a triangle are lattice points. The triangle contains no other lattice points but its interior contains exactly one lattice point.

Prove that the interior lattice point is the triangle's centroid.

(In reply to re: One Solution (spoiler) by Dej Mar)

There are at least 2 more ways to draw a triangle as required:
Here are the four I found each given so that its centroid is the origin

(0,-1) (1,0) (-1,1)
(0,-1) (1,-1) (-1,2)
(0,-1) (1,-2) (-1,3)
(0,-1) (1,-3) (-1,4)

Posted by Jer on 2011-04-11 11:40:09