From $25$ points in a plane, both of whose coordinates are integers of the set $\{-2,-1, 0, 1, 2\}$, some $17$ points are marked. Prove that there are three points on one line, one of them is the midpoint of two others.
Problem
Source: 2004 Estonia National Olympiad Final Round grade 11 p 3
Tags: combinatorics, combinatorial geometry