The no-three-in-a-line problem is the problem of placing points on an n×n grid such that no three points lie on a common line. This includes lines of any direction, not just lines that are parallel to the grid axes.

Trivially, this can be done with at most 2n points, since a set of 2n+1 points must contain at least three that are in the same row (and at least 3 in the same column), and are thus colinear. It is known that solutions containing exactly 2n points exist for n ≤ 46, but it is not known whether they exist for all n.