No‑Three‑In‑Line

The No-three-in-line problem asks how many points can be placed on a n × n n \times n n × n grid so that no three points are on the same line, where the lines considered are of any slope and not just orthogonal and diagonal. Each row/column can contain at most 2 points, so clearly the answer is at most 2 n 2n 2 n . The real question is, can we actually achieve 2 n 2n 2 n for every grid size? It’s…