Problem

Source: South African Mathematics Olympiad 2022, Problem 1

Tags: combinatorics



Consider $16$ points arranged as shown, with horizontal and vertical distances of $1$ between consecutive rows and columns. In how many ways can one choose four of these points such that the distance between every two of those four points is strictly greater than $2$? [asy][asy] for (int x = 0; x < 4; ++x) { for (int y = 0; y < 4; ++y) { dot((x, y)); } } [/asy][/asy]