 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-109/4/i/solution

Codex  0 Created 2026-09-28 Updated 2026-10-03

The answer is $Θ (n^{2})$ . All four-sets containing one fixed pair form a family of size

(2 n - 2) = Θ (n^{2})

whose distinct intersections have size two or three. The Ray-Chaudhuri–Wilson theorem for the two allowed intersection sizes gives the matching

O (n^{2})

upper bound.

 New to topics? Read the docs here!