Problem

Source: 2024 Korea Summer Program Practice Test Junior P5

Tags: combinatorics



Call a set \(\{a,b,c,d\}\) epic if for any four different positive integers \(a, b, c, d\), there is a unique way to select three of them to form the sides of a triangle. Find all positive integers \(n\) such that \(\{1, 2, \ldots, 4n\}\) can be partitioned into \(n\) disjoint epic sets.