Find maximal N such that no two are pairs
Source: Greece National Olympiad 2023, Problem 4
February 19, 2023
combinatorics
Problem Statement
A class consists of 26 students with two students sitting on each desk. Suddenly, the students decide to change seats, such that every two students that were previously sitting together are now apart. Find the maximum value of positive integer such that, regardless of the students' sitting positions, at the end there is a set consisting of students satisfying the following property: every two of them have never been sitting together.