MathDB

4

Part of 2023 Greece National Olympiad

Problems(1)

Find maximal N such that no two are pairs

Source: Greece National Olympiad 2023, Problem 4

2/19/2023
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 NN such that, regardless of the students' sitting positions, at the end there is a set SS consisting of NN students satisfying the following property: every two of them have never been sitting together.
combinatorics