Problem

Source: European Mathematical Cup 2012, Junior Division, Problem 4

Tags: induction, strong induction, combinatorics proposed, combinatorics, Tournament graphs, Hamiltonian path



Let k be a positive integer. At the European Chess Cup every pair of players played a game in which somebody won (there were no draws). For any k players there was a player against whom they all lost, and the number of players was the least possible for such k. Is it possible that at the Closing Ceremony all the participants were seated at the round table in such a way that every participant was seated next to both a person he won against and a person he lost against. Proposed by Matija Bucić.