Chess Tournament
Source: 2003 IrMO Paper 1 Problem 4
December 28, 2017
combinatorics
Problem Statement
Eight players, Ann, Bob, Con, Dot, Eve, Fay, Guy and Hal compete in a chess tournament. No pair plays together more than once and there is no group of five people in which each one plays against all of the other four.(a) Write down an arrangement for a tournament of games satisfying these conditions.(b) Show that it is impossible to have a tournament of more than games satisfying these conditions.