2-day team competition in chess, 3 schools with 15 pupils each attend
Source: Norwegian Mathematical Olympiad 2001 - Abel Competition p4
February 22, 2020
combinatorics
Problem Statement
At a two-day team competition in chess, three schools with pupils each attend. Each student plays one game against each player on the other two teams, ie a total of chess games per student.
a) Is it possible for each student to play exactly games after the first day?
b) Show that it is possible for each student to play exactly games after the first day.
c) Assume that each student has played exactly games after the first day. Show that there are three students, one from each school, who have played their three parties