Volleyball championship
Source: Moscow mathematic olympiad 2022, Day 2 P11.2
September 29, 2022
combinatorics
Problem Statement
The volleyball championship with teams was held in one round (each team played with each exactly one
times, there are no draws in volleyball). It turned out that some two teams won the same number of matches.
Prove there are the three teams that beat each other in a round robin (i.e. A beat B, B beat C, and C beat A).