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in a tournament every team plays every other team just once

Source: 1976 Swedish Mathematical Competition p1

March 26, 2021
combinatorics

Problem Statement

In a tournament every team plays every other team just once. Each game is won by one of the teams (there are no draws). Each team loses at least once. Show that there must be three teams AA, BB, CC such that AA beat BB, BB beat CC and CC beat AA.
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