MathDB

6

Part of 2006 Switzerland - Final Round

Problems(1)

A won against B, B won against C and C won against A

Source: Switzerland - 2006 Swiss MO Final Round p6

12/26/2022
At least three players have participated in a tennis tournament. Evey two players have played each other exactly once, and each player has at least one match won. Show that there are three players A,B,CA,B,C such that AA won against BB, BB won against CC and CC won against AA.
combinatorics