MathDB
A wins against B, B wins against C, and C wins against A, in tennis tournament

Source: Dutch NMO 2009 p3

September 6, 2019
combinatoricsTournament

Problem Statement

A tennis tournament has at least three participants. Every participant plays exactly one match against every other participant. Moreover, every participant wins at least one of the matches he plays. (Draws do not occur in tennis matches.) Show that there are three participants A,BA, B and CC for which the following holds: AA wins against B,BB, B wins against CC, and CC wins against AA.
Back to ProblemsView on AoPS