MathDB
Cyclical 3-subsets

Source: Italian TST , day 1, n°2

June 1, 2007
modular arithmeticcombinatorics proposedcombinatorics

Problem Statement

In a competition, there were 2n+12n+1 teams. Every team plays exatly once against every other team. Every match finishes with the victory of one of the teams. We call cyclical a 3-subset of team A,B,C{ A,B,C } if AA won against BB, BB won against CC , CC won against AA. (a) Find the minimum of cyclical 3-subset (depending on nn); (b) Find the maximum of cyclical 3-subset (depending on nn).