Cyclical 3-subsets
Source: Italian TST , day 1, n°2
June 1, 2007
modular arithmeticcombinatorics proposedcombinatorics
Problem Statement
In a competition, there were 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 if won against , won against , won against .
(a) Find the minimum of cyclical 3-subset (depending on );
(b) Find the maximum of cyclical 3-subset (depending on ).