Tournament
Source: Taiwan 1st TST 2005, final exam, first day, problem 3
August 12, 2005
linear algebramatrixquadraticscombinatorics proposedcombinatorics
Problem Statement
teams take part in a tournament, in which every two teams compete exactly once, and that no draws are possible. It is known that for any two teams, there exists another team which defeated both of the two teams. Find all for which this is possible.