MathDB

In a sport competition,

m

teams have participated. We know that each two teams have competed exactly one time and the result is winning a team and losing the other team (i.e. there is no equal result). Prove that there exists a team

x

such that for each team

y,

either

x

wins

y

or there exists a team

z

for which

x

wins

z

and

z

wins

y.

[i.e. prove that in every tournament there exists a king.]

Problem Statement