Question 15
Martha is a chicken who lives in a coop whose finitely many residents have a definite "pecking order": for every pair of distinct chickens, exactly one pecks the other. (However, it is not necessarily true that if $X$ pecks $Y$ and $Y$ pecks $Z$, then $X$ pecks $Z$.) A chicken $X$ is called a "leader" of the coop if every other chicken is pecked by $X$ or pecked by a chicken who is pecked by $X$. Prove that if no one in the coop pecks more chickens than Martha, then Martha is a leader.