Suppose a finite number of players play a round-robin tournament, with everyone playing everyone else exactlyonce. each match has a winner and a loser (no ties). we say that the tournament has acycle of length mif there exist m players {p_1,p_2, . . ,p_m} such that p_1 beats p_2, who beats p_3, who beats p_m, who beats p_1. clearly this is possible only form ≥ 3.using mathematical induction, prove that if such a tournament has a cycle of length m, for some m≥3, then ithas a cycle of length 3.