In a badminton tournament, each of n players play all the other n−1 players. Each game results in either a win, or a loss. The players then write down the names of those whom they defeated, and also of those who they defeated. For example, if A beats B and B beats C, then A writes the names of both B and C. Show that there will be one person, who has written down the names of all the other n−1 players.
[hide="Clarification"]
Consider a game between A,B,C,D,E,F,G where A defeats B and C and B defeats E,F, C defeats E. Then A's list will have (B,C,E,F), and will not include G.
inductioncombinatorics proposedcombinatorics