In a badminton singles tournament, each player played against all the others exactly once and each game had a winner. After all the games, each player listed the names of all the players she defeated as well as the names of all the players defeated by the players defeated by her. For instance, if A defeats B and B defeats C, then in the list of A both B and C are included. Prove that at least one player listed the names of all other players.
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Did you try induction? – Leif Sabellek May 10 '14 at 15:21
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This is not a question about probablity. You will find more help if you tag your question under "discrete mathematics". – user137481 May 10 '14 at 22:15
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@Leif Sabellek no idea how to proceed with induction. I have only tried trial and error. – Rudstar May 11 '14 at 03:42
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This is basically reformulation of the problem given here. The solution can be also found here and in Bona's book A Walk through Combinatorics. – Martin Sleziak Nov 21 '16 at 17:25