### IMO Shortlist 2010 problem C5

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Avg: 8.0 players participated in a tennis tournament. Any two players have played exactly one game, and there was no tie game. We call a company of four players if one player was defeated by the other three players, and each of these three players won a game and lost another game among themselves. Suppose that there is no bad company in this tournament. Let and be respectively the number of wins and losses of the -th player. Prove that

Proposed by Sung Yun Kim, South Korea

Proposed by Sung Yun Kim, South Korea

Source: Međunarodna matematička olimpijada, shortlist 2010