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MathNet 2011 Question 81

Math Olympiad Vault · MathNet 2011

Question 81

In volleyball tournament there are 8 teams, that play one-round tournament (each team plays exactly one game with another). Each win worth 1 point, each lose worth 0 points, there are no draws in volleyball. After tournament is finished, if the difference between the first and the second place, does not exceed 1 point, then they play one extra game. The same applies for the teams that scored 3-d and 4-th, 5-th and 6-th, and 7-th and 8-th respectively. What is the least number of extra games can occur?

Note. After tournament is finished each place takes only one team, even though two teams can have the same number of points.