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MathNet 2011 Question 28

Math Olympiad Vault · MathNet 2011

Question 28

Several chess players took part in a chess tournament. Each participant played exactly one game with any other participant. A participant received 1 point for a win, 0.5 point for a draw, and 0 point for a lose. Any two players received different numbers of points.
What is the smallest number of the wins of the participant taking the first place?
Find the greatest possible value of the points received by the participant taking the last place.
(Jury)