In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero points.…
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In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero points. Which of the following sequences cannot represent the scores of the five players?
- 2, 2, 2, 2, 2
- 3, 2, 2, 2, 1
- 3, 3, 2, 1, 1
- 4, 4, 1, 1, 0
Answer and explanation
Correct answer: D - 4, 4, 1, 1, 0
Each player plays 4 games; the 10 games give 10 points in total. In 4,4,1,1,0 two players would both be unbeaten, impossible since they played each other. The other sequences sum to 10 and satisfy the score-sequence (Landau) conditions.
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