AMC 8 2006 Problem 20
AMC8 2006 年第 20 题
基本计数原理★★★☆☆
A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did Monica win?
某个单打比赛有六名选手。每个选手和其他每个选手都比赛一次，没有平局。如果 Helen 赢了 4 场比赛，Ines 赢了 3 场比赛，Janet 赢了 2 场比赛，Kendra 赢了 2 场比赛，Lara 赢了 2 场比赛，则 Monica（第六个选手）赢了多少场比赛？
- A.0
- B.1
- C.2
- D.3
- E.4
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Since there are 6 players, a total of games are played. So far, 4+3+2+2+2=13 games finished (one person won from each game), so Monica needs to win 15-13 = 2. SOLUTION NUMBER 2 (Similar to the first one) There are six players, so to find the total number of games played, we must do 5+4+3+2+1=15. Next we add 4+3+2+2+2=13. Since, every win represents one game and there are 15 games, Monica has to win 15-13=2 games. So the answer is (c). -This is by someone SOLUTION NUMBER 2 (Similar to the first one) There are six players, so to find the total number of games played, we must do 5+4+3+2+1=15. Next we add 4+3+2+2+2=13. Since, every win represents one game and there are 15 games, Monica has to win 15-13=2 games. So the answer is (c). -This is by someone.
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