2016 AMC 8 第 18 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

18.

在一次全地区田径赛中,216216 名短跑运动员参加 100100 米短跑比赛。跑道有 66 条道,所以一次只能有 66 名运动员比赛。每场比赛结束后,五名非获胜者被淘汰,获胜者将在后面的比赛中继续参赛。

需要多少场比赛才能决出短跑冠军?

In an All-Area track meet, 216216 sprinters enter a 100100-meter dash competition. The track has 66 lanes, so only 66 sprinters can compete at a time. At the end of each race, the five non-winners are eliminated, and the winner will compete again in a later race.

How many races are needed to determine the champion sprinter?

3636

4242

4343

6060

7272

答案:C
知识点:基本计数
难度评级:1170
视频讲解:
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文字解答:

每场比赛淘汰 55 人。 要决出冠军,需要淘汰 215215 人。 因此需要 215/5=43215 / 5 = 43 场比赛。

所以正确答案是 C

Note that each race eliminates 55 people. For there to be a winner, 215215 must be eliminated. Therefore, 215/5=43215 / 5 = 43 races are required to eliminate this number of people.

Thus, C is the correct answer.

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