AMC 8 2016 Problem 18

AMC8 2016 年第 18 题

基本计数原理★★★☆☆

In an All-Area track meet, 216 sprinters enter a 100- meter dash competition. The track has 6 lanes, so only 6 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?

在一次全区田径比赛中，共有 216 个短跑运动员角逐 100 米冲刺赛。比赛一共有 6 个赛道，因此一次只允许 6 个短跑运动员同时比赛。每场比赛结束后，会淘汰掉其中 5 人，胜者将参与到下一次比赛中。问一共需要多少场比赛才能确定整个比赛最终的冠军？

A.36
B.42
C.43
D.60
E.72

正确答案 · Correct Answer

解析 · Solution

Solution 1

From any n- th race, only

\displaystyle \frac{1}{6}

will continue on. Since we wish to find the total number of races, a column representing the races over time is ideal. Starting with the first race:

\displaystyle \frac{216}{6}=36

\displaystyle \frac{36}{6}=6

\displaystyle \frac{6}{6}=1

Adding all of the numbers in the second column yields 43

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