AMC8 2016

AMC8 2016 · Q18

AMC8 2016 · Q18. It mainly tests Basic counting (rules of product/sum), Counting & probability misc.

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?

在全区田径比赛中，有 216 名短跑运动员参加 100 米短跑比赛。跑道有 6 条道，因此每次只能有 6 名运动员比赛。每场比赛结束后，五名非获胜者被淘汰，获胜者将在稍后的比赛中再次参赛。需要多少场比赛才能确定冠军短跑运动员？

(A) 36 36

(B) 42 42

(D) 60 60

(E) 72 72

Answer

Correct choice: (C)

正确答案：（C）

Solution

Divide the 216 sprinters into 36 groups of 6. Run 36 races to eliminate 180 sprinters, leaving 36 winners. Divide the 36 winners into 6 groups of 6, run 6 races to eliminate 30 sprinters, leaving 6 winners. Finally run the last race to determine the champion. The number of races run is $36+6+1 = 43$.

将216名短跑选手分成36组，每组6人。进行36场比赛淘汰180名选手，剩下36名获胜者。把这36名获胜者再分成6组，每组6人，再进行6场比赛淘汰30名选手，剩下6名获胜者。最后再进行一场决赛以确定冠军。比赛总场数为 $36+6+1 = 43$。

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