Question

一场单打网球锦标赛有 $100$ 名选手。比赛采用单败淘汰制，即输一场就被淘汰。第一轮中最强的 $28$ 名选手轮空，其余 $72$ 名选手配对比赛。之后每轮剩余选手继续比赛，直到只剩一名未败选手。总比赛场数

There are $100$ players in a singles tennis tournament. The tournament is single elimination, meaning that a player who loses a match is eliminated. In the first round, the strongest $28$ players are given a bye, and the remaining $72$ players are paired off to play. After each round, the remaining players play in the next round. The match continues until only one player remains unbeaten. The total number of matches played is

是质数

a prime number

能被 $2$ 整除

divisible by $2$

能被 $5$ 整除

divisible by $5$

能被 $7$ 整除

divisible by $7$

能被 $11$ 整除

divisible by $11$

答案：E

知识点：基本计数不变量

难度评级：1280

解答：

每场比赛淘汰一名选手。共有 $100$ 名选手开始，除冠军外都被淘汰，所以有 $99$ 场比赛。

因为 $99=9 \cdot 11$ ，所以比赛场数能被 $11$ 整除。

所以正确答案是 E。

Each match eliminates exactly one player. Since $100$ players start and all but the champion are eliminated, there are $99$ matches.

Because $99=9 \cdot 11,$ it is divisible by $11$ but satisfies none of the other options.

Thus, the correct answer is E.

2003 AMC 10B 第 15 题

答案：E

难度评级：1280

解答：

其他年份的第 15 题