2000 AMC 8 第 5 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。

5.

Lincoln High School 的每位校长任期恰好为 33 年。在一段 88 年期间,这所学校最多可能有多少位校长?

Each principal of Lincoln High School serves exactly one 33-year term. What is the maximum number of principals this school could have during an 88-year period?

22

33

44

55

88

答案:C
知识点:最优化
难度评级:770
解答:

为了让校长人数最多,假设这段时间的第一年是某位校长任期的最后一年。

接着可以有 22 位校长完成接下来的 66 年,然后再有一位校长任最后一年。

总共是 44 位校长。

所以正确答案是 C

To maximize the number of principals, assume that the first year of this period is the final year of some principal's term.

Then, there can be 22 more principals for 66 years, followed by another principal who works the final year.

This is 44 principals.

Thus, C is the correct answer.

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