1991 AMC 8 第 17 题
先试着解答 1991 AMC 8 第 17 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1991 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
17.
一个礼堂有 排座位，第一排有 个座位。之后每一排都比前一排多一个座位。如果参加考试的学生可以坐在任何一排，但同一排中不能与另一个学生相邻，那么最多能安排多少名学生考试？
An auditorium with rows of seats has seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, then the maximum number of students that can be seated for an exam is
小提示：
一排有 个座位时，若不能相邻，最多可坐 人
In a row of seats, the most students with no two adjacent is
大提示：
第 排有 个座位；将 在前 排中相加
Row has seats; add over the rows
解答：
第 排有 个座位，所以最多坐 人。第 到第 排的座位数从 到 ，对应最大人数为 、、、、、、、、、、。
这些数相加为 。
所以正确答案是 C。
Row has seats, so it holds students. For rows through (seats through ) the maxima are
These sum to
Thus, the correct answer is C .
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