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  3. A marching band of 240 musicians are to march in a rectangular formation with m rows of exactly n musicians each. There can be n

A marching band of 240 musicians are to march in a rectangular formation with m rows of exactly n musicians each. There can be n

admin2021-10-21  125
问题 A marching band of 240 musicians are to march in a rectangular formation with m rows of exactly n musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations are possible?
选项 A、7
B、4
C、6
D、7
E、8
答案E
解析 题意是240个乐师要排成m排，每排n个，组成一个长方形阵，并且每排人数8≤n≤30，问能够组成多少个不同的矩形形状?
240=m×n，此题其实问的是240有多少个因子在8到30之间；
240=3×5×24，用枚举法列出8到30的因子：8，10，12，15，16，20，24，30，一共8个，选择E。
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