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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
admin
2021-10-21
115
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=3×5×2
4
,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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