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A band has 72 members who will all be marching during halftime. They need to march in rows with the same number of students per row. If there must be between 5 and 20 students per row, in how many possible row-lengths can the band be arranged?

Guest Oct 14, 2018
 #1
avatar+3167 
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\(72 = 2^3 3^2 \\ \text{This gets us, given the constraints on row length,}\\ 6\times 12,~8\times 9,~9\times 8,~12\times 6\\ \text{so 4 different row lengths}\)

Rom  Oct 14, 2018
 #2
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Rom: I think you skipped one:
Listfor(n, 5, 20, (72 % n)) = 6 x 12,  8 x 9,  9 x 8,  12 x 6,  18 x 4 

Guest Oct 14, 2018
 #3
avatar+92505 
+1

We just need to find all the divisors  of 72  between 5 and 20

 

These are

 

 6, 8, 9 ,12, 18

 

So

 

Students   per row     X   rows     =      72

     

       6                               12

       8                                 9

       9                                 8

      12                                6

      18                                3

 

5 possible row lengths

 

 

cool cool cool

CPhill  Oct 15, 2018
 #4
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I think it's supposed to be 18 and 4 in the last row

Guest Oct 15, 2018

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