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If a marching band has 72 members that always march in fo

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If a marching band has 72 members that always march in fo  [#permalink]

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New post Updated on: 20 Aug 2012, 11:42
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If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8


Many thanks guys!

Originally posted by NYC5648 on 20 Aug 2012, 11:27.
Last edited by Bunuel on 20 Aug 2012, 11:42, edited 1 time in total.
Edited the question.
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Re: If a marching band has 72 members that always march in fo  [#permalink]

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New post 20 Aug 2012, 11:34
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NYC5648 wrote:
If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8

Many thanks guys!


ROWS - PEOPLE IN EACH ROW
3 ------------- 24 (3*24=72)
4 ------------- 18
6 ------------- 12
8 ------------- 9

9 ------------- 8
12 ----------- 6
18 ----------- 4
24 ----------- 3

Total of 8 different formations.
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Re: If a marching band has 72 members that always march in fo  [#permalink]

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New post 20 Aug 2012, 18:58
1
Bunuel wrote:
NYC5648 wrote:
If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8

Many thanks guys!


ROWS - PEOPLE IN EACH ROW
3 ------------- 24 (3*24=72)
4 ------------- 18
6 ------------- 12
8 ------------- 9

9 ------------- 8
12 ----------- 6
18 ----------- 4
24 ----------- 3

Total of 8 different formations.



How did you find out that the number of people in each row is the same ??
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Re: If a marching band has 72 members that always march in fo  [#permalink]

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New post 16 Dec 2016, 05:55
1
NYC5648 wrote:
If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8


Many thanks guys!


We have \(X\) rows and \(Y\) columns (members in each row)

\(X*Y = 72\)

We need to find out the number of ways 72 can be expressed as a product of 2 factors.
\(72 = 2^3*3^2\)

# of ways = \(\frac{(3+1)*(2+1)}{2} = 6\)

But we can’t use this answer because in our question ORDER MATTERS. Rows are different from the columns (number of people in a row). \(3*24\) here is different from \(24*3\). Hence we should not divide by 2 and we get 12 total possibilities.

Next step: we need to take into consideration additional restriction: \(X ≥ 3\), \(Y ≥ 3\).

We need to deduct following 4 cases from our total set: \(1*72\), \(2*36\) and \(72*1\), \(36*2\)

Final answer: \(12 – 4 = 8\)
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Re: If a marching band has 72 members that always march in fo  [#permalink]

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New post 20 Feb 2019, 16:09
Bunuel wrote:
NYC5648 wrote:
If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8

Many thanks guys!


ROWS - PEOPLE IN EACH ROW
3 ------------- 24 (3*24=72)
4 ------------- 18
6 ------------- 12
8 ------------- 9

9 ------------- 8
12 ----------- 6
18 ----------- 4
24 ----------- 3

Total of 8 different formations.


Bunuel
The issue with this solution is that it´s assumed that all rows will request the same number of participants. However whether we consider minimum of 3 row within 3 people in each, we will have a significant increase in this number...
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Re: If a marching band has 72 members that always march in fo   [#permalink] 20 Feb 2019, 16:09
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