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Number of possible Rectangular Pens

by Jed
(Kilmore, Australia)











































Number of possible Rectangular Pens

How many rectangular pens can you make with 28 fence panels which measure 1 metre?

The smallest side each rectangular pen can have is 1 metre.

Comments for Number of possible Rectangular Pens

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Nov 22, 2012
Rectangular Pens
by: Staff



Answer

Part I

Since there are 28 fence panels, find all the prime factors of the number 28

28 = 2 * 2 * 7

The combinations of the prime factors

4 * 7

2 * 14


The number 4 can be divided: (1 + 1 + 1 + 1) * 7 square pens = 28 panels

The number 14 can be divided: (6 + 6 + 1 + 1) * 2 rectangular pens = 28 panels

The number 14 can be divided: (5 + 5 + 2 + 2) * 2 rectangular pens = 28 panels

The number 14 can also be divided: (4 + 4 + 3 + 3) * 2 rectangular pens = 28 panels

The number 7 can be used four times: (7 + 7 + 7 + 7) * 1 square pen = 28 panels

You have five choices:

          1) a large square pen with 7 panels on each side

          2) 2 rectangular pens (6 panels + 6 panels + 1 panel + 1 panel)

          2) 2 rectangular pens (5 panels + 5 panels + 2 panels + 2 panels)

          3) 2 rectangular pens (4 panels + 4 panels + 3 panels + 3 panels)

          4) 7 small square pens with 1 panel on each side


The final answer is:

If the pens are “completely separate pens”, the maximum number which pens which can be constructed from 28 panels is 7. Each of the pens uses 1 panel on each side.

7 square pens 1 meter by 1 meter


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Dec 12, 2012
Rectangular Pens
by: Staff


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Part II



Math – If the pens are “completely separate pens”, the maximum number which pens which can be constructed from 28 panels is 7.  Each of the pens uses 1 panel on each side.







Additional options:


If the pens can be lined up next to one another, so that the pens share the panel which separates them, then 9 square pens can be constructed.

(Number of pens)(3 unique panels per pen) + 1 = 28

3N + 1 = 28

3N + 1 - 1 = 28 - 1

3N + 0 = 27

3N = 27

3N / 3 = 27 / 3

N = 9



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Dec 12, 2012
Rectangular Pens
by: Staff


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Part III



Math – If the pens can be lined up next to one another, so that the pens share the panel which separates them, then 9 square pens can be constructed.







----------------------------------------------

Dec 12, 2012
Rectangular Pens
by: Staff


----------------------------------------------




Part IV

If the pens can be lined up next to one another, so that the some pens share their panels on all four sides, some pens share their panels on 3 sides, and some share their panels on 2 sides, then 9 square pens can be constructed with four panels left over. The leftover panels can be used to construct a 10th pen (which will be completely separate from the others).




Math – If the pens can be lined up next to one another, so that the some pens share their panels on all four sides, some pens share their panels on 3 sides, and some share their panels on 2 sides,  then 9 square pens can be constructed with four panels left over.  The leftover panels can be used to construct a 10th pen (which will be completely separate from the others).









Thanks for writing.

Staff
www.solving-math-problems.com



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