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Farmland Rectangles


Best Answer bonanova, 08 March 2013 - 03:25 AM

Spoiler for Looks like

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#1 BMAD

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Posted 07 March 2013 - 09:45 PM

While flying over farmland, a pilot notices the rectangular shape of the fields below. She sketches the lines that divide the fields.

When she returns to the airport, she wonders how many different rectangles can be formed by the lines drawn?

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#2 bonanova

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Posted 08 March 2013 - 03:25 AM   Best Answer

Spoiler for Looks like


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#3 Krishna Kutty

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Posted 09 March 2013 - 04:39 PM

Spoiler for Looks like

 

 

Aren't there more?2 squares can make a rectangle.That will give two more rectangles.

If you have counted thaem, then it's probably the longer rectangles made by 2rectangles+2squares on the same line that you have missed.

That will make the answer 20!(won't it)


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#4 phil1882

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Posted 09 March 2013 - 09:17 PM

Spoiler for i also get 16

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#5 dms172

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Posted 10 March 2013 - 12:47 AM


Spoiler for Looks like

Spoiler for even more

Edited by dms172, 10 March 2013 - 12:50 AM.

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#6 bonanova

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Posted 10 March 2013 - 10:52 PM


Spoiler for Looks like

Spoiler for even more

 

dms, I'm having difficulty seeing the extra ones.

 

Although, the ones I found seemed straightforward, making me think there are others not readily seen.

Any rectangle has to have an upper left corner, which therefore can't be any of the bottom or right nodes.

Using the order that I gave, what is your count for the six other nodes?

That will help me see the ones I missed.


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#7 Krishna Kutty

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Posted 11 March 2013 - 02:56 PM

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Again and again...i see that i made a mistake again.When i tried drawing them, i could find only 18.Actually, i did not understand what you said about nodes.

This is what i got when i tried to draw them.

Farmland.png


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#8 bonanova

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Posted 11 March 2013 - 03:15 PM

By nodes I just meant corners: places where the lines intersect.

(In graph theory, those points are called nodes, and lines that connect them are called edges.)


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#9 Krishna Kutty

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Posted 12 March 2013 - 08:37 AM

By nodes I just meant corners: places where the lines intersect.

(In graph theory, those points are called nodes, and lines that connect them are called edges.)

 

I meant i didn't understand how you found out the answer using the number of nodes.How did you find the rectangles that are combinations of two or more rectangles using the number of nodes?Is there some formula or you just simply counted them?


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#10 bonanova

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Posted 12 March 2013 - 09:33 AM

By nodes I just meant corners: places where the lines intersect.

(In graph theory, those points are called nodes, and lines that connect them are called edges.)

 

I meant i didn't understand how you found out the answer using the number of nodes.How did you find the rectangles that are combinations of two or more rectangles using the number of nodes?Is there some formula or you just simply counted them?

 

Just counted them.

Using nodes just put them into piles sort of. A convenient way to keep track.


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