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# Farmland Rectangles

### #2

Posted 08 March 2013 - 03:25 AM Best Answer

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #3

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)

### #4

Posted 09 March 2013 - 09:17 PM

### #5

Posted 10 March 2013 - 12:47 AM

Spoiler for Looks like

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

### #6

Posted 10 March 2013 - 10:52 PM

Spoiler for Looks likeSpoiler 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.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #8

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.)

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #9

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?

### #10

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.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

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