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Griffin
Daedalian Member
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 Posted: Mon Feb 25, 2002 9:19 pm Post subject: 1 |
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Joe has a grid that consists of dots in rows and columns, place one unit apart. By connecting these dots, Joe can create a variety of polygons. In creating a particular polygon, Joe's pencil goes through n dots. The polygon completely encloses m dots. In terms of n and m, what is the area of the polygon? Proof?
[This message has been edited by Griffin (edited 02-25-2002 04:20 PM).] |
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dethwing
DeTheeThaw
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| Posted: Mon Feb 25, 2002 10:09 pm Post subject: 2 |
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| i have no idea, but i'm wondering if he draws in straight lines, or can he do curves? Or does it not matter? |
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mith
Pitbull of Truth
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| Posted: Mon Feb 25, 2002 10:20 pm Post subject: 3 |
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| (n+2m-2)/2 seems to work. Don't have a clue how to prove it though. |
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quercitron
Don't trust Robinson
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| Posted: Mon Feb 25, 2002 10:20 pm Post subject: 4 |
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How about (n/2 + m - 1)
The proof is tricky though. |
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quercitron
Don't trust Robinson
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| Posted: Mon Feb 25, 2002 10:21 pm Post subject: 5 |
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yeah, mith has the same answer I do  |
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mith
Pitbull of Truth
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| Posted: Mon Feb 25, 2002 10:24 pm Post subject: 6 |
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maybe some sort of induction, but there's no way you are getting me to spend time writing it up 
time for class |
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mith
Pitbull of Truth
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| Posted: Mon Feb 25, 2002 10:32 pm Post subject: 7 |
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| Griffin, you should post more. I always enjoy your puzzles. |
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tigg
Daedalian Member
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Griffin
Daedalian Member
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| Posted: Tue Feb 26, 2002 3:10 am Post subject: 9 |
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Mith - When I come up with a good puzzle, I post it.
Anyway, thankyou tigg for the link. I had a feeling when I stumbled across this relation that it was probably a famous theorem of some sort. |
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tigg
Daedalian Member
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| Posted: Tue Feb 26, 2002 1:39 pm Post subject: 10 |
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Glad to be a help, Griffin.
And nice job too, if you discovered it on your own.
You must like playing around with that stuff. Reminds me of me when I was in high school. I remember I discovered Pascal's triangle when I was in seventh grade, and I was all proud of myself. Some time later I was disappointed to find that Pascal discovered it several hundred years before. ("Hey- that's not Pascal's triangle. That's my triangle!") Oh well.
I'm 33 now and still think math is cool. Some things don't change.
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