# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

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Griffin
Daedalian Member

 Posted: Mon Feb 25, 2002 9:19 pm    Post subject: 1 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).]
dethwing
DeTheeThaw

 Posted: Mon Feb 25, 2002 10:09 pm    Post subject: 2 i have no idea, but i'm wondering if he draws in straight lines, or can he do curves? Or does it not matter?
mith
Pitbull of Truth

 Posted: Mon Feb 25, 2002 10:20 pm    Post subject: 3 (n+2m-2)/2 seems to work. Don't have a clue how to prove it though.
quercitron
Don't trust Robinson

 Posted: Mon Feb 25, 2002 10:20 pm    Post subject: 4 How about (n/2 + m - 1) The proof is tricky though.
quercitron
Don't trust Robinson

 Posted: Mon Feb 25, 2002 10:21 pm    Post subject: 5 yeah, mith has the same answer I do
mith
Pitbull of Truth

 Posted: Mon Feb 25, 2002 10:24 pm    Post subject: 6 maybe some sort of induction, but there's no way you are getting me to spend time writing it up time for class
mith
Pitbull of Truth

 Posted: Mon Feb 25, 2002 10:32 pm    Post subject: 7 Griffin, you should post more. I always enjoy your puzzles.
tigg
Daedalian Member

 Posted: Mon Feb 25, 2002 10:35 pm    Post subject: 8 Pick's Theorem
Griffin
Daedalian Member

 Posted: Tue Feb 26, 2002 3:10 am    Post subject: 9 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.
tigg
Daedalian Member

 Posted: Tue Feb 26, 2002 1:39 pm    Post subject: 10 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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