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Topic: The Circle and Lines (Read 814 times) |
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TenaliRaman
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I am no special. I am only passionately curious.
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The Circle and Lines
« on: Jul 23rd, 2004, 7:18am » |
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You are given 21 lines and a circle. What is the maximum number of parts that you can divide the circle with the help of the 21 lines?
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Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
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Grimbal
wu::riddles Moderator
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Re: The Circle and Lines
« Reply #1 on: Jul 23rd, 2004, 1:30pm » |
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Is que question equivalent to: in how many pieces can you cut a round pizza with 21 straight cuts?
It should be ::1+21*(21+1)/2 = 232:: then
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tseuG
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Re: The Circle and Lines
« Reply #2 on: Jul 23rd, 2004, 1:33pm » |
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Proceeding from one line segment seems to simplify things.
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TenaliRaman
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Re: The Circle and Lines
« Reply #3 on: Jul 24th, 2004, 11:51pm » |
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Bravo Grimbal and TseuG!
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Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
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Noke Lieu
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pen... paper... let's go! (and bit of plastic)
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Re: The Circle and Lines
« Reply #4 on: Jul 25th, 2004, 11:53pm » |
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for our irregulars:
In case discombobulated by Grimbal's equation, try:
(x[sup2]+x+2)/2
Its the same thing, I just find it nice when people put brackets in places where I expect them.... 
and its hidden for postderity. In 6 months, when new folk turn up, it isn't in their face straight away, only being an early post.
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| « Last Edit: Jul 25th, 2004, 11:56pm by Noke Lieu » |
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a shade of wit and the art of farce.
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Speaker
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Re: The Circle and Lines
« Reply #5 on: Jul 26th, 2004, 1:56am » |
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So, what sort of shape are those pizza pieces? They are not wedge slices are they. So, are they squares? Does anybody have a picture?
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towr
wu::riddles Moderator
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Re: The Circle and Lines
« Reply #6 on: Jul 26th, 2004, 2:18am » |
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they're not all the same sort of shape.. Some include a part of the edge of the pizza which is a curve, other piece are bounded solely by straight lines, some by three, some by four.
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Wikipedia, Google, Mathworld, Integer sequence DB
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towr
wu::riddles Moderator
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Here's one way of dividing the circle/pizza..
It does mean some people get an awfully small piece though, and one person get's a disproportionately large piece (feel free to determine how much)..
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| « Last Edit: Jul 26th, 2004, 3:46am by towr » |
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Speaker
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Re: The Circle and Lines
« Reply #8 on: Jul 26th, 2004, 4:53pm » |
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Thanks towr
That is a great image. The rule I learned is that the guy who cuts the pizza (or cake or whatever) had to choose last. That made the cutter be carefule to keep all the pieces the same size. 
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They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. <Ben Franklin>
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Grimbal
wu::riddles Moderator
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Re: The Circle and Lines
« Reply #9 on: Jul 27th, 2004, 5:41am » |
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If you are last to chose, you better make a mess with the cake and make a lot of crumbs. Since you are last to take your piece, you can have all the crumbs.
I am from a large family. I know this by experience.
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