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Topic: Sir George's Land Grant (Read 459 times) |
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TimMann
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Sir George's Land Grant
« on: Oct 24th, 2003, 11:33pm » |
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Here's a puzzle that I cribbed from the online book celebrating G4G1 (the Gathering for [Martin] Gardner #1), available at http://www.g4g4.com/contentsmmpp.html.
"To reward you for killing the dragon," the Queen said to Sir George, "I grant you the land you can walk around in a day." She pointed to a pile of wooden stakes. "Take some of these stakes with you," she continued. "Pound them into the ground along your way, and be back at your starting point in 24 hours. All the land in the convex hull of your stakes will be yours." (The Queen had read a little mathematics.) Assume that it takes Sir George 1 minute to pound a stake and that he walks at a constant speed between stakes. How many stakes should he take with him to get as much land as possible?
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Edit: changed link to point to a legitimate copy of the book.
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| « Last Edit: Oct 25th, 2003, 11:25pm by TimMann » |
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towr
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Re: Sir George's Land Grant
« Reply #1 on: Oct 25th, 2003, 9:55am » |
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::since the world is round, one stake could claim the world.. Though the queen would probably not (want to) see it that way..::
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TimMann
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Re: Sir George's Land Grant
« Reply #2 on: Oct 25th, 2003, 11:09am » |
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Hee hee, towr. No need to hide that answer.
Sir George lived long before Columbus, so he and the queen were assuming a flat earth. This should be obvious, as convex hulls aren't well-defined on a sphere. 
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Barukh
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Re: Sir George's Land Grant
« Reply #3 on: Oct 26th, 2003, 12:29am » |
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Here's my attempt: [smiley=blacksquare.gif]17 stakes. It's the number that maximizes (1440-n)2*cot([pi]/n)/n[smiley=blacksquare.gif]
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towr
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Re: Sir George's Land Grant
« Reply #4 on: Oct 26th, 2003, 9:08am » |
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[edit]I can't seem to get it right..
Anyway, I finally get the same answer as Barukh so forget whatever I wrote here before 
Well, a slight difference, I maximized v2·(n - 1440)2·cot(pi/n)/(4·n), but that doesn't matter for n, just for the final area[/edit]
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| « Last Edit: Oct 26th, 2003, 9:55am by towr » |
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