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Topic: Inimical Dictators (Read 2407 times) |
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Barukh
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Inimical Dictators
« on: Sep 23rd, 2006, 12:07am » |
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N dictators live on a planet that has a form of an ideal sphere. Every dictator wants to build a palace of his own so that the minimal distance from other dictators is as big as possible.
What are the best arrangements of the palaces for N = 2, …, 10?
I apologize if this was already posted eariler.
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Whiskey Tango Foxtrot
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Sorry Goose, it's time to buzz a tower.
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Re: Inimical Dictators
« Reply #1 on: Sep 23rd, 2006, 7:01am » |
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The answers for 1 to 6 are quite obvious, and up to a dozen is doable, but after that it gets a little more complex.
A quick google search produced this:
http://www.enginemonitoring.com/sphere/
Believe me when I say I would have liked to do the math on this one, but it is part of the Fejes Tóth problem, and that is one of the hardest unsolved problems out there.
[edit] I just realized you only wanted for N=1 to 10 and not a generalized solution. Much easier... hiding post.
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| « Last Edit: Sep 23rd, 2006, 7:14am by Whiskey Tango Foxtrot » |
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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