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        riddles >> hard >> Inimical Dictators
        
(Message started by: Barukh on Sep 23^rd, 2006, 12:07am)

Title: Inimical Dictators
Post by Barukh on Sep 23^rd, 2006, 12:07am

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.

Title: Re: Inimical Dictators
Post by Whiskey Tango Foxtrot on Sep 23^rd, 2006, 7:01am

[hide]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.[/hide]

[edit] I just realized you only wanted for N=1 to 10 and not a generalized solution. Much easier... hiding post.