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Clumsy Planets

Posted: Thu Oct 25, 2012 9:19 am
by Phlembac Adib Hasan
On each planet of a star system, there is an astronomer observing the nearest planet. The number of planets is odd and pairwisely distances between them are different. Prove that at least one planet is not under observation.

Re: Clumsy Planets

Posted: Thu Oct 25, 2012 6:58 pm
by zadid xcalibured
Hint:
Use induction.Look at the smallest (extreme) length.And notice that we need exactly n observers to observe all n planets.

Re: Clumsy Planets

Posted: Fri Oct 26, 2012 11:17 am
by Phlembac Adib Hasan
I myself did it using contradiction.