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Anonymous

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Anonymous Wed 06 Jun 2018 21:43:22 No.5407238 View View Report

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>>5407219
Human society is made for average simpletons, it's to be expected that smart people will feel ostracised, there is no need to let one self to be drawn to extreme destructive policies, what we need to do is to subdue society to become more apt to us, a combination of libertarianism and technocracy will do the job, just keep trolling lads.

Anonymous

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Anonymous Thu 05 Oct 2017 07:07:03 No.2395319 View View Report

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>no one's posted the actual answer yet

>As it is usually presented (on a flat two-dimensional plane), the solution to the utility puzzle is "no": there is no way to make all nine connections without any of the lines crossing each other. In other words, the graph K3,3 is not planar. Kazimierz Kuratowski stated in 1930 that K3,3 is nonplanar,[10] from which it follows that the problem has no solution. Kullman, however, states that "Interestingly enough, Kuratowski did not publish a detailed proof that [ K3,3 is ] non-planar".[4]

>One proof of the impossibility of finding a planar embedding of K3,3 uses a case analysis involving the Jordan curve theorem. In this solution, one examines different possibilities for the locations of the vertices with respect to the 4-cycles of the graph and shows that they are all inconsistent with a planar embedding.[11]

>Alternatively, it is possible to show that any bridgeless bipartite planar graph with V vertices and E edges has E ≤ 2V − 4 by combining the Euler formula V − E + F = 2 (where F is the number of faces of a planar embedding) with the observation that the number of faces is at most half the number of edges (the vertices around each face must alternate between houses and utilities, so each face has at least four edges, and each edge belongs to exactly two faces). In the utility graph, E = 9 and 2V − 4 = 8, violating this inequality, so the utility graph cannot be planar.[12]

https://en.wikipedia.org/wiki/Three_utilities_problem

Anonymous

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Anonymous ID:XTYgl9ll Tue 16 May 2017 02:41:19 No.500559 View View Report

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