Autism test Sup Forums can't pass

Autism test Sup Forums can't pass

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en.wikipedia.org/wiki/Planar_graph#Euler's_formula
twitter.com/NSFWRedditVideo

Done

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Top kek

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Good job user
*pats on head*

K3,3

Kek

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That is some advanced goatse

Kek

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>using red for lightning and yellow for fire

Ok autist

Oh crap, this is harder than I thought. Guess I'm an autist then.

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The houses should be able to be heated by the electricity and the water if the owners have the needed technology installed in their homes.

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Not possible:
en.wikipedia.org/wiki/Planar_graph#Euler's_formula
It would have 6 points, 6 lines thus the number of faces should be 2. But it can't be done with 2 faces.

Congrats!

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fire not connected to sec house autist

>2019
>believing *tism is real
You just failed THE test

they dont. they have gas boilers you stupid cuck. run the lines for it or the freeze to death. they live in northern canada.

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im an engineer

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>each house can "tap" a main line
Just three straight lines through all houses and connect to utilities.

>houses are not infinitesimal points or lines for one house can go through another house
Can be accomplished by putting down lines in a completely ad hoc fashion before having one final line going through a single house supplying another house.

>houses are considered infinitesimal points and lines cannot go through them
Impossible. Connect any two utilities to all three houses in a completely arbitrary fashion of your choice, leaving one last utility of your choice to connect. Note this defines two four-sided areas with utility lines as edges and houses or utilities as vertices. The middle house will lie on a shared boundary of both areas, and completely surrounded by both (there exists no point in an arbitrarily small neighborhood of the middle house that is external to the union of both areas). For simplicity, we shall call these two areas A1 and A2, and their union U.

If the last utility to connect lies outside of U, then the line that would connect it to the middle house must clearly cross the perimeter of U (formed by utility lines) to reach the middle house which is interior to U, which is not a valid solution.

If lines have been drawn such that the last utility lies within A1, we note that we must cross the boundary of A1 (again, utility lines) itself to reach the house that is NOT a vertex of A1 and thus exterior to A1. An analogous argument can be made for the case in which the last utility lies within A2.

Since there cannot exist a solution when the third utility lies in A1, A2, or the complement of U and the union of all three of these spans the plane, we deduce that the task presented cannot be achieved with any arrangement of utility lines. QED.

Fun fact; changing the position of anything won't make the last case solvable, but changing topology from a plane to a toroid (which would give a "wrap around" effect) will.

t. Autist

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Use solar for electricity.

This is a test made by someone who lives where homes have chimneys and gas is supplied to their homes.

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My sides

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