Is there a way to prove mathematically whether this is possible?

No clue, maybe topology/knot theory?

>>7959512
Does notbsay you cannot connect between nodes, therefore rather easy, all 3 connect to one node, then that node connects to second, which connects to third

>>7959521
wtf

>>7959512
I proved its possible in the last time you made this thread faggot.

Steps
1. Save png
2. Print
3. Fold in half, top over bottom
4. Fold into thirds
5. Confirm all 3 houses and supplies are lined up
6. Stab paper with pencil

Gratz, you now have an imaginary 'line' that connects all 3 houses with all 3 resources. This is possible because the puzzle exists in a two dimensional world where as we exist in a three dimensional world so to solve it we create wormholes by bending the two dimensional world.

My solution is correct where as the answer involving the torus is incorrect because placing the three houses and resources on a torus and drawing multiple lines around it is modifying the very fundamentals of the original puzzle.
The torus changes the puzzle into a three dimensional puzzle.
My solution maintains the puzzle's original 2 dimensional form but applies a third dimension "over" it, not "into" it.

>>7959523
Each house is a node, A, B, C. Connect all three to A, connect A to B, then B to C, or any variation there of, will always work.

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

The graph of K(3,3) is not planar therefore its not possible to do in 2D

>>7959512
Protip: It doesn't say the lines have to be straight and it doesn't say you cannot run lines through the utility symbols.

It's one of those 'think outside the box' problems.

>>7959563
No, it's a graph theory problem.

Any CS student could tell you this.

>>7959534
thanks bro

>>7959600
I'm a chemist. thanks.

File: 1459042974540.png (841KB, 751x746px) Image search: [Google]

841KB, 751x746px

:^)