# Thread: Time wasting Line Connection Problem

1. ## Time wasting Line Connection Problem

Hey guys

Just came across this problem in a math puzzle book, took me about 3 weeks and I didn't figure out what the answer is, thought I might share with you guys

H H H

G w E

H: House G: Gas E: Electricity W: Water

Obviously all three houses need gas electricity and water, draw line connecting them to it. No lines can cross and line cannot go through houses but does not have to be straight lines. You can re-arrange the structure and layout of the houses and appliances. No 3D, everything stays planar

Happy Puzzling
Derg

2. ## Impossible

There is no planar solution: the topology of the plane forbids it. There's been proofs of this for more than 60 years (such as in the paper: G. T. Kneebone, "The Three Houses Problem" The Mathematical Gazette, Vol. 25, No. 264 (May, 1941), pp. 78-81). It can, however, be done on a surface topologically equivalent to the torus, or other multiply-connected surfaces.

--Kevin C.

3. You can simply prove it with a little knowledge of Graph Theory. Graph K(3,3) is not planar, it means it can't be drawn without any intersections.