How To Tell Fake North Face Backpack

The three houses

I wanted to offer an interesting variation of the classic game of three houses. For those not familiar, this is the problem. There are three houses and three plants (of water, gas and electricity). The game is to connect each house to the three stations. But it is not possible that these connections are crossed.

The original should be resolved on a flat surface, such as a sheet. It is therefore not valid to pass the pipes below one another. If you want to try it, but know that it is impossible (if you wish you would be able to prove it?)

The variant that I propose is this: connect the three cottages on a two-dimensional surface, but not necessarily flat. For example, the surface of a sphere is an example of two-dimensional surface is not flat. What surfaces admit a solution? What feature è necessaria?