On utilities -- a teaser Suppose there are three houses. Each needs to be hooked to three utilities: water, electricity and gas. Can it be made so that the (underground) connections do not intersect?

Here is an unsuccessful attempt. What is left is the connection of gas to Alice, and there is no way to do it without intersections.

The puzzle has no solution. The graph of connections forms K3,3 (see figure) -- one of the two Kuratowski's graphs the occurane of which as a subgraph makes the graph non-plannar (see Kuratowski's theorem). Click on the image to see two forms of K3,3.