Solution 4.0.2.1.

We will answer this question later. For now, notice how we would ask this question in the context of graph theory. We are really asking whether it is possible to redraw the graph below without any edges crossing (except at vertices). Think of the top row as the houses, bottom row as the utilities.

A graph with six vertices arranged in two rows of three.  There are nine edges, connecting each dot in the top row to each dot in the bottom row.
in-context