The problem of the three houses
The problem of the three houses: every house must be joined to each of the three points indicated in the figure, is there a way to do that provided that the 9 paths don't cross?
You can see other versions of the problem.
You can also try to solve this problem online with the interactive animation Paths without crossings.
Exhibit from matemilano, section "Topology".
The image belongs to the sections...:
From the exhibition matemilano (Topology)
Jordan's theorem and the three houses problem (Topology)
Images from the topology section (From the exhibitions of matematita)