Suppose there are three cottages that each need to be connected to the gas, water, and electric companies. Is there a way to do so without any of the lines crossing each other?
In more formal terms, this asks whether the bipartite graph K3,3 is planar. Kazimierz Kuratowski proved in 1930 that K3,3 is nonplanar, and thus that the three cottage problem has no solution.
