draw non-crossing lines from three houses to three utilities
... that it is impossible to draw non-crossing lines from three houses to three utilities in a plane?
... that it is impossible to <b id="mwAg8"><a href="./Three_utilities_problem" id="mwAhA" rel="mw:WikiLink" title="Three utilities problem">draw non-crossing lines from three houses to three utilities</a></b> <i id="mwAhE">(pictured)</i> in a plane?