Henry Ernest Dudeney/Modern Puzzles/156 - Water, Gas and Electricity/Historical Note

== Historical Note on by : $156$: Water, Gas and Electricity == , on publishing this puzzle in his, claims that the proof of the impossibility of a non-tricksy solution to this puzzle is:
 * for the first time in a book.

Whether this is true or not remains to be investigated.

This is now known in the field of graph theory as the utilities problem, and this particular non-planar graph is known as the Thomsen graph.