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

Historical Note on Modern Puzzles by Henry Ernest Dudeney: $156$: Water, Gas and Electricity

Henry Ernest Dudeney, on publishing this puzzle in his Modern Puzzles, 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.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $156$. -- Water, Gas and Electricity
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $413$. Water, Gas and Electricity