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Three utilities problem

The three utilities problem, also known as water, gas and electricity, is a mathematical puzzle that asks for non-crossing connections to be drawn between three houses and three utility companies on a plane. When posing it in the early 20th century, Henry Dudeney wrote that it was already an old problem. It is an impossible puzzle: it is not possible to…

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Overview

History

Statement

Puzzle solutions

Properties of the utility graph

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Map overview Semantic statistics

Three utilities problem

Nodes56
Edges55
Triples19
Avg. degree1.96
Density0.035714
Components1

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Three utilities problem

Top relations

related to history · 12
Three utilities problem → Another, Dudeney, He, HenryDudeney, However, In, It, Kullman, Loyd's, Sam Loyd, The Quarrelsome Neighbors, The Strand Magazine
related to Statement · 3
Three utilities problem → An, Its, The

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Important terminology

graph displaystyle problem puzzle utilities utility houses one graphs three planar plane vertices connections bipartite two nine complete crossings embedding

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
a torus or Möbius stripinstance ofVersions of the problem on nonplanar surfaces0.80text
or that allow connections to pass through other houses or utilitiesinstance ofVersions of the problem on nonplanar surfaces0.80text
can be solved.This puzzle can be formalized as a problem in topological graph theory by asking whether the complete bipartite graph K 3instance ofVersions of the problem on nonplanar surfaces0.80text
3instance ofVersions of the problem on nonplanar surfaces0.80text
Three utilities problemrelated to historyKullman0.60section
Three utilities problemrelated to historyHe0.60section
Three utilities problemrelated to historyIn0.60section
Three utilities problemrelated to historyHenryDudeney0.60section
Three utilities problemrelated to historyHowever0.60section
Three utilities problemrelated to historyDudeney0.60section
Three utilities problemrelated to historyThe Strand Magazine0.60section
Three utilities problemrelated to historySam Loyd0.60section

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    Min side: 3
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