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Henry Dudeney
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Illustration of the gas, water, and electricity problem showing three utility buildings labeled W, G, and E, and three houses labeled A, B, and C. Colored lines connect each utility to each house, forming a complete bipartite graph K3,3, with a key identifying water pipes, gas lines, and electrical wires. The diagram demonstrates the non-planar nature of K3,3 in graph theory, as the connections cross over each other.
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Henry Dudeney

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Illustration of the gas, water, and electricity problem showing three utility buildings labeled W, G, and E, and three houses labeled A, B, and C. Colored lines connect each utility to each house, forming a complete bipartite graph K3,3, with a key identifying water pipes, gas lines, and electrical wires. The diagram demonstrates the non-planar nature of K3,3 in graph theory, as the connections cross over each other.
Dudeney puzzle The English recreational problemist Henry Dudeney claimed to have a solution to a problem that he posed in 1913 that required each of three houses to be connected to three separate utilities such that no utility service pipes intersected. Dudeney's solution involved running a pipe through one of the houses, which would not be considered a valid solution in graph theory. In a two-dimensional plane, a collection of six vertices (shown here as the vertices in the homes and utilities) that can be split into two completely separate sets of three vertices (that is, the vertices in the three homes and the vertices in the three utilities) is designated a K3,3 bipartite graph. The two parts of such graphs cannot be interconnected within the two-dimensional plane without intersecting some paths.

Henry Ernest Dudeney was an English mathematician and author known for his puzzle compositions. He supplemented his income as a clerk by selling ingenious puzzles to magazines and newspapers. Dudeney published collections of his puzzles, including The Canterbury Puzzles in 1907 and Amusements in Mathematics in 1917. He collaborated with American puzzle creator Sam Loyd, providing commentary on Loyd's puzzles under the pseudonym "The Sphinx." Dudeney also contributed to logic puzzles and word puzzles, such as word squares.12

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  1. number game
  2. puzzle

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