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Icosian (Hamiltonian game)



Category Math, Graph


The Icosian Game was invented in 1857 by William Rowan Hamilton. It is also called the Hamiltonian game (Ball and Coxeter 1987, p. 262), is the problem of finding a Hamiltonian cycle along the edges of a dodecahedron. Hamilton sold this game to a London game dealer in 1859 for 25 pounds, and the game was subsequently marketed in Europe in a number of forms (Gardner 1957). The game marketed two versions of it, under the name Around the World. One version, for the parlor, was played on a flat board; another, for the traveler, consisted of an actual dodecahedron. In both cases, nails at each vertex stood for a major city of the world and the player wrapped a piece of string around these nails as they went. In the event, the game was a complete sales flop, mainly because it was too easy, even for children – but not for Hamilton himself who always used the icosian calculus to figure out his moves, instead of just trying different paths like everyone else!


The player aims to make a Hamiltonian cycle, which is a path in which each vertex is visited once, no edge is visited twice, and the ending point is the same as the starting point.


Sir William Rowan Hamilton

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mathworld and daviddarling



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