The Icosian game, also called the Hamiltonian game, is the problem of finding a Hamiltonian cycle along the edges of an dodecahedron, i.e., a walk through the graph such that every vertex is visited a single time, no edge is visited twice, and the ending point is the same as the starting point. The puzzle was distributed commercially as a pegboard with holes at the nodes of the dodecahedral graph. The Icosian Game was invented in 1857 by William Rowan Hamilton. Hamilton sold it to a London game dealer in 1859 for 25 pounds, and the game was subsequently marketed in Europe in a number of forms. The 30 solutions corresponding to the 30 Hamiltonian cycles of the dodecahedral graph are illustrated above.
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