Mathematical recreations and essays . n next to consider some problems where it is desiredto find a route which will pass once and only once througheach node of a given geometrical figure. This is the reciprocalof the problem treated in the first part of this chapter, and isa far more difficult question. I am not aware that the generaltheory has been considered by mathematicians, though twospecial cases—namely, the Hamiltonian (or Icosian) Game andthe Knights Path on a Chess-Board—have been treated insome detail. The Hamiltonian Game. The Hamiltonian Game consistsin the determination of a rout
Mathematical recreations and essays . n next to consider some problems where it is desiredto find a route which will pass once and only once througheach node of a given geometrical figure. This is the reciprocalof the problem treated in the first part of this chapter, and isa far more difficult question. I am not aware that the generaltheory has been considered by mathematicians, though twospecial cases—namely, the Hamiltonian (or Icosian) Game andthe Knights Path on a Chess-Board—have been treated insome detail. The Hamiltonian Game. The Hamiltonian Game consistsin the determination of a route along the edges of a regulardodecahedron which will pass once and only once throughevery angular point. Sir William Hamilton*, who inventedthis game—if game is the right term for it—denoted thetwenty angular points on the solid by letters which stand forvarious towns. The thirty edges constitute the only possiblepaths. The inconvenience of using a solid is considerable,and the dodecahedron may be represented conveniently in.
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