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The game is related to Euler's Knight's Tour problem since, in today's terminology, it asks for a Hamiltonian circuit in a certain graph.
In particular if you try to use the mapping in this manner, you will end up creating qubit Hamiltonians with very nonlocal interactions.
In 1834, Dublin mathematician William Rowan Hamilton applied his work on characteristic functions in optics to Newtonian mechanics, and what is now called the Hamiltonian formalism of mechanics was born.
In mathematics he worked on the calculus of variations, Fourier series, function spaces, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity.
More expansive still was the attitude towards Hamilton, again almost wholly in the North, that emerged from the carnage of the Civil War and the perception that Hamiltonian centralization would have prevented the war.
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