Icosian Game A century after Euler’s discovery (see Problem 4), another famous puzzle—th...

Icosian Game A century after Euler’s discovery (see Problem 4), another famous puzzle—this one invented by the renowned Irish mathematician Sir William Hamilton (1805–1865)—was presented to the world under the name of the Icosian Game. The game’s board was a circular wooden board on which the following graph was carved:

Find a Hamiltonian circuit—a path that visits all the graph’s vertices exactly once before returning to the starting vertex—for this graph.