Icosian Game
William Rowan Hamilton invented a puzzle that was manufactured and sold in 1857. On a graph, a Hamiltonian path is one that visits each vertex once without revisiting an edge. See the entry at the Puzzle Museum.
Try Hamilton's puzzle here. Click on an edge to light it up, and try to make a path to visit each vertex. If you need to begin again, use the reset icon. Does it matter where you start?
The puzzle is named for this graph being isomorphic to the vertices and edges on an icosahedron.