Puzzles
Visit every corner of a twenty-cornered solid exactly once, then return home
Hamilton's 1857 board game challenges players to trace a path along the edges of a dodecahedron — twelve pentagonal faces, twenty corners — that visits every corner exactly once before returning to the start. It looks like a warm-up puzzle. Can you find such a route, or show why one must exist?
Reveal the answer
Yes, it's solvable — the dodecahedron's edge network contains a full 'Hamiltonian cycle,' a closed loop touching every vertex once. Hamilton sold the game's rights to a toy maker for 25 pounds, but it flopped commercially because most buyers found it too easy once shown the trick. Its lasting legacy is the term 'Hamiltonian cycle,' now central to graph theory and problems like circuit design and the travelling salesman problem.