Another famous problem involving chessboards is the Knight’s Tour, in which a knight (the horse-shaped chess piece) must visit every square on an empty chessboard exactly once, using only knight moves. Computer programming classes often have students create a program to find a knights tour. The path is “closed” if at the end of the knight’s tour, the knight is exactly one knight’s move away from where it started. This is also known as a Hamiltonian Cycle, as opposed to the Hamiltonian Path we heard about in the Virus Riddle.

A very famous problem that involves weighted Hamiltonian Cycles is known as The Traveling Salesman problem (TSP). In this problem, a salesman starts from home and visits every city on his route exactly once and returns home, and does so in the shortest possible (or cheapest) way (thus the graph is weighted with distance.) This is a problem involving optimization and is an example of how mathematics can be used in operations research.

The Icosian Game was a wooden dodecahedron puzzle where each peg was a city and the object was to find a Hamiltonian Cycle. It was invented in 1857 by Irish mathematician Sir William Rowan Hamilton. Try the game here.

Another fun Hamiltonian Path Puzzle from the New York Times can be found here. Love the challenge of solving riddles? TED Ed has more! Click here and find one that looks interesting and give it a try.

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