The Tower of Hanoi

The French mathematician Édouard Lucas brought out the puzzle in Paris in 1883, under a made-up name, “Professor N. Claus of Siam”. The name is a puzzle too: “N. Claus” rearranges into “Lucas”, and the school he gave, “Li-Sou-Stian”, into Saint Louis, where he taught.

One thing to hold: Disks on three pegs, sold in a box that called it a game brought back from Tonkin.

Why it matters: Each extra disk doubles the work: n disks need 2ⁿ − 1 moves, and no fewer. Lucas’s 64 golden disks would take 2⁶⁴ − 1 moves — at one move a second, about 585 billion years.

What we don’t know: The story that came with it — monks moving 64 golden disks, and the world ending when they finish — was Lucas’s own invention. No older version of the legend has been found.

Sources: MacTutor History of Mathematics, “The Towers of Hanoi” (University of St Andrews) · ETH Library, “Tower of Hanoi” (virtual exhibition It’s all math and games) · Wikipedia, “Tower of Hanoi”