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The end of the tower

According to a popular myth, the solution of a 64-piece Tower of Hanoi puzzle will herald the end of the world.

You’ve probably tried a Tower of Hanoi before. This mathematical puzzle is simple to explain. Three poles arranged in a line hold a stack of discs of different sizes. The largest disc is on the bottom, the smallest on top. You can move a disc from one pole to another at any time, as long as you do so one disc at a time. Your task is to move the discs from the first pole to the third, one by one, without ever placing a larger disc on top of a smaller one.

It’s always possible to solve this puzzle with three poles, no matter how many discs are in the pile. If there are x discs, then it will take a minimum of 2x-1 moves to solve it. So a one-disc tower takes one move (obviously). A two-disc tower takes three moves. A three-disc tower takes seven moves, and so on.

The puzzle was invented 137 years ago by the French mathematician Édouard Lucas, but some popular myths cropped up soon after suggesting a more ancient provenance. Specifically, a myth holds that there is a huge Tower of Hanoi in a temple somewhere, in Vietnam, hence the name, or sometimes India. The priests of this temple are tasked with solving the puzzle, and they do so day and night, all year long. When they finish, the world will end.

(Side note: sorry about yet another end-of-the-world post. I cannot imagine what series of current events could put me on such an eschatological bent!)

I wouldn’t worry too much about this mythological tower, though. If it is 64 pieces high, it will take 264-1 moves to solve it. At one move a second, that puts the end of the world around 585 billion years from now. Based on current cosmological estimates, by that time all of the galaxies in the universe will be so far away from each other that none of them will be visible from our galaxy. And, of course, by then the Earth will be long gone anyway. So yeah, I wouldn’t worry about that.

Categories: Games & sport Mathematics & statistics Sciences

The Generalist

I live in Auckland, New Zealand, and am curious about most things.

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