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Calculating How Randomness Creeps In

I loved the 15-puzzle — the game with 15 tiles and a single empty space in a 4x4 grid — when I was a kid.

The goal is to slide the tiles around and put them in numerical order or, in some versions, arrange them to form an image.

The first 15 puzzle I was able to complete was a picture of a cat with a mouse sitting on its head. It seemed difficult at first, but after trying the game countless times throughout the days and weeks, I was able to get the hang of it.

The game has become a staple of party-favor bags since it was introduced in the 1870s. It has also caught the attention of mathematicians, who’ve spent more than a century studying solutions to puzzles of different sizes and startling configurations.
Now, a new proof solves the 15 puzzle, but in reverse. The mathematicians Yang Chu and Robert Hough of Stony Brook University have identified the number of moves required to turn an ordered board into a random one.

Check out this story over at Nautilus.

(Image Credit: Wikimedia Commons)


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