To solve a 15 puzzle, the user must order 15 tiles on a 4×4 grid. The puzzle has consistently attracted the attention of mathematicians, most recently Yang Chu and Robert Hough. They set out to calculate how many moves are needed to turn the solved puzzle into a random initial setup. The research has a great application to the natural world, which frequently involves ordered systems unwinding into mixed-up states. Ice melts one step at a time, much the way the 15 puzzle position is randomized. Chu and Hough concluded that it takes longer than expected to completely remove order from a system, whether it be a 15 puzzle or a natural process.

Key Takeaways:

- Many randomization problems relate to fundamental features of the natural world, such as how molecules split apart and become disordered.
- A 15 puzzle slips into a state of disorder one step at a time, much the way in which melting ice does.
- The work of mathematicians Yang Chu and Robert Hough suggests that it takes longer than previously thought to erase randomness from a system.

“By understanding problems like how a 15 puzzle scrambles, Diaconis hoped to get a handle on how ordered systems in general unwind into a uniformly mixed-up state.”

Read more: https://www.quantamagazine.org/mathematicians-calculate-how-randomness-creeps-in-20191112/