20 Moves or Less Will Solve Rubik’s Cube

People have been solving Rubik’s Cube since it was invented in 1974, and some have gotten quite fast at it. But just how fast is possible? In other words, if you were an omniscient solver, what’s the most number of moves it would take you to solve any starting position of Rubik’s cube? Since there are 43,252,003,274,489,856,000 possible starting positions, many of which require different strategies to solve, answering that question seemed outside the realm of possibility: a computer dealing with each starting position in less than 20 seconds would still require 35 years of analysis. But by using some high-powered mathematics to chop the problem down to size, a team consisting of a mathematician, a Google engineer, a math teacher, and a programmer (and yes, a powerful computer) have indeed answered the question, determining that all starting positions are solvable in 20 moves or less. The story was picked up by a number of news outlets, including NPR, Discover, BBC News, and others.

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