Here’s a serious question: If you handed a Rubik’s Cube to almighty God, what’s the fewest number of moves he could solve it in, regardless of starting position?
It may sound like the stuff of hazy basement hangouts, but this question has fueled fierce debate among mathematicians and Rubik’s Cube fanatics for decades. The answer is what cubeheads call “God’s Number” — the absolute fewest number of moves required to solve even the hardest scramble, assuming an omniscient being knew the optimal step to take for any given configuration.
Such beings were once hard to come by; in the early ’70s, it took Hungarian architecture professor Erno Rubik a solid month of twisting his hands and his mind to solve the world’s first Rubik’s Cube (he initially invented the puzzle, which has since sold more than 350 million units, as “a good task for my students”). But today, the calculating power of modern machines has reduced cube-solving to a simple science. Recently, a group of computer savvy researchers enlisted the help of Google to solve God’s optimal Rubik’s Cube algorithm once and for all — and the answer is shockingly low.
Ready for some humbling math? There are exactly 43,252,003,274,489,856,000 (that’s 43 quintillion) possible configurations of the 27 multicolored squares that make up Rubik’s Cube, and all of them can be solved in 20 moves or fewer.
Twenty moves… for the untrained masses, that’s barely enough to get two like-colored squares next to each other, but apparently it’s all you ever need. To reach this number, a programmer, two mathematicians, and an engineer collaborated to write a set of algorithms teaching a computer the optimal ways to solve every unique starting position (they were able to significantly cut down the 43 quintillion possibilities by accounting for symmetry—that is, when one starting position was just the upside-down version of another). A single desktop PC running the program would have taken 1.1 billion seconds (about 35 years) to perform the calculations, the researchers note, but with the help of “lots of computers” donated to the project by Google, the researchers were able to complete their program in just a few weeks. Take this as a reminder that there are plenty of cool Google tricks the world doesn’t know about (but Google knows a lot more about you than you think.)
While the team proved that no starting Rubik’s Cube position requires more than 20 moves to solve, there are only about 490,000,000 that absolutely need that many. Hundreds of billions of positions can be solved in 10 moves or fewer. Mastering them all won’t make you a God… but it might make you a world speedcubing champion. And that’s gotta be worth something.
