Even on my laptop’s tinny speakers, the sound is unmistakable: the click-clacking, slip-sliding sound of a Rubik’s Cube whipping into shape. “It’s my first solve of the day,” says Australian speedcuber Feliks Zemdegs, somewhat sheepishly. It’s early in Sydney, where he’s speaking to me over video chat from his apartment. Over his shoulder, I can see his unmade bed. On it: a big, squishy, Rubik’s Cube novelty pillow. He looks like he hasn’t been awake for more than 20 minutes. No matter: It takes him less than seven seconds to transfigure the cube in his hands from scrambled to solved.
Zemdegs holds numerous cubing records, but he is best known as the most consistently swift solver of the 3 by 3: the canonical three-layered, Mondrian-colored cube. (The toy you're probably picturing is just one of many mechanical riddles belonging to the genus of so-called twisty puzzles.) Last month, at a speedcubing competition in Brisbane, he set a new world record of 5.69 seconds in the Average of 5 event, wherein contestants each solve five cubes that have been scrambled according to computer-generated instructions. When they're finished, competitors eliminate their fastest and slowest times and calculate the mean of the remaining three. Zemdegs’ 5.69-second average was an 0.11-second improvement over his previous best, which was also a world record. “Since 2010, I’ve broken the Average-of-5 record probably 10 times,” he says.
[#video: https://www.youtube.com/embed/awa4TAp8WZE)https://www.youtube.com/watch?v=awa4TAp8WZE
Short-lived records are common in speedcubing, a relatively young sport. (Sport? Sure, why not?) The first world tournament was held in 1982, eight years after the cube’s invention by Hungarian architect Erno Rubik. There, competitors took up to a minute to solve the cube. But by 2009, the fastest speedsolvers (many of them too young to drive) were unscrambling cubes in a little over 10 seconds. And today, the hundred best speedcubers on earth all average below 7.7 seconds per solve, with the top 10 all coming in at under 6.5.
And yet, improvements are becoming more incremental; graph the progression of cubing records, and the resulting curves are unmistakably asymptotic. As speedcubers like Zemdegs approach the limits of their finger-flicking craft, an irresistible question arises: What might that limit be?
It’s tempting to arithmetize the problem—to divide the most efficient solution to the cube (as measured in turns) by the solve rate of a world-class cuber (as measured in turns per second). The result would provide a theoretical limit to speedcubing.
Solve rates are pretty straightforward: In competition, elite cubers like Zemdegs average just shy of 10 turns per second. (It’s mesmerizing to watch, and makes fidget spinners seem quaint.) As for the fewest number of turns required to solve the puzzle, that’s trickier to pin down.
For one thing, it depends on the complexity of a cube’s scramble. At one end of the spectrum are configurations that require almost no effort to solve. There exist 18 starting positions, for instance, that require a single turn of a single face to resolve. Such simple scrambles would probably never be permitted in a tournament. Then again, the odds of them ever cropping up at random during a competition are, shall we say, small.
