A history of the Rubik’s cube

The cube didn’t start life as a toy company’s product plan. It was built in a classroom, and the man who made it couldn’t solve it himself the day he finished.

It started as a classroom model

In 1974, Ernő Rubik was teaching architecture and design at the Academy of Applied Arts in Budapest. He wanted to walk his students through a problem that sounded simple but felt awkward the moment you tried to explain it in three dimensions: take a cube, slice it into 27 little blocks, rotate one face, and ask what happens to each small block’s relationship with its neighbours. Talking about it with hand gestures only got so far, and drawing it on a blackboard was worse.

What he wanted was a teaching aid, not a toy. To keep those 27 blocks from flying apart whenever a face turned, he spent weeks designing an internal mechanism — a clever set of axes and tracks that let any face rotate freely while the rest of the cube held itself together. There were no screws holding the outside in place; the pieces gripped each other through their shape alone. The day he finished the wooden prototype, he painted each face a different colour, twisted it a few times to see how it moved, and then stopped: he had no idea how to get it back to where it started. It took him over a month of evenings to find his own way home.

From teaching aid to toy

Rubik filed a Hungarian patent in 1975, but the cube only reached store shelves in 1977 — sold inside Hungary under the name “Magic Cube” (Bűvös Kocka). Behind the Iron Curtain, nobody in Western toy circles had heard of it until the Hungarian state trading company Konsumex put it on display at the Nuremberg Toy Fair in 1979, where Ideal Toy Corp in the United States spotted it.

Ideal picked up the overseas licence in 1980, renamed it Rubik’s Cube, and pushed it into the global market. Between 1980 and 1983 it sold more than one hundred million units — a level toy historians still call out as unusual, and unusual enough that “Rubik’s” entered the dictionary as a generic English word for any twisting puzzle. It cooled off, slid to the bottom of toy boxes, and then a new generation rediscovered it a few years later. That cycle has roughly repeated ever since.

The first speedcubing wave

The craze brought competition. The first World Championship was held in Budapest in 1982, and a nineteen-year-old Vietnamese-American student named Minh Thai won it in 22.95 seconds — a time that sounds slow today but was, at the time, almost unthinkable. Around the same period, hand-written solution guides started passing between students and showing up in magazines. The layer-by-layer approach that most people learn today took shape in those early years, with David Singmaster’s notation (the R, U, F you still see in tutorials) becoming the common vocabulary.

How vast is the state space

The cube looks like a small object, but the number of legal configurations it can hold is genuinely hard to picture. The count of legal states on a 3×3 is:

8! × 3⁷ × 12! × 2¹¹ / 2 ≈ 4.325 × 10¹⁹

Spelled out, that’s 43,252,003,274,489,856,000 — about forty-three quintillion. The factors in the formula come from the cube’s structure: eight corners that can be permuted in any order with seven of them freely twisted, twelve edges with eleven freely flipped, and a parity rule that halves the total because corner permutations and edge permutations can’t move independently.

To get a feel for the scale: a standard Rubik’s cube is 5.7 cm on a side, so if you manufactured one physical cube for every legal state and laid them flat across the entire surface of the Earth (around 510 million square kilometres), you’d need roughly 170,000 layers stacked on top of each other to fit them all.

Put differently: if you scramble a cube right now, the state it lands on is almost certainly one no human being has ever held before — including the one you scrambled a minute ago.

God’s Number

Given how many states there are, an obvious question follows: in the worst case, how many moves does it take to solve any cube? That worst-case shortest move count is called God’s Number — the idea being that an omniscient solver would always pick the shortest path.

The upper bound on God’s Number was squeezed down by a relay of mathematicians across three decades. In 1981, the British mathematician Morwen Thistlethwaite proved that any state could be solved in at most 52 moves. Through the 1990s and 2000s the bound kept dropping: 50, 29, 25, 22 — each step powered by better group-theoretic tricks and smarter search.

The final punch landed in 2010. Tomas Rokicki, Morley Davidson, John Dethridge, and Herbert Kociemba borrowed time on Google’s machines, burned roughly 35 CPU-years of compute, and worked through every one of those forty-three quintillion states by symmetry class, proving the upper bound is exactly 20. They also identified configurations that genuinely require 20 moves to solve — the well-known superflip is one — which means 20 is tight and can’t be pushed any lower.

Kociemba’s two-phase algorithm

Knowing God’s Number is 20 is one thing. Actually finding a near-optimal solution on a laptop, in milliseconds, is another. In 1992 the German mathematician Herbert Kociemba published an elegant two-phase strategy: use a restricted set of moves to drive the cube into a well-behaved subgroup G1 (where the corner and edge pieces are all correctly oriented, leaving only their positions to resolve), then finish from G1 to the solved state using only the moves that preserve those orientations.

Each phase searches a much smaller space than the cube as a whole, so the algorithm produces solutions of 20 to 25 moves within milliseconds on commodity hardware — vastly faster than brute-forcing the whole state space and good enough for any interactive application. It’s still the backbone of most cube solvers in use today, including the ones running in browser JavaScript.

Back to F1 Cube

The “fastest solve” mode in F1 Cube runs on cubejs — a JavaScript port of Kociemba’s two-phase algorithm. The twenty-something-move path you see in your browser is a direct beneficiary of more than thirty years of group-theory research.

If you want to understand the cube itself — what corners, edges, and centres are, and why R and U aren’t the same kind of move — head over to Getting started with the cube next.