You pick up a Rubik’s Cube. Six colors. A few rotating layers. It looks like a child’s toy.
And yet: if you give it one good shake, you enter a labyrinth with 43,252,003,274,489,856,000 possible positions. That’s the number often called “43 quintillion” in English. In Dutch (long scale), that amounts to about 43 trillion.
43 trillion. For one small cube that fits in your hand.
The number that’s bigger than your sense of size
Try this for a moment: imagine looking at one new position every second, without a break, day and night. It would still take an absurdly long time to see everything. And that’s precisely the point: the Rubik’s Cube isn’t just “difficult,” it’s mathematically gigantic.
What many people don’t realize: that enormous number isn’t “marketing.” It’s a real, exact number that follows from how the cube is constructed.
Where do those 43,252,003,274,489,856,000 positions come from?
The magic is in the “pieces”:
- 8 corner pieces (with 3 colors)
- 12 edge pieces (with 2 colors)
- The 6 center pieces only determine which color belongs to which side and remain in place.
Then the combinatorics begin:
- The corner pieces can be swapped and rotated in many ways.
- The edge pieces can be swapped and flipped in many ways.
- However, the cube has physical rules. Some apparent “positions” are simply impossible due to mechanics (for example, rotating a single corner piece without affecting the rest).
If you correctly factor in those possibilities and limitations, you arrive at that famous number: 43,252,003,274,489,856,000.
Why you almost never see the same scramble
People often shuffle “a little”: single turns, sometimes halfway back, sometimes in patterns. But true randomness is rare.
Even if you scrambled dozens of times every day for your entire life, you’d still occupy a minuscule corner of the total universe of positions. The chance that you’d accidentally get the exact same scramble back as last month is so small in practice that you can treat it as zero.
This makes the Rubik’s Cube feel infinite, even though it isn’t.
Plot twist: every position can be solved in a maximum of 20 moves.
And here’s where it gets truly movie-worthy.
Despite those 43 trillion positions, there’s a proven limit: every legal position of a 3x3x3 Rubik’s Cube is solvable in 20 moves or less, if you know the correct moves and define “move” as a quarter or half turn of a face.
This limit is called God’s Number. It sounds like a joke, but it’s a serious term in the cubing world. In 2010, the result was computationally proven by a research team using heavy computing power and later extensively documented.
So yes: the cube has a ridiculously large number of positions… but none are further than 20 perfect steps from the solution.
The real reason the cube feels so hard
If every position is a maximum of 20 moves away from being solved, why do people spend hours slaving over it?
Because “20 moves” means 20 perfect moves. Not 20 that you happen to try. Not 20 that you remember as a beginner. But 20 that precisely form the shortest route through that gigantic maze.
The Rubik’s Cube isn’t a test of strength. It’s a search problem in a space too large for intuition. That’s why one wrong step feels like you’re “ruining everything,” when in reality, you’re just choosing a different path in the labyrinth.
