A standard 3x3 Rubik's Cube has exactly 43,252,003,274,489,856,000 possible positions — roughly 43 quintillion. Exactly one of them is solved. That staggering number is why the cube feels impossible by trial and error, and why a solver has to be clever rather than just fast.
The short version
- A 3x3 Rubik's Cube has 43,252,003,274,489,856,000 states — about 43 quintillion.
- Only one of those positions is the solved cube.
- The number comes from how the corners and edges can be arranged and twisted.
- Despite the size, any position can be solved in 20 moves or fewer — a fact called God's number.
How many positions does a Rubik's Cube have?
A 3x3 Rubik's Cube has 43,252,003,274,489,856,000 reachable positions. Written out, that's 43 quintillion, 252 quadrillion, and change. The figure counts only positions you can actually reach by turning the cube — not ones you'd have to reach by peeling off stickers or taking it apart.
To picture the scale: if you had one solved cube for every position, they'd cover the Earth's surface many times over. Turning randomly, you could go a lifetime without stumbling onto the solved state.
Where does 43 quintillion come from?
The number comes from combining how the cube's pieces can be arranged and oriented. A cube has 8 corner pieces and 12 edge pieces, and each can be both moved to different spots and twisted or flipped in place.
Here's the breakdown:
- The 8 corners can be arranged in 8! ways and twisted in 3⁷ ways (the last corner's twist is fixed by the rest).
- The 12 edges can be arranged in 12! ways and flipped in 2¹¹ ways (the last edge's flip is fixed).
- Then you divide by 2, because corner and edge arrangements can't be swapped independently.
Multiply it out — 8! × 3⁷ × 12! × 2¹¹ ÷ 2 — and you land exactly on 43,252,003,274,489,856,000. The centers don't add to the count, because they're fixed relative to each other.
Why can't you solve it by guessing?
Because 43 quintillion is far too many positions to stumble through. Even trying a billion positions every second, checking them all would take longer than the age of the universe. Random turning has essentially no chance of finding the one solved state.
That's the whole point of a method. The beginner's layer-by-layer method and speedcubing's CFOP don't search the space — they follow a sequence of moves that's guaranteed to reach the solution. A computer solver does the same thing, just optimally.
The 43 quintillion vs God's number
Here's the twist that surprises people: despite 43 quintillion positions, every single one can be solved in 20 moves or fewer. That proven maximum is called God's number, established in 2010 after a massive computer search.
So the cube is enormous but shallow. No matter how tangled it looks, the solution is never more than 20 turns away — a computer just has to find the short path. Cuby's solver does exactly that, then walks you through it move by move.
Frequently asked questions
How many combinations does a 3x3 Rubik's Cube have?
A 3x3 Rubik's Cube has 43,252,003,274,489,856,000 possible positions — about 43 quintillion — and only one is solved. The number comes from the ways its 8 corners and 12 edges can be arranged and oriented, divided by 2 for parity.
What is God's number for a Rubik's Cube?
God's number is 20 — the maximum number of moves needed to solve any position of a 3x3 cube. It was proven in 2010 with a large computer search. So however scrambled a cube looks, an optimal solution is always 20 turns or fewer away.
How long would it take to try every combination?
Effectively forever. At a billion positions per second, working through all 43 quintillion states would take far longer than the age of the universe. That's why solving relies on a method or an algorithm, not on trying combinations at random.
Does a bigger cube have more combinations?
Yes — much more. A 4x4 has around 7.4 quattuordecillion positions and a 5x5 far more still. The 3x3's 43 quintillion is already unimaginably large, but it's small compared with the higher-order cubes.
See it solved from any of them
43 quintillion positions, and only one is solved — but every one is at most 20 moves from finished. That's the gap Cuby closes.
Open Cuby → and enter any scramble: it finds a guaranteed solution and shows you every turn. New to solving? Start with how to solve a Rubik's Cube.