How many of the 3x3 states have we approximately reached?

[Kivvi]

I figured I’d just create this thread because it’s an interesting topic and you can do some fun calculations and estimations around it.
Getting an estimation even remotely close to the actual number is going to be quite difficult, but I think it’s worth to try it.

Some starting numbers:
- The Rubik’s cube has 43 quintillion different permutations (43,252,003,274,489,856,000)
- About 500 Million Rubik’s cubes have been sold
- The average CFOP solves lasts 55-60 moves, Roux takes 45-50, while the beginner’s method lasts 70-100 moves.
-253509 cubers have officially competed in 3x3.


Current Estimate: N/A

 

[Bingus cuber]

At least 4

 

[Mike Hughey]

When calculating, don't forget all the states reached during scrambling, warming up, fidgeting, etc.

I would guess we have likely covered (with actual real world puzzles, not simulations) all states 9 moves or less from solved, and I think we might be really close to covering all of them 10 moves from solved. But after that I suspect we're a long way from covering them all. And that is honestly just a guess.

 

[Filipe Teixeira]

Don't think, just solve

 

[Filipe Teixeira]

‎Gemini - Continuing the Conversation

Created with Gemini

gemini.google.com

 

[Herbert Kociemba]

Gemini says

Computer Simulations: This estimation doesn't account for states reached through computer simulations or programs designed to explore the state space. If we consider all computational efforts, the number of reached states would be higher, but still a tiny fraction of the total.

This is wrong. All cube states have been reached by programs designed to explore the state space. Or at least more than 1/48 of those states if you count states which are related by cube symmetry as different states.

 

[Filipe Teixeira]

Gemini says

Computer Simulations: This estimation doesn't account for states reached through computer simulations or programs designed to explore the state space. If we consider all computational efforts, the number of reached states would be higher, but still a tiny fraction of the total.

This is wrong. All cube states have been reached by programs designed to explore the state space. Or at least more than 1/48 of those states if you count states which are related by cube symmetry as different states.

there

 

[eeeeeeeee]

this month there have been ≈175 comps with 3s3
assuming all comps have 3 rounds of 3x3
175x3x7(scrambles)x200(months)=735000

 

[Filipe Teixeira]

this month there have been ≈175 comps with 3s3
assuming all comps have 3 rounds of 3x3
175x3x7(scrambles)x200(months)=735000

 

[qq280833822]

There were more than 400 million solves on csTimer last year.