How many configurations have you possibly seen?

[jamessorsona]

This thought just came up to my head while I was cubing. So, how many configurations of the Rubik's cube have you possibly seen? I know this question is hard to answer and isn't meant to be any way. It's just to make people think about it you know. The 43 quintillion configurations, just think about it.

 

[Eduard Khil]

Considering Im sub 20, possibly ive done 10000 solves, so only some 2x10^-14 percent of the 43 quintillion.
I bet Faz has only encountered ~20% of the 43 qt cases throughout the 7 years of cubing P rough estimate, correct me if Im wrong)

 

[TDM]

I bet Faz has only encountered ~20% of the 43 qt cases throughout the 7 years of cubing P rough estimate, correct me if Im wrong)

Nowhere near that. Even including other people at competition, and all the states you see when solving, it's VERY unlikely anyone has got close to 1%. 43 quintillion is a huge number.

 

[qqwref]

If you turned randomly at 20 tps for 70 years straight without breaks, you would see about 4.4 * 10^10 positions - this is still about one part in a billion of the number of total 3x3x3 states.

 

[guysensei1]

If you turned randomly at 20 tps for 70 years straight without breaks, you would see about 4.4 * 10^10 positions - this is still about one part in a billion of the number of total 3x3x3 states.

How many repeat positions are expected?

 

[DizzypheasantZZ]

It is possible to that without repeat positions.

 

[joshsailscga]

One thing I've been confused about is, does 43 quintillion possible positions include any possible combination of colors, or is it only positions that can be achieved by normal turning of the cube? e.g., is one edge flipped one of the 43 quintillion, or are positions like that excluded from the calculation?

 

[TDM]

One thing I've been confused about is, does 43 quintillion possible positions include any possible combination of colors, or is it only positions that can be achieved by normal turning of the cube? e.g., is one edge flipped one of the 43 quintillion, or are positions like that excluded from the calculation?

Those states are excluded from 43 quintillion. 43 quintillion is only the number of solvable combinations. Allowing any combination of pieces (so allowing for single edge flips/corner twists and piece swapping) would increase the number to 12 times 43 quintillion.

 

[StachuK1992]

Probably 100k-300k.

 

[hcfong]

Just to show what a huge number 43 quintillion is:

The Rubik's cube came on the market in 1980, so it's been around for 25 years. Suppose that at the moment it came on the market, every person in the world got one and since then everybody has been turning the cube with 1 turn per second non-stop. That would give us the following:

In the 1980s the world population was about 4.5 billion.
25 years = 9134 days = 7.9 * 10^8 seconds.
This means that after 25 years, if everybody has been turning non-stop with 1 turn per second and every turn gave a unique state of the cube, by this time 'only' 3.6 * 10^18 permutations have appeared of the 43 * 10^18. Less than 10% after 25 years.

 

[JustinTimeCuber]

Just to show what a huge number 43 quintillion is:

The Rubik's cube came on the market in 1980, so it's been around for 25 years. Suppose that at the moment it came on the market, every person in the world got one and since then everybody has been turning the cube with 1 turn per second non-stop. That would give us the following:

In the 1980s the world population was about 4.5 billion.
25 years = 9134 days = 7.9 * 10^8 seconds.
This means that after 25 years, if everybody has been turning non-stop with 1 turn per second and every turn gave a unique state of the cube, by this time 'only' 3.6 * 10^18 permutations have appeared of the 43 * 10^18. Less than 10% after 25 years.

35*

 

[rokicki]

This thought just came up to my head while I was cubing. So, how many configurations of the Rubik's cube have you possibly seen? I know this question is hard to answer and isn't meant to be any way. It's just to make people think about it you know. The 43 quintillion configurations, just think about it.

Another interesting question: has any official scramble, in any competition, ever *required* 20 moves to solve?

Both a probability-based answer and (if possible; are the actual official scrambles published?) an actual measurement
would be interesting.

 

[EMI]

^ And if so, was it a FMC scramble?

 

[biscuit]

Another interesting question: has any official scramble, in any competition, ever *required* 20 moves to solve?

Both a probability-based answer and (if possible; are the actual official scrambles published?) an actual measurement
would be interesting.

Yes the scrambles are published not sure where but probably somewhere in the results section of the WCA site. But there are a lot of them

 

[hcfong]

35*

You're right. 35 years. That'll give us about 5 * 10^18 permutations that have appeared since 1980. A bit more than 10%.

 

[00]

I bet Faz has only encountered ~20% of the 43 qt cases throughout the 7 years of cubing P rough estimate, correct me if Im wrong)

To get through 20% of all cases he would have been needed to turn at 20 tps non stop since the start of the universe. 6.8 quintillion positions in 7 years = 39 billion cases per second.