beingforitself
Regular
- Joined
- Dec 14, 2008
- Messages
- 52
Yo,
Take every 6-color 3x3x3 ever produced. Of the approximately 4.3252 x 10^19 possible unique states a cube can be in, what percentage of these has ever been actually physically attained by any cube for any duration of time? This includes scrambling, solving, messing around, etc. by anyone anywhere at any time.
I am posting my calculations in white below; I'd like to compare with what/how other people estimate.
Some (not really) random numbers that may or may not be useful in this calculation:
According to this and this article "more than 350 million" cubes have been sold worldwide since it's introduction.
Kociemba has got some numbers here.
20 face turn metric moves (MOST ULTRA VERY LIKELY PROBABLY BUT NOT DEFINITELY) suffice to reach any state on the cube.
The WCA ranking and statistics pages are not fully working right now, but I am estimating that:
5000 people have any recorded average of 5 for 3x3x3
1500 people have a sub-20 average of 5 for 3x3x3
(will change if someone tells me the correct numbers)
My estimate:
Let us treat non-cubers, sup-20, and sub-20 cubers as three distinct subgroups of move-generating apparati:
Assume that
non-cubers (or to be more precise, single cubes that pass around between multiple non-cubers) number 3.5 x 10^8
sup-20 cubers number 10000
sub-20 cubers number 2000
For the first subgroup, assume that the cubes net an average of 10 hours mindless turn time at 20 turns a minute, making for a total cubespace exploration of 10 hours x 20x60 turns an hour x 3.5x10^8 cubes = 4.2 x 10^12 cubestates generated.
For the second subgroup, assume to reach a sup-20 average requires an average of 250 hours of cubing. Assume that this cubing time averages 2 TPS. This would give us 250 hours x 2x60x60 turns per hour x 10000 sup-20 cubers = 1.8 x 10^10 cubestates generated.
For the third subgroup, assume to reach a sub-20 average requires an average of 5000 hours to reach sub-20. Assume that this cubing time averages 3 TPS. This would give us 5000 hours x 3x60x60 turns per hour x 2000 sub-20 cubers = 1.1 x 10^11 cubestates generated.
The latter two subgroups (somewhat predictably) contribute negligibly to the total cubestate count according to my calculations, but I am leaving them there in the case that someone makes a comment / suggests different numbers that would make them matter.
Therefore we have 4.211 x 10^12 / 4.3252 x 10^19 =~ 9.73 x 10^-7 = .0000973 (or around one ten thousandth of one) percent of possible cube states have been explored in the history of the Rubik's cube's existence.
MAIN PROBLEMS WITH THIS METHOD (as I see it):
-> Assuming total turns = cubestates generated. I tried to make the numbers fairly conservative to "compensate" for this.
-> Actual numbers plugged in
Take every 6-color 3x3x3 ever produced. Of the approximately 4.3252 x 10^19 possible unique states a cube can be in, what percentage of these has ever been actually physically attained by any cube for any duration of time? This includes scrambling, solving, messing around, etc. by anyone anywhere at any time.
I am posting my calculations in white below; I'd like to compare with what/how other people estimate.
Some (not really) random numbers that may or may not be useful in this calculation:
According to this and this article "more than 350 million" cubes have been sold worldwide since it's introduction.
Kociemba has got some numbers here.
20 face turn metric moves (MOST ULTRA VERY LIKELY PROBABLY BUT NOT DEFINITELY) suffice to reach any state on the cube.
The WCA ranking and statistics pages are not fully working right now, but I am estimating that:
5000 people have any recorded average of 5 for 3x3x3
1500 people have a sub-20 average of 5 for 3x3x3
(will change if someone tells me the correct numbers)
My estimate:
Let us treat non-cubers, sup-20, and sub-20 cubers as three distinct subgroups of move-generating apparati:
Assume that
non-cubers (or to be more precise, single cubes that pass around between multiple non-cubers) number 3.5 x 10^8
sup-20 cubers number 10000
sub-20 cubers number 2000
For the first subgroup, assume that the cubes net an average of 10 hours mindless turn time at 20 turns a minute, making for a total cubespace exploration of 10 hours x 20x60 turns an hour x 3.5x10^8 cubes = 4.2 x 10^12 cubestates generated.
For the second subgroup, assume to reach a sup-20 average requires an average of 250 hours of cubing. Assume that this cubing time averages 2 TPS. This would give us 250 hours x 2x60x60 turns per hour x 10000 sup-20 cubers = 1.8 x 10^10 cubestates generated.
For the third subgroup, assume to reach a sub-20 average requires an average of 5000 hours to reach sub-20. Assume that this cubing time averages 3 TPS. This would give us 5000 hours x 3x60x60 turns per hour x 2000 sub-20 cubers = 1.1 x 10^11 cubestates generated.
The latter two subgroups (somewhat predictably) contribute negligibly to the total cubestate count according to my calculations, but I am leaving them there in the case that someone makes a comment / suggests different numbers that would make them matter.
Therefore we have 4.211 x 10^12 / 4.3252 x 10^19 =~ 9.73 x 10^-7 = .0000973 (or around one ten thousandth of one) percent of possible cube states have been explored in the history of the Rubik's cube's existence.
MAIN PROBLEMS WITH THIS METHOD (as I see it):
-> Assuming total turns = cubestates generated. I tried to make the numbers fairly conservative to "compensate" for this.
-> Actual numbers plugged in
Last edited:
I doubt I'm right, there are probably a lot of fully scrambled combinations that have never been done.
