Big Weird Numbers (from Small Things) That Amuse Me

One of my random new year resolutions I will disclose is that I'm trying to smarten up mathematically again, and to regain some comfort with doing hard core ciphers: learning and getting reacquainted with stuff like calculus, matrices, statistics, and the like; plus trying to find some practical use and application for such arithmetical methods in my own life. Right now though, it is all impractical, yet interesting and impressive (to me anyway). I thought about simple objects and puzzles around my home; they didn't involve high tech things either. I did some recreational computations (with the help of the Wolfram Alpha app) and found research results to get some of these wild figures . . .

1. 6,670,903,752,021,072,936,960 ( ≈ 6.67 x10²¹) : The number of possible valid complete solutions there are for a 9 x 9 Sudoku grid. That's about 16.67 billion times the highest estimate of the number
   of stars in our Milky Way galaxy. Some lucky bastard mathematician out there also got some grant money to prove that the absolute minimum number of clue digits needed to solve one is 17.
   
2. 20,822,964,865,671,167 ( ≈ 2.08 x 10¹⁶) : The total number of  all unique sets of counter bead position configurations on my 2 bead upper deck/5 bead lower deck/13 column standard Chinese suan pan (abacus). That's 18 possible bead configurations (a base of 18, represented from numbers 0 to 17) for each of the 13 columns, representing the exponential powers from 0  to 12. That then is {(17 x 18⁰) + (17 x 18¹) + (17 x 18²) . . .  + (17 x 18¹²)}, leading to a maximum total up to the aforementioned number in the heading converted to decimal/base 10 scientific notation form. Meaning, if I flicked a bead (or beads) at one interval per second to tally all possible counter bead configurations on this abacus, it would take approximately 660.7 million years to do it. It seems crazy on such a little frame with only a total of 91 counting beads, but that's the math talking. If the figure for the placements on an 81 spot Sudoku grid is as high as it is, why not this lesser figure for the 91 counter abacus? If I'm wrong about this calculation, I won't mind being corrected. It seems too strange and mind-blowing to be right.

   

   It reads 2017 in base 10. Happy New Year!

3.  43,252,003,274,489,856,000 ( ≈  4.33 x 10¹⁹): The number of possible of configurations a Rubik's Cube can have. Amazingly, it has been calculated (by supercomputers) that the cube can be solved, with the proper programmed algorithms, from any one of these configurations in 20 moves or less. The last time I tried, it took me about 32 minutes to solve it . . . most definitely not in the same league as a Cray supercomputer.
4. 1 in 6,227,020,800 (or 13!): the chance of taking a full suit of 13 playing cards, shuffling them, and then turning them over, one by one, and having them turn up in exact ranking order from ace to king (A,2,3,4,5,6,7,8,9,10,J,Q,K). In contrast, I learned that the chance of winning the jackpot for Lotto 6/49 is roughly 1 in 14 million, and 1 in 28.6 million for the Lotto Max*.
5. 6.53 x 10⁹⁰⁹⁰⁵²: The number of 9 word sentences (a fairly average length of sentence) that can be composed out of randomly selected words from the language with the largest vocabulary in the world: English. From the sentences, "A, a, a, a, a, a, a, a, a, a." to "We will never run out of things to say!", to "Big Weird Numbers (from Small Things) that Amuse Me.", to written onomatopoeia to denote sleeping,  "Zzz, zzz, zzz, zzz, zzz, zzz, zzz, zzz, zzz"**. _, inclusive. There's nothing around materially or temporally as an example to bring that number into comparison for adequate comprehension for the mind, since there are only an estimated 1 x 10⁸⁰ atoms in the entire universe, and its age is only about 4.3 x 10³⁵ in attoseconds***(super small time increments) since the Big Bang. Sure, a grand majority of them would be nonsensical, like "Shiver melon herring quickly kind zipper handy aardvark nipple". Like the random shit in English scrawled on teenagers' T-shirts in the Harajuku fashion district in Tokyo. If a password of nine random words like that were used, I would think that the world would be long vanished into oblivion before it could be hacked. Thankfully, we have few rules of grammar, syntax, context, articles, pronouns, prepositions, verbal tenses and conjugations, gerunds, participles, etc., to set limits and boundaries to things that would statistically and numerically whittle down that figure a lot. Even so, what is left is still more than what would have been, or will be, ever said by humans, past, present, and presumably the future. There's still lots of nonsense that comes from it, but we manage pull a few out that are real gems, and not from the cold dry probabilities of it, but from what's in the spirit of us as human beings. This fact brings to light a quote from Einstein: "Imagination is more powerful than knowledge". He think he got it bang on right . . . and with only seven words too.

*- This is someone else's findings, not mine. Actually, for Lotto Max, the chance of winning on a single line of 7 numbers is roughly in the neighbourhood of 1 in 85.8 million, but you are given three lines, so divide those chances by 3, so 28.6 million. That's a little more optimistic!
**-An edit. Initially I thought that Zyzygy was the alphabetically last defined word that I could think of, but it was a misspelling of the word syzygy: an alignment of celestial bodies in a gravitational system.
***- 1x 10¹⁸ attoseconds = 1 second. Very few things or motions in the physical universe exist that can be timed within ten attoseconds, but who knows what will happen in the future as using measurements such as these become realities as advances in research and development of nanotechnology and quantum computing come about.