Simple question. How many RotMG names can there be, as there is a limit of 10 letters for each name and CAPS don’t matter (i’m pretty sure) how many accounts with unique names can be created before no name can be ever chosen.
How many names can there be?
Mynamerr
#3
(26^11-1)/25-1
(Simple geometric series)
Edit with explanaition:
First consider the names with only 1 letter: there are 26 of them, taking each letter exactly once.
Now for each name with 1 letter, there are 26 names with letters that start with that name, so there are 26^2 letters with 2 names.
Similarly there are 26^i names with exactly i letters.
Therefore the total number of names is 26^1+26^2+…+26^10. Now define x by 1+26^1+…+26^10. Then 26*x=26^1+26^2+…+26^11.
Therefore 25x=26x-x=26^11-1. Now by definition the number we are looking for is x-1=(26^11-1)/25-1
Redox
#4
10 characters, 26 letters of the alphabet and many different combinations.
- 1+2+3+4+5+6+7+8+9+10 = 55
- 55*26 = 1,430
- 26*10 = 270
- 1,430 x 260 = 371,800 possible names.
371,800 - Total amount of named players = names free.
If you need an explanation to my logic, just ask.
Nameness
#5
That seems very wrong
It would be up in the millions
Did you take the ability to repeat characters into account?
Rysaw
#6
Assuming a name can be anywhere between 3 to 10 characters inclusive and each character in the name may be any of 26 letters,
A name of length 3
The first character can be one of 26 letters
26
The second character can be one of 26 letters
26*26
And so can be the third.
26*26*26 = 17576 different names that are 3 letters long
Similarly, there are 26^4 4-letter names, which would be 456,976, and 26^5 5-letter names, which would be 11,881,376.
Wolfram tells me that
26^3 + 26^4 + 26^5 + 26^6 + 26^7 + 26^8 + 26^9 + 26^10
is 146,813,779,478,808
Of course, a vast majority of these names are gibberish and a few names are swear words.
Redox
#7
Sadfahlsdj
#8
Just names with 10 letters would be 26^10 which is a colossal amount of names. Most would be gibberish but hey that’s what mine is so…
Seelpit
#11
Actually, capitalization DOES matter! Which is why you can imitate some people by replacing a lowercase L with an uppercase i.
Additionally, the first letter is always capital - which is why The Servers That Must Not Be Named feel weird when you enter them with other people on.
Therefore, there are 26 single-letter names; then, there are 26*52 possibilities (First: 26 possible, second: 26 capital possible, 26 lowercase), et cetera, et cetera.
I’m too unfit to calculate it, do so for me if you wish.
Unicorn
#12
It technically does, but at the same time it doesn’t. There is only one Uniqourn, and only one Seelpit, despite the different caps v. lower-case permutations possible (i.e UnIqOuRn, UNIqourn, SEELPIT, SeelPIT).
Mynam is right but let’s take a look at theoretically how many usable usernames might be out there. Disclaimer that this is fake math and fake science, so numbers will be wildly inaccurate. 
I couldn’t find any website that would definitively list “how many ‘x’-letter english words are there?” so let’s just use the Scrabble one. We get the following numbers:
| # of letters in word | # of English words |
|---|---|
| 1 | 1 |
| 2 | 101 |
| 3 | 1004 |
| 4 | 4002 |
| 5 | 8887 |
| 6 | 15727 |
| 7 | 23958 |
| 8 | 29718 |
| 9 | 29130 |
| 10 | 22314 |
I would guess these numbers underestimate the number of words that have ‘x’-characters although there are some weird ones like “zygomorphy” or “adz” that most people don’t consider or use as actual words. Adding these up gives 134842 names.
However, this doesn’t account for conjunction words like “Underraker” or “MrUnibro”. Here is where I stop because I’m lazy and have lost my functional brain cells to summer amnesia, so thanks for wasting your time and good day.
system
#13
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